Layout Design and Verification of a Space Payload Distributed ...

Citation: Wang, G.; Yao, Y.; Wang, J.;

Huo, W.; Xu, G.; Hu, X. Layout

Design and Verification of a Space

Payload Distributed Capture and

Lock System. Aerospace 2022, 9, 345.

https://doi.org/10.3390/

aerospace9070345

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aerospace

Article

Layout Design and Verification of a Space Payload DistributedCapture and Lock SystemGang Wang, Yimeng Yao, Jingtian Wang, Weiye Huo * , Guosheng Xu and Xi Hu

College of Aerospace Engineering, North China Institute of Aerospace Engineering, Langfang 065000, China;[email protected] (G.W.); [email protected] (Y.Y.); [email protected] (J.W.);[email protected] (G.X.); [email protected] (X.H.)* Correspondence: [email protected]; Tel.: +86-1993-365-1887

Abstract: In this paper, the mechanism scheme and parametric design of a capture and lock systemare studied based on the high reliability of locking systems. By analyzing the workflow and boundaryconditions of the capture and lock system, a positioning design is carried out by combining it withthe layout of a distributed capture and lock system. Based on the error domain for the passive endin the presence of errors in the manipulator, planning for the capture trajectory and configurationof the design for the active end are carried out. The influence of the passive end on the dynamicperformance of the system is comprehensively considered to design the configuration of the passiveend. According to the structure of the active end, a mathematical model for the capture and lockmechanism is established, and an analysis of the influence of trajectory parameters on the active endis carried out. The layout design of the capture hook for the active end is carried out based on ananalysis of the influence of its layout on posture adjustment. The large-tolerance capability of thesystem layout is verified with a tolerance simulation analysis and a ground simulation capture test.

Keywords: distributed capture and lock system; structural design; trajectory planning; layout design;capture experiment

1. Introduction

With the development of major aerospace projects such as global manned spaceflight,space observation, and deep space exploration, the needs for tasks such as the constructionof on-orbit service platforms, space station construction, and space load transportation havebecome increasingly urgent. As a key technology for on-orbit service, repeated captureand lock technology plays an extremely important role in space construction and routinemaintenance operations. The load transfer between the space station and the carrier space-craft, and the connection and separation between the space station and the target spacecraftneed to be completed through repeated capture and lock technology. The success or failureof the capture and lock task directly determines whether the subsequent on-orbit controltasks of the space station can be carried out smoothly. As the core component of a captureand lock system, the configuration of the capture and lock mechanism not only affects theoverall size and quality of the capture and lock system but also determines the toleranceand reliability of the system. The layout of the capture and lock mechanism is also relatedto the tolerance capacity of the system, which directly determines its reliability. This paperaims to improve the tolerance capability of the capture system to obtain high-reliabilitycapture. In addition, the positioning and layout of the capture system are designed, theconfiguration of the capture system is designed, and the parameters are optimized.

Zhu et al. [1] added a spring damping device between the joint motor and the ma-nipulator to prevent the joint from being damaged by an impact force when the spacerobot captures a satellite. The device can limit the impact force through a reasonabledesign compliance control strategy within safe limits. Carignan et al. [2] introduced a

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Aerospace 2022, 9, 345 2 of 27

hardware-in-the-loop simulation method for replicating satellites based on parallel mo-tion platforms. Rekleitis et al. [3] describes the autonomy and teleoperation aspects ofautonomously capturing tumbling satellites. Kaiser et al. [4] used the finite element methodwith a polygonal contact model for high-fidelity simulation of physical contact betweensatellites. Jianbin et al. [5] introduced a universal docking mechanism with an underac-tuated design and a force-limited Cartesian impedance control method, which reducesthe difficulty of non-cooperative satellite control for capturing tumbling satellites, andensures continuity, synchronization, and force uniformity. Jaworski et al. [6] experimentedwith collecting debris with satellite jigs under laboratory conditions. Rouleaut et al. [7]implemented a redundant solution to maximize the operability of the robot and increaseits functional workspace and developed a trajectory generation algorithm based on onlinevision to generate velocity commands to safely approach the target satellite and match itsmovement. Wang et al. [8–10] proposed a step-by-step docking strategy based on adaptivesensing for an orthogonally distributed container docking device, then tested whether thecapture was successful, and further determined a capture tolerance analysis method forthe capture system. Ma et al. [11] studied the optimal control problem associated withapproaching and aligning one rigid body with another arbitrarily rotating rigid body andapplied it to the satellite docking problem. The projection algorithm proposed by Wangand Xie [12] can ensure consistent positive definiteness of inertia in the manipulator duringthe parameter adaptation process. Wang et al. [13] conducted an overall study of the robotbase and the manipulator to carry out a gravity-free control simulation and obtained adynamic model describing orbital mechanics. Rybus et al. [14] proposed an optimizationmethod to improve the trajectory of the manipulator for systems with non-conservedmomentum and angular momentum, such as the on-orbit service of a space manipulatoror the removal of space debris. Xu et al. [15] studied two typical capture conditions: (a)when the base is free-floating, the arms are coordinated to capture moving targets; (b)one arm is used to capture the target and the other arm is used to fix the target pedestal.An autonomous motion control method for the coordinated motion of a dual-arm spacerobot for capturing targets was proposed. Tortopidis and Papadopoulos [16] proposed apath planning method that satisfies the requirement that the position of the end effectorand the attitude of the base is controlled only by the manipulator actuator. Aghili [17]proposed a coordinated control method for the combined system of a space robot and atarget satellite and designed two optimal trajectories before and after capture. Piersigilliet al. [18] developed an unresponsive trajectory generation strategy for intercepting targetswithout affecting the attitude of the base, which can avoid attitude control of the baseduring manipulator operation. Wang et al. [19,20] proposed a design method for a modularreusable locking release device and applied the mechanical stability principle of plant rootgrowth for layout optimization of the locking unit on the bottom surface of a satellite.Lim and Chung [21] studied the dynamic behavior of tethered satellite systems for spacedebris capture considering a large deformation of the tether. From the perspective ofangular momentum distribution, Yoshida et al. [22,23] proposed a bias momentum methodapproaching the phase for space robots to capture tumbling satellites and discussed theimpedance matching problem when an impedance-controlled manipulator approaches andcollides with a passive target. At present, there are many mature and successful applica-tions of spatial locking technology such as the following: in 1967, Russia used a cone-rodlocking system to achieve the docking lock for two space modules, Cosmos 186 and Cosmos188; the Shuttle Remote Manipulator System SRMS was the first space arm officially usedon the Shuttle, named the Canadarm, and has played a key role in the construction of aspace station and has performed maintenance on multiple on-orbit cooperative targets overthe past 30 years to date; and in 2005, the United States implemented the Orbital Expressprogram, which used a three-pronged repeat trap system in the process of capturing spacecooperative loads.

At present, the relevant research on space load capture has made great progress,and the structure and layout of the lock system have also been solved to a certain extent.

Aerospace 2022, 9, 345 3 of 27

However, there is no complete, reliable, and universal method for the layout design of adistributed capture and lock system for space loads. In this paper, starting with the high-reliability capture of space loads by a distributed capture and lock system, the workflow ofthe capture and lock system is analyzed, the positioning of the capture and lock systemis carried out, the trajectory of the active capture end is further planned, and the specificconfigurations for the active and passive ends are obtained. According to the influence ofthe capture hook and the active end layout on the attitude adjustment function, the layoutdesign of the capture and lock mechanism is carried out, and the tolerance of the systemlayout is simulated and experimentally analyzed.

2. Materials and Methods2.1. Positioning and Layout Design of the Capture and Lock System2.1.1. Analysis of the Working Process of the Capture and Lock System

A space station can be used by astronauts to live for a long time and carry out a largenumber of scientific research experiments. During the operation and maintenance of a spacestation, living materials and experimental equipment must be continually replenished,updated, and maintained. The specific implementation plan for the replacement of spacestation material is: (1) load the materials and equipment required by the space stationinto payload 1, and lock payload 1 in the spacecraft cargo compartment; (2) the spacecraftcarrying payload 1 is launched from the ground into a predetermined orbit in space, anddocks with the space station; (3) use a manipulator and a capture and lock system toreplace payload 1 in the cargo compartment with the abandoned payload 2 from the spacestation platform to complete the update of the space station materials and equipment;(4) abandoned payload 2 is released and deorbited so that it crashes into the atmosphereand burns up while the spacecraft returns to the ground for maintenance, as shown inFigure 1. During the process of on-orbit replacement of the payload in space, the mainfunction of the capture and lock system is to complete attitude adjustment, capture andconnection of the payload with the assistance of a seven-degrees-of-freedom manipulator.Both the manipulator and the capture and lock system are fixed to the spacecraft payloadplatform. Before the capture and lock system works, the end effector of the manipulatoris connected with the payload handle to form a whole, then it carries the payload to thesystem capture area, as shown in Figure 2a.

Aerospace 2022, 9, x FOR PEER REVIEW 3 of 28

At present, the relevant research on space load capture has made great progress, and the structure and layout of the lock system have also been solved to a certain extent. How-ever, there is no complete, reliable, and universal method for the layout design of a dis-tributed capture and lock system for space loads. In this paper, starting with the high-reliability capture of space loads by a distributed capture and lock system, the workflow of the capture and lock system is analyzed, the positioning of the capture and lock system is carried out, the trajectory of the active capture end is further planned, and the specific configurations for the active and passive ends are obtained. According to the influence of the capture hook and the active end layout on the attitude adjustment function, the layout design of the capture and lock mechanism is carried out, and the tolerance of the system layout is simulated and experimentally analyzed.

2. Materials and Methods 2.1. Positioning and Layout Design of the Capture and Lock System 2.1.1. Analysis of the Working Process of the Capture and Lock System

A space station can be used by astronauts to live for a long time and carry out a large number of scientific research experiments. During the operation and maintenance of a space station, living materials and experimental equipment must be continually replen-ished, updated, and maintained. The specific implementation plan for the replacement of space station material is: (1) load the materials and equipment required by the space sta-tion into payload 1, and lock payload 1 in the spacecraft cargo compartment; (2) the space-craft carrying payload 1 is launched from the ground into a predetermined orbit in space, and docks with the space station; (3) use a manipulator and a capture and lock system to replace payload 1 in the cargo compartment with the abandoned payload 2 from the space station platform to complete the update of the space station materials and equipment; (4) abandoned payload 2 is released and deorbited so that it crashes into the atmosphere and burns up while the spacecraft returns to the ground for maintenance, as shown in Figure 1. During the process of on-orbit replacement of the payload in space, the main function of the capture and lock system is to complete attitude adjustment, capture and connection of the payload with the assistance of a seven-degrees-of-freedom manipulator. Both the manipulator and the capture and lock system are fixed to the spacecraft payload platform. Before the capture and lock system works, the end effector of the manipulator is connected with the payload handle to form a whole, then it carries the payload to the system capture area, as shown in Figure 2a.

Figure 1. Schematic diagram of the space station material replacement task.

Figure 1. Schematic diagram of the space station material replacement task.

Aerospace 2022, 9, 345 4 of 27Aerospace 2022, 9, x FOR PEER REVIEW 4 of 28

0P 4P

0y

0x0z 0O

1 2x x

1y

1z

2 3y y

2z

Δα

ΔαΔβ

Δβ

Δγ

Δγ

3 4z z

3x

4x

4y

1O

0y

0x0z

0o01r 2O3O4O

(a) (b)

Figure 2. Schematic diagram of the position and attitude error working conditions for the capture and lock system. (a) Working conditions of the capture and lock system; (b) schematic diagram of load pose error.

Due to the joint error of the manipulator and deformation of the arm, the actual pose P4 of the load has a certain pose error relative to the ideal capture pose P0. O0 is the capture point for the end effector of the manipulator on the payload handle and is also the origin of the translation and rotation of the payload relative to the ideal position. If the payload translation error is 、、Δ Δ Δx y z , the actual payload conjoined coordinate system O1 is translated by 、、Δ Δ Δx y z along the x0 axis, y0 axis, and z0 axis, respectively, relative to the ideal payload conjoined coordinate system O0, as shown in Figure 2b. The translation error vector of the payload can represented as:

= Δ Δ Δ01 ( , , )x y zr (1)

The rotation error is represented by the Cardan angle: if the payload rotation error is α β γΔ Δ Δ、、 , then the actual payload connected coordinate system O1 becomes coordi-

nate system O2 after rotation around axis X1, coordinate system O2 becomes coordinate system O3 after rotation around axis Y2, and coordinate system O3 becomes coordinate system O4 after rotation around axis Z3. When the pose error e is α β γΔ Δ Δ Δ Δ Δ, , , , ,[ ]x y z, the coordinate system O4 is the actual payload connected coordinate system. If there is a pose error and the payload can still be captured by the capture and lock system, it means that the tolerance capability of the system reaches e.

2.1.2. Single Point Positioning Analysis and Multi-Point Over-Positioning Evaluation Model

Precise positioning is an important link in the process of locking the space payload, and it is also an important function of the capture and lock system. The precise positioning of the payload provides a position guarantee for on-orbit control tasks, such as payload locking, electrical connection port insertion and removal, and module replacement. There-fore, the distributed multi-point positioning components of the capture and lock system are designed and analyzed in detail.

The distributed capture and lock system is composed of multiple locking units, each of which is composed of a capture and lock mechanism, a reducer, and a motor. The active end of the capture and lock mechanism is fixed to the payload platform, and the passive end is fixed to the bottom surface of the payload. After the capture is completed, and before pressing and locking, precise positioning is performed between the active end and the corresponding passive end through a positioning assembly. Multi-point positioning is performed between the distributed capture and lock system and the payload through multiple sets of positioning components. Before designing a multi-point positioning

Figure 2. Schematic diagram of the position and attitude error working conditions for the captureand lock system. (a) Working conditions of the capture and lock system; (b) schematic diagram ofload pose error.

Due to the joint error of the manipulator and deformation of the arm, the actual poseP4 of the load has a certain pose error relative to the ideal capture pose P0. O0 is thecapture point for the end effector of the manipulator on the payload handle and is also theorigin of the translation and rotation of the payload relative to the ideal position. If thepayload translation error is ∆x, ∆y, ∆z, the actual payload conjoined coordinate system O1is translated by ∆x, ∆y, ∆z along the x0 axis, y0 axis, and z0 axis, respectively, relative to theideal payload conjoined coordinate system O0, as shown in Figure 2b. The translation errorvector of the payload can represented as:

r01 = (∆x, ∆y, ∆z) (1)

The rotation error is represented by the Cardan angle: if the payload rotation error is∆α, ∆β, ∆γ, then the actual payload connected coordinate system O1 becomes coordinatesystem O2 after rotation around axis X1, coordinate system O2 becomes coordinate systemO3 after rotation around axis Y2, and coordinate system O3 becomes coordinate systemO4 after rotation around axis Z3. When the pose error e is [∆x, ∆y, ∆z, ∆α, ∆β, ∆γ], thecoordinate system O4 is the actual payload connected coordinate system. If there is a poseerror and the payload can still be captured by the capture and lock system, it means thatthe tolerance capability of the system reaches e.

2.1.2. Single Point Positioning Analysis and Multi-Point Over-PositioningEvaluation Model

Precise positioning is an important link in the process of locking the space payload, andit is also an important function of the capture and lock system. The precise positioning of thepayload provides a position guarantee for on-orbit control tasks, such as payload locking,electrical connection port insertion and removal, and module replacement. Therefore,the distributed multi-point positioning components of the capture and lock system aredesigned and analyzed in detail.

The distributed capture and lock system is composed of multiple locking units, eachof which is composed of a capture and lock mechanism, a reducer, and a motor. The activeend of the capture and lock mechanism is fixed to the payload platform, and the passiveend is fixed to the bottom surface of the payload. After the capture is completed, andbefore pressing and locking, precise positioning is performed between the active end andthe corresponding passive end through a positioning assembly. Multi-point positioningis performed between the distributed capture and lock system and the payload throughmultiple sets of positioning components. Before designing a multi-point positioningscheme, it is necessary to analyze positioning methods and the characteristics of a single

Aerospace 2022, 9, 345 5 of 27

positioning point. Therefore, based on positioning methods for machine tool fixtures,common positioning methods were summarized and analyzed, as shown in Table 1.

Table 1. Summary of common positioning methods.

SerialNumber Positioning Form Positioning

Piece (a)Positioning

Piece (b)Positioning

DiagramRestricted Degrees

of Freedom

1 Point positioning Support nails Flat piece


scheme, it is necessary to analyze positioning methods and the characteristics of a single positioning point. Therefore, based on positioning methods for machine tool fixtures, common positioning methods were summarized and analyzed, as shown in Table 1.


Serial Number Positioning Form

Position-ing Piece

(a)

Positioning Piece (b) Positioning Diagram

Restricted Degrees of Freedom

1 Point positioning Support nails

Flat piece

One movement degree of freedom

2 Line positioning

Linear position-ing

Long sup-port plate Flat piece

One movement degree of freedom and one ro-tational degree of free-

dom

Curve position-ing

Taper pin Cylinder

Two movement de-grees of freedom

V-groove Circular shaft

Two movement de-grees of freedom and

two rotational degrees of freedom

3 Face positioning

Plane positioning

Support plate Flat piece

One movement degree of freedom and two ro-tational degrees of free-

dom

Rectangu-lar pin

Rectangular tube


three rotational degrees of freedom V-groove V-block

Surface position-ing

Round pin Cylinder



Circular cone Tapered hole

Three movement de-grees of freedom and


Common positioning methods can be divided into three categories: point position-ing, line positioning, and surface positioning. Line positioning includes linear and curve positioning, and surface positioning includes plane and surface positioning. Different po-sitioning elements are used for each positioning method, and the six spatial degrees of freedom of the positioned piece are restricted to different degrees. According to the num-ber of degrees of freedom to be limited and the positioning reference characteristics of the positioned part, a single-point positioning method is selected.

Multi-point positioning is performed between a distributed capture and lock system and the payload through multiple sets of positioning components. The main difference

One movementdegree of freedom

2Line

positioning

Linearpositioning

Long supportplate Flat piece





Position-ing Piece

(a)




Flat piece


2 Line positioning

Linear position-ing



dom

Curve position-ing

Taper pin Cylinder





3 Face positioning

Plane positioning



dom

Rectangu-lar pin

Rectangular tube




Round pin Cylinder








One movementdegree of freedomand one rotationaldegree of freedom

Curvepositioning

Taper pin Cylinder





Position-ing Piece

(a)




Flat piece


2 Line positioning

Linear position-ing



dom

Curve position-ing

Taper pin Cylinder





3 Face positioning

Plane positioning



dom

Rectangu-lar pin

Rectangular tube




Round pin Cylinder








Two movementdegrees of freedom






Position-ing Piece

(a)




Flat piece


2 Line positioning

Linear position-ing



dom

Curve position-ing

Taper pin Cylinder





3 Face positioning

Plane positioning



dom

Rectangu-lar pin

Rectangular tube




Round pin Cylinder








Two movementdegrees of freedomand two rotationaldegrees of freedom

3Face

positioning

Planepositioning






Position-ing Piece

(a)




Flat piece


2 Line positioning

Linear position-ing



dom

Curve position-ing

Taper pin Cylinder





3 Face positioning

Plane positioning



dom

Rectangu-lar pin

Rectangular tube




Round pin Cylinder








One movementdegree of freedomand two rotationaldegrees of freedom

Rectangular pin Rectangulartube





Position-ing Piece

(a)




Flat piece


2 Line positioning

Linear position-ing



dom

Curve position-ing

Taper pin Cylinder





3 Face positioning

Plane positioning



dom

Rectangu-lar pin

Rectangular tube




Round pin Cylinder








Two movementdegrees of freedomand three rotationaldegrees of freedom

V-groove V-block





Position-ing Piece

(a)




Flat piece


2 Line positioning

Linear position-ing



dom

Curve position-ing

Taper pin Cylinder





3 Face positioning

Plane positioning



dom

Rectangu-lar pin

Rectangular tube




Round pin Cylinder








Surfacepositioning

Round pin Cylinder





Position-ing Piece

(a)




Flat piece


2 Line positioning

Linear position-ing



dom

Curve position-ing

Taper pin Cylinder





3 Face positioning

Plane positioning



dom

Rectangu-lar pin

Rectangular tube




Round pin Cylinder








Two movementdegrees of freedomand two rotationaldegrees of freedom






Position-ing Piece

(a)




Flat piece


2 Line positioning

Linear position-ing



dom

Curve position-ing

Taper pin Cylinder





3 Face positioning

Plane positioning



dom

Rectangu-lar pin

Rectangular tube




Round pin Cylinder








Three movementdegrees of freedomand two rotationaldegrees of freedom

Common positioning methods can be divided into three categories: point positioning,line positioning, and surface positioning. Line positioning includes linear and curvepositioning, and surface positioning includes plane and surface positioning. Differentpositioning elements are used for each positioning method, and the six spatial degreesof freedom of the positioned piece are restricted to different degrees. According to thenumber of degrees of freedom to be limited and the positioning reference characteristics ofthe positioned part, a single-point positioning method is selected.

Multi-point positioning is performed between a distributed capture and lock systemand the payload through multiple sets of positioning components. The main differencebetween multi-point positioning and single-point positioning is that multi-point positioningis prone to over-positioning. Over-positioning means that one or more degrees of freedomof the positioned member are jointly restricted by multiple positioning members, resulting

Aerospace 2022, 9, 345 6 of 27

in repeated positioning, termed hyperstatic constraint. In general, over-positioning is notallowed, since it will cause uncertainty and unreliability in positioning, resulting in a largeposition error between the positioning surface of the positioned piece and the positioningelement. However, positioning is often used in the positioning process of heavy-duty orhigh-speed components to improve the stress and deformation of the positioned partsand enhance the rigidity of the system. In multi-point positioning, the degree of over-positioning is related to the positioning method and the number of positions. To effectivelyevaluate the degree of over-positioning, a multi-point over-positioning evaluation model isestablished.

Before the space payload is captured and locked by the capture and lock system, itsdegree of freedom is F = 6, and after multi-point positioning, the degree of freedom is F =0. Taking the total number C of over-constrained payloads in the six degrees of freedom,

the direction of payload→X,→Y ,→Z,

_X,

_Y ,

_Z is an objective function, and a multi-point over-

constrained evaluation model is established:

C = C0 − 6 (2)

where C0 is the total number of payload restraints.Through the calculation of a large number of multi-point positioning hyperstatic

constraints, the following rules can be summarized: It is assumed that multiple anchorpoints for the payload are added in sequence. Starting with the addition of the secondanchor point, if the new multi-point positioning combination forms a coupling constraint lcthat does not exist at every single point, the single-point constraint kc of the newly addedpoint must be consumed.

C0 = C1 + (C2 + C2l − C2k) + . . . + (Ci + Cil − Cik) + . . . + (Cn + Cnl − Cnk) (3)

where n is the number of registration points; Ci is the number of constraints introducedby the i-th anchor point; Cil is the number of coupling constraints lc formed after theintroduction of the i-th anchor point; Cik consumes itself when the number of single pointconstraints kc after the i-th anchor point is introduced.

Ci =6

∑j=1

cij (4)

where cij is the constraint in the j direction introduced by the i-th anchor point with a value

of 1 if there is a constraint, and value of 0 if there is no constraint; ci1 is the number of→X

direction constraints introduced by the i-th anchor point; ci2 is the number of direction

constraints introduced by the i-th anchor point; ci3 is the number of→Z direction constraints

introduced by the i-th anchor point; ci4 is the number of_X direction constraints introduced

by the i-th anchor point; ci5 is the number of_Y direction constraints introduced by the

i-th anchor point; ci6 is the number of_Z direction constraints introduced by the i-th

anchor point.The payload multi-point over-constraint evaluation model takes the number for hyper-

static constraint C as the evaluation index, analyzes the coupling relationship between thepositioning points, and can be calculated for any form of multi-point positioning. The largerthe number for hyperstatic constraint C, the higher the degree of hyperstatic constraint,and vice versa. If C = 0, there is isostatic constraint.

2.1.3. Analysis of Positioning Mode and Layout Design for the Capture and Lock System

The selection of a multi-point positioning mode for a distributed capture and locksystem is closely related to the layout of the capture and lock system. As the dynamicperformance of the capture and lock system is optimized, the number of capture and lock

Aerospace 2022, 9, 345 7 of 27

mechanisms and the position of connecting points are determined, as shown in Figure 3.The best positioning mode is then selected according to the position of the four captureand lock mechanism connection points.


performance of the capture and lock system is optimized, the number of capture and lock mechanisms and the position of connecting points are determined, as shown in Figure 3. The best positioning mode is then selected according to the position of the four capture and lock mechanism connection points.

3A 2A

4A 1A

Figure 3. Layout of the connection point for the capture and lock mechanism on the bottom of the payload.

According to the working characteristics of the distributed capture and lock system, three candidate positioning methods with guiding function are selected: circular shaft-V-groove positioning, V-block-V-groove positioning, and circular cone-tapered hole posi-tioning. The four points are analyzed by the same positioning method. In order to ensure the payload degree of freedom F = 0 after positioning, there needs to be a vertical relation-ship among the four axes of the positioning shaft for circular shaft-V-groove positioning. The arrangement can be divided into two types—three parallel axes perpendicular to the fourth, or two parallel axes that are perpendicular to the other two, as shown in Figure 4. The arrangement of V-block-V-groove positioning is the same as that for circular shaft-V-groove positioning, and the centerlines of the four cones for circular cone-tapered posi-tioning are all perpendicular to the payload connection surface. The three positioning methods are calculated according to the multi-point over-positioning evaluation model, and the key parameters are shown in Table 2.

(a) (b)

Figure 4. Schematic diagram of a circular shaft-V-groove positioning arrangement. (a) Three-one orthogonal arrangement diagram; (b) two-two orthogonal arrangement diagram.

Table 2. Three positioning methods to evaluate the key parameters of the model.

Positioning Method C1 C2 C2l C2k C3 C3l C3k C4 C4l C4k C

Circular shaft-V-groove Three-one orthogonal 4 4 0 0 4 1 1 4 1 1 10 Two-two orthogonal 4 4 0 0 4 2 2 4 0 0 10

V-block-V-groove Three-one orthogonal 5 5 0 0 5 0 0 5 1 1 14 Two-two orthogonal 5 5 0 0 5 1 1 5 0 0 14

Circular cone-tapered hole 5 5 1 1 5 0 0 5 0 0 14

Through the comparative analysis of the total number of over-constrained C for the three positioning methods, it can be found that circular shaft-V-groove positioning has

Figure 3. Layout of the connection point for the capture and lock mechanism on the bottom ofthe payload.

According to the working characteristics of the distributed capture and lock sys-tem, three candidate positioning methods with guiding function are selected: circularshaft-V-groove positioning, V-block-V-groove positioning, and circular cone-tapered holepositioning. The four points are analyzed by the same positioning method. In order toensure the payload degree of freedom F = 0 after positioning, there needs to be a verticalrelationship among the four axes of the positioning shaft for circular shaft-V-groove posi-tioning. The arrangement can be divided into two types—three parallel axes perpendicularto the fourth, or two parallel axes that are perpendicular to the other two, as shown inFigure 4. The arrangement of V-block-V-groove positioning is the same as that for circularshaft-V-groove positioning, and the centerlines of the four cones for circular cone-taperedpositioning are all perpendicular to the payload connection surface. The three positioningmethods are calculated according to the multi-point over-positioning evaluation model,and the key parameters are shown in Table 2.


performance of the capture and lock system is optimized, the number of capture and lock mechanisms and the position of connecting points are determined, as shown in Figure 3. The best positioning mode is then selected according to the position of the four capture and lock mechanism connection points.

3A 2A

4A 1A

Figure 3. Layout of the connection point for the capture and lock mechanism on the bottom of the payload.

According to the working characteristics of the distributed capture and lock system, three candidate positioning methods with guiding function are selected: circular shaft-V-groove positioning, V-block-V-groove positioning, and circular cone-tapered hole posi-tioning. The four points are analyzed by the same positioning method. In order to ensure the payload degree of freedom F = 0 after positioning, there needs to be a vertical relation-ship among the four axes of the positioning shaft for circular shaft-V-groove positioning. The arrangement can be divided into two types—three parallel axes perpendicular to the fourth, or two parallel axes that are perpendicular to the other two, as shown in Figure 4. The arrangement of V-block-V-groove positioning is the same as that for circular shaft-V-groove positioning, and the centerlines of the four cones for circular cone-tapered posi-tioning are all perpendicular to the payload connection surface. The three positioning methods are calculated according to the multi-point over-positioning evaluation model, and the key parameters are shown in Table 2.

(a) (b)

Figure 4. Schematic diagram of a circular shaft-V-groove positioning arrangement. (a) Three-one orthogonal arrangement diagram; (b) two-two orthogonal arrangement diagram.



Circular shaft-V-groove Three-one orthogonal 4 4 0 0 4 1 1 4 1 1 10 Two-two orthogonal 4 4 0 0 4 2 2 4 0 0 10

V-block-V-groove Three-one orthogonal 5 5 0 0 5 0 0 5 1 1 14 Two-two orthogonal 5 5 0 0 5 1 1 5 0 0 14


Through the comparative analysis of the total number of over-constrained C for the three positioning methods, it can be found that circular shaft-V-groove positioning has

Figure 4. Schematic diagram of a circular shaft-V-groove positioning arrangement. (a) Three-oneorthogonal arrangement diagram; (b) two-two orthogonal arrangement diagram.



Circularshaft-V-groove

Three-one orthogonal 4 4 0 0 4 1 1 4 1 1 10Two-two orthogonal 4 4 0 0 4 2 2 4 0 0 10

V-block-V-groove Three-one orthogonal 5 5 0 0 5 0 0 5 1 1 14Two-two orthogonal 5 5 0 0 5 1 1 5 0 0 14


Aerospace 2022, 9, 345 8 of 27

Through the comparative analysis of the total number of over-constrained C for thethree positioning methods, it can be found that circular shaft-V-groove positioning has thelowest degree of over-positioning, so it is selected as the positioning method. As shown inFigure 5, under the combined action of preload force Fl and the V-groove support reactionforces FN1 and FN2, the positioning shaft has two degrees of freedom of movement androtation along the z-axis, so the positioning shaft cooperates with the V-groove. The rigidityof the positioning method is larger in the x-axis direction and smaller in the z-axis direction.Considering the balanced stiffness of the capture and lock system in these directions, twopositioning shafts and two V-grooves are required for positioning in the x-axis and z-axisdirections. As the distance between the positioning shafts increases in the same direction,the internal forces in the payload base plate caused by over-positioning will decrease, sothe positioning shafts in the same direction should be arranged diagonally, as shown inFigure 6. In the plane of the payload base plate, the combination of shafts and grooves ingroup a and group c limit the degree of freedom in the x-axis direction of the payload, andthe combination of shafts and grooves in group b and group d limit the degree of freedomin the z-axis direction of the payload. This shaft positioning layout is called two-twoorthogonal distribution. In practical engineering applications, the normal positioning andlocking functions of the capture and lock system are ensured by controlling the machiningaccuracy of the positioning structure and a reasonable assembly process.


the lowest degree of over-positioning, so it is selected as the positioning method. As shown in Figure 5, under the combined action of preload force Fl and the V-groove sup-port reaction forces FN1 and FN2, the positioning shaft has two degrees of freedom of move-ment and rotation along the z-axis, so the positioning shaft cooperates with the V-groove. The rigidity of the positioning method is larger in the x-axis direction and smaller in the z-axis direction. Considering the balanced stiffness of the capture and lock system in these directions, two positioning shafts and two V-grooves are required for positioning in the x-axis and z-axis directions. As the distance between the positioning shafts increases in the same direction, the internal forces in the payload base plate caused by over-position-ing will decrease, so the positioning shafts in the same direction should be arranged diag-onally, as shown in Figure 6. In the plane of the payload base plate, the combination of shafts and grooves in group a and group c limit the degree of freedom in the x-axis direc-tion of the payload, and the combination of shafts and grooves in group b and group d limit the degree of freedom in the z-axis direction of the payload. This shaft positioning layout is called two-two orthogonal distribution. In practical engineering applications, the normal positioning and locking functions of the capture and lock system are ensured by controlling the machining accuracy of the positioning structure and a reasonable assembly process.

αlF

2NF1NF

Figure 5. Schematic diagram of positioning shaft and V-groove.

Figure 6. Schematic diagram of the positioning shaft and V-groove layout.

2.2. Structural Design and Trajectory Planning for the Capture and Lock System 2.2.1. Analysis of Passive End Error Domain and Configuration Design of Capture Frame

The capture and lock mechanism is composed of an active end and a passive end. The active end is fixed to the payload platform, and the passive end is fixed to the bottom surface of the payload. During the process of capturing and locking, the active end to the passive end completes the tasks of capturing, positioning, and locking in turn. To maxim-ize the tolerance capability, the active and passive locking components are selected ac-cordingly. There are four geometric forms in three-dimensional space: point, line, surface, and volume. In limited space, a point passing through a surface is the easiest way to real-ize the combination. If the captured area of the passive end is a surface, and the captured feature of the active end is a point, then the feature point of the active end can easily pass through the captured area of the passive end, and this area is defined as the capture



the lowest degree of over-positioning, so it is selected as the positioning method. As shown in Figure 5, under the combined action of preload force Fl and the V-groove sup-port reaction forces FN1 and FN2, the positioning shaft has two degrees of freedom of move-ment and rotation along the z-axis, so the positioning shaft cooperates with the V-groove. The rigidity of the positioning method is larger in the x-axis direction and smaller in the z-axis direction. Considering the balanced stiffness of the capture and lock system in these directions, two positioning shafts and two V-grooves are required for positioning in the x-axis and z-axis directions. As the distance between the positioning shafts increases in the same direction, the internal forces in the payload base plate caused by over-position-ing will decrease, so the positioning shafts in the same direction should be arranged diag-onally, as shown in Figure 6. In the plane of the payload base plate, the combination of shafts and grooves in group a and group c limit the degree of freedom in the x-axis direc-tion of the payload, and the combination of shafts and grooves in group b and group d limit the degree of freedom in the z-axis direction of the payload. This shaft positioning layout is called two-two orthogonal distribution. In practical engineering applications, the normal positioning and locking functions of the capture and lock system are ensured by controlling the machining accuracy of the positioning structure and a reasonable assembly process.

αlF

2NF1NF



2.2. Structural Design and Trajectory Planning for the Capture and Lock System 2.2.1. Analysis of Passive End Error Domain and Configuration Design of Capture Frame

The capture and lock mechanism is composed of an active end and a passive end. The active end is fixed to the payload platform, and the passive end is fixed to the bottom surface of the payload. During the process of capturing and locking, the active end to the passive end completes the tasks of capturing, positioning, and locking in turn. To maxim-ize the tolerance capability, the active and passive locking components are selected ac-cordingly. There are four geometric forms in three-dimensional space: point, line, surface, and volume. In limited space, a point passing through a surface is the easiest way to real-ize the combination. If the captured area of the passive end is a surface, and the captured feature of the active end is a point, then the feature point of the active end can easily pass through the captured area of the passive end, and this area is defined as the capture


2.2. Structural Design and Trajectory Planning for the Capture and Lock System2.2.1. Analysis of Passive End Error Domain and Configuration Design of Capture Frame

The capture and lock mechanism is composed of an active end and a passive end.The active end is fixed to the payload platform, and the passive end is fixed to the bottomsurface of the payload. During the process of capturing and locking, the active end tothe passive end completes the tasks of capturing, positioning, and locking in turn. Tomaximize the tolerance capability, the active and passive locking components are selectedaccordingly. There are four geometric forms in three-dimensional space: point, line, surface,and volume. In limited space, a point passing through a surface is the easiest way to realizethe combination. If the captured area of the passive end is a surface, and the capturedfeature of the active end is a point, then the feature point of the active end can easilypass through the captured area of the passive end, and this area is defined as the capturedomain of the passive end. According to the positioning method selected in Section 2.1.3

Aerospace 2022, 9, 345 9 of 27

(circular shaft-V-groove matching), the passive end configuration is called the captureframe, as shown in Figure 7, where the height and width of the capture domain are Ha andWa, respectively.


domain of the passive end. According to the positioning method selected in Section 2.1.3 (circular shaft-V-groove matching), the passive end configuration is called the capture frame, as shown in Figure 7, where the height and width of the capture domain are Ha and Wa, respectively.

The shape of the passive end capture frame is a rectangle, and the active end feature point trajectory must be captured by the capture frame, where the main reason for failing to capture the active end is caused by manipulator error . Therefore, the error domain for the capture frame should be analyzed before the overall design of the capture and lock mechanism. Once the error range of the manipulator is determined, the error range of the capture frame relative to the initial ideal position can be determined, where the capture frame error range is the capture frame error domain. Key points that represent the error range of the capture frame must be selected for analysis. The length of the capture frame (i.e., the axial distance of the positioning shaft) must be longer, whereas the height is con-strained by the size of the frame. Therefore, during the capture process, the main factor affecting the result is the height of the capture frame. Thus, an error domain analysis is carried out for the height, where the top plate center A and the positioning shaft center B in the capture frame are selected as the key points for the analysis, as shown in Figure 7.

Figure 7. Capture frame configuration. (A: The top plate center of capture frame; B: The position-ing shaft center of capture frame.)

The error field of the key point can be obtained by transforming the coordinates of the key point. The specific method is as follows: Firstly, the key points are translated and rotated in the coordinate system at the end of the robot arm, and the error range of the key points can be obtained. The error range coordinate is then transformed into the global coordinate system to obtain the key point error field for the capture frame that can guide the design of the capture and lock mechanism. This section takes the key points A and B on the locking unit Ub as an example. The coordinate system is established as shown in Figure 8. The global coordinate system is established at the geometric center of the instal-lation base plate of the capture and lock system with the coordinate origin O1, and the local coordinate system is established at the geometric center of the end of the manipula-tor, that is, the upper surface of the payload, with the coordinate origin O2.

0M2O

1OaU bU

cUdU

Figure 8. Schematic diagram of the payload coordinate system.

Figure 7. Capture frame configuration. (A: The top plate center of capture frame; B: The positioningshaft center of capture frame.)

The shape of the passive end capture frame is a rectangle, and the active end featurepoint trajectory must be captured by the capture frame, where the main reason for failingto capture the active end is caused by manipulator error. Therefore, the error domainfor the capture frame should be analyzed before the overall design of the capture andlock mechanism. Once the error range of the manipulator is determined, the error rangeof the capture frame relative to the initial ideal position can be determined, where thecapture frame error range is the capture frame error domain. Key points that represent theerror range of the capture frame must be selected for analysis. The length of the captureframe (i.e., the axial distance of the positioning shaft) must be longer, whereas the height isconstrained by the size of the frame. Therefore, during the capture process, the main factoraffecting the result is the height of the capture frame. Thus, an error domain analysis iscarried out for the height, where the top plate center A and the positioning shaft center B inthe capture frame are selected as the key points for the analysis, as shown in Figure 7.

The error field of the key point can be obtained by transforming the coordinates ofthe key point. The specific method is as follows: Firstly, the key points are translated androtated in the coordinate system at the end of the robot arm, and the error range of thekey points can be obtained. The error range coordinate is then transformed into the globalcoordinate system to obtain the key point error field for the capture frame that can guidethe design of the capture and lock mechanism. This section takes the key points A andB on the locking unit Ub as an example. The coordinate system is established as shownin Figure 8. The global coordinate system is established at the geometric center of theinstallation base plate of the capture and lock system with the coordinate origin O1, and thelocal coordinate system is established at the geometric center of the end of the manipulator,that is, the upper surface of the payload, with the coordinate origin O2.


domain of the passive end. According to the positioning method selected in Section 2.1.3 (circular shaft-V-groove matching), the passive end configuration is called the capture frame, as shown in Figure 7, where the height and width of the capture domain are Ha and Wa, respectively.

The shape of the passive end capture frame is a rectangle, and the active end feature point trajectory must be captured by the capture frame, where the main reason for failing to capture the active end is caused by manipulator error . Therefore, the error domain for the capture frame should be analyzed before the overall design of the capture and lock mechanism. Once the error range of the manipulator is determined, the error range of the capture frame relative to the initial ideal position can be determined, where the capture frame error range is the capture frame error domain. Key points that represent the error range of the capture frame must be selected for analysis. The length of the capture frame (i.e., the axial distance of the positioning shaft) must be longer, whereas the height is con-strained by the size of the frame. Therefore, during the capture process, the main factor affecting the result is the height of the capture frame. Thus, an error domain analysis is carried out for the height, where the top plate center A and the positioning shaft center B in the capture frame are selected as the key points for the analysis, as shown in Figure 7.

Figure 7. Capture frame configuration. (A: The top plate center of capture frame; B: The position-ing shaft center of capture frame.)

The error field of the key point can be obtained by transforming the coordinates of the key point. The specific method is as follows: Firstly, the key points are translated and rotated in the coordinate system at the end of the robot arm, and the error range of the key points can be obtained. The error range coordinate is then transformed into the global coordinate system to obtain the key point error field for the capture frame that can guide the design of the capture and lock mechanism. This section takes the key points A and B on the locking unit Ub as an example. The coordinate system is established as shown in Figure 8. The global coordinate system is established at the geometric center of the instal-lation base plate of the capture and lock system with the coordinate origin O1, and the local coordinate system is established at the geometric center of the end of the manipula-tor, that is, the upper surface of the payload, with the coordinate origin O2.

0M2O

1OaU bU

cUdU

Figure 8. Schematic diagram of the payload coordinate system. Figure 8. Schematic diagram of the payload coordinate system.

Aerospace 2022, 9, 345 10 of 27

Based on the established coordinate system, a homogeneous coordinate transformationmatrix is used to transform the key points from the local coordinate system at the end ofthe manipulator to the global coordinate system:

1P2 = xR yR zR 2T 1T2 (5)

where xR is the homogeneous coordinate rotation transformation matrix around the x-axisof the O2 coordinate system; yR is the homogeneous coordinate rotation transformationmatrix around the y-axis of the O2 coordinate system; zR is the homogeneous coordinaterotation transformation matrix around the z-axis of the O2 coordinate system; 2T is thehomogeneous coordinate translation transformation matrix for the O2 coordinate system;1T2 is the homogeneous translation transformation matrix from the local coordinate systemO2 at the end of the manipulator to the global coordinate system O1.

The position error for the end of the manipulator is comprised of translation along thex-axis, y-axis, and z-axis, ∆x, ∆y and ∆z, respectively, and attitude deviation due to rotationabout the x-axis, y-axis, and z-axis, ∆α, ∆β and ∆γ, respectively. If the distance between thecoordinate origin O1 and the coordinate origin O2 is h, then 1P2 can be expressed as:

1P2 =cos ∆β cos ∆γ − cos ∆β sin ∆γ sin ∆β ∆x

sin ∆α sin ∆β cos ∆γ + cos ∆α sin ∆γ − sin ∆α sin ∆β sin ∆γ + cos ∆α cos ∆γ − sin ∆α cos ∆β ∆y + h− cos ∆α sin ∆β cos ∆γ + sin ∆α sin ∆γ cos ∆α sin ∆β sin ∆γ + sin ∆α cos ∆γ cos ∆α cos ∆β ∆z

0 0 0 1

(6)

Assuming that the homogeneous coordinates for the key points in the coordinatesystem at the end of the manipulator are A2 = [x2 y2 z2 1]T , then after rotation and trans-lation, and conversion to the global coordinate system, the homogeneous coordinate isA2 = [x1 y1 z1 1]T :

A1 = 1P2A2 (7)

To analyze the key point error domain more intuitively, the capture frame can beprojected onto a yz coordinate plane with a cross-sectional view as shown in Figure 9a.According to the accuracy parameters for the manipulator and considering the safetyfactor, a range for the pose error e can be obtained and programed in MATLAB. Usingthe transformation matrix to transform the coordinates of the two key points within theerror range, the error domain of the key points in the global coordinate system O1 can beobtained, as shown in Figure 9b. The height of the capture domain is Ha. After coordinatetransformation of the key point, it can be seen that the height of the capture frame thatallows the feature point at the active end to pass through becomes ha. The error field of thekey point and the allowable height for the capture frame provide the basis for designingthe trajectory of the active end feature point.

The capture frame is installed at the bottom of the payload and is captured by thecapture hook in the capture state, and the payload is fixed to the capture lock system inthe connected state, so the configuration of the capture frame directly affects capture andconnection. The shape of the contact surface between the capture frame and the payloaddetermines the stiffness distribution of the capture and lock mechanism, which has animportant influence on the fundamental frequency of the system. To improve the dynamicperformance of the capture and lock system, ensure the regularity of the contact surface,and facilitate bolt connection, the contact surface is determined to be a rectangle where theratio of the long side to the short side is 4.

La

Lb=

kz

kx=

14

(8)

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aH ah

(a) (b)

Figure 9. Schematic diagram of capture frame error field. (a) Capture box cutaway view; (b) sche-matic diagram of the key point error field. (A: The top plate center of capture frame; B: The posi-tioning shaft center of capture frame.)

The capture frame is installed at the bottom of the payload and is captured by the capture hook in the capture state, and the payload is fixed to the capture lock system in the connected state, so the configuration of the capture frame directly affects capture and connection. The shape of the contact surface between the capture frame and the payload determines the stiffness distribution of the capture and lock mechanism, which has an important influence on the fundamental frequency of the system. To improve the dynamic performance of the capture and lock system, ensure the regularity of the contact surface, and facilitate bolt connection, the contact surface is determined to be a rectangle where the ratio of the long side to the short side is 4.

14

a z

b x

L kL k

= = (8)

By synthesizing the contact surface shape of the capture frame and the orthogonal layout of the passive-end capture lock assembly, the overall configuration of the capture frame can be obtained, as shown in Figure 10.

aL

bL

sM

aK

bKz

xy

Figure 10. Schematic diagram of the capture frame configuration.

The parametric design of the capture and lock mechanism is completed through the positioning design, error domain analysis, the design of the active and passive end locking components, and the layout design of the capture and lock mechanism. The contact sur-faces of the four capture and lock mechanisms and the orientations of the positioning shafts are in a two-two orthogonal layout, and the resulting system is called an orthogonal distributed capture and lock system.

Figure 9. Schematic diagram of capture frame error field. (a) Capture box cutaway view; (b) schematicdiagram of the key point error field. (A: The top plate center of capture frame; B: The positioningshaft center of capture frame.)

By synthesizing the contact surface shape of the capture frame and the orthogonallayout of the passive-end capture lock assembly, the overall configuration of the captureframe can be obtained, as shown in Figure 10.


aH ah

(a) (b)

Figure 9. Schematic diagram of capture frame error field. (a) Capture box cutaway view; (b) sche-matic diagram of the key point error field. (A: The top plate center of capture frame; B: The posi-tioning shaft center of capture frame.)

The capture frame is installed at the bottom of the payload and is captured by the capture hook in the capture state, and the payload is fixed to the capture lock system in the connected state, so the configuration of the capture frame directly affects capture and connection. The shape of the contact surface between the capture frame and the payload determines the stiffness distribution of the capture and lock mechanism, which has an important influence on the fundamental frequency of the system. To improve the dynamic performance of the capture and lock system, ensure the regularity of the contact surface, and facilitate bolt connection, the contact surface is determined to be a rectangle where the ratio of the long side to the short side is 4.

14

a z

b x

L kL k

= = (8)

By synthesizing the contact surface shape of the capture frame and the orthogonal layout of the passive-end capture lock assembly, the overall configuration of the capture frame can be obtained, as shown in Figure 10.

aL

bL

sM

aK

bKz

xy


The parametric design of the capture and lock mechanism is completed through the positioning design, error domain analysis, the design of the active and passive end locking components, and the layout design of the capture and lock mechanism. The contact sur-faces of the four capture and lock mechanisms and the orientations of the positioning shafts are in a two-two orthogonal layout, and the resulting system is called an orthogonal distributed capture and lock system.


The parametric design of the capture and lock mechanism is completed through thepositioning design, error domain analysis, the design of the active and passive end lockingcomponents, and the layout design of the capture and lock mechanism. The contact surfacesof the four capture and lock mechanisms and the orientations of the positioning shafts arein a two-two orthogonal layout, and the resulting system is called an orthogonal distributedcapture and lock system.

2.2.2. Planning the Capture Trajectory of the Active End and the Configuration Design ofthe Capture Hook

According to the error field for the key points in the capture frame, the motion trend forthe trajectory of the ideal active end feature point can be inferred, as long as the trajectorypasses through the capture frame and provides linear travel for the locked positioningaxis. The ideal active-end feature point trajectory can be roughly divided into two stages:as shown in Figure 11, the first stage is the trajectory passing through the capture frame,which can be realized by using smooth curves a–c; the second stage is to lock the trajectoryof the positioning axis, which can be realized by using the straight-line c–d, and there is asmooth transition between the two trajectories.

Aerospace 2022, 9, 345 12 of 27


2.2.2. Planning the Capture Trajectory of the Active End and the Configuration Design of the Capture Hook

According to the error field for the key points in the capture frame, the motion trend for the trajectory of the ideal active end feature point can be inferred, as long as the trajec-tory passes through the capture frame and provides linear travel for the locked position-ing axis. The ideal active-end feature point trajectory can be roughly divided into two stages: as shown in Figure 11, the first stage is the trajectory passing through the capture frame, which can be realized by using smooth curves a–c; the second stage is to lock the trajectory of the positioning axis, which can be realized by using the straight-line c–d, and there is a smooth transition between the two trajectories.

1Q2Q

3Q

4Q Figure 11. Schematic diagram of the ideal active end feature point trajectory. (A: The top plate center of capture frame; B: The positioning shaft center of capture frame.)

In order to select the appropriate capture and lock mechanism according to the ideal active end feature point trajectory curve, the basic mechanisms that can independently complete the linear trajectory and the curved trajectory must be considered. These include the crank–slider mechanism, Robert mechanism, λ mechanism, and Watt mechanism, as shown in Figure 12, as well as the crank-rocker mechanism, disc cam mechanism, moving cam mechanism and double-rocker mechanism, as shown in Figure 13. Among them, the λ mechanism and the moving cam mechanism provide both straight lines and curves for the key point trajectories. It is obviously not feasible to use two mechanisms to form a trajectory that meets the requirements; therefore, it is necessary to use one mechanism or a series combination of two mechanisms.

(a) (b) (c) (d)

Figure 12. Linear track mechanisms. (a) Crank–slider mechanism (A, B, C: Hinge; B: Key point.); (b) Robert mechanism (A, B, C, D, M: Hinge; A, B, M: Key point.); (c) λ mechanism (A, B, C, D: Hinge; M: Key point.); (d) Watt mechanism(A, B, C, D: Hinge; M: Key point.).

DC

BA

(a) (b) (c) (d)

Figure 11. Schematic diagram of the ideal active end feature point trajectory. (A: The top plate centerof capture frame; B: The positioning shaft center of capture frame.)

In order to select the appropriate capture and lock mechanism according to the idealactive end feature point trajectory curve, the basic mechanisms that can independentlycomplete the linear trajectory and the curved trajectory must be considered. These includethe crank–slider mechanism, Robert mechanism, λ mechanism, and Watt mechanism, asshown in Figure 12, as well as the crank-rocker mechanism, disc cam mechanism, movingcam mechanism and double-rocker mechanism, as shown in Figure 13. Among them, theλ mechanism and the moving cam mechanism provide both straight lines and curves forthe key point trajectories. It is obviously not feasible to use two mechanisms to form atrajectory that meets the requirements; therefore, it is necessary to use one mechanism or aseries combination of two mechanisms.




1Q2Q

3Q



(a) (b) (c) (d)


DC

BA

(a) (b) (c) (d)

Figure 12. Linear track mechanisms. (a) Crank–slider mechanism (A, B, C: Hinge; B: Key point.);(b) Robert mechanism (A, B, C, D, M: Hinge; A, B, M: Key point.); (c) λ mechanism (A, B, C, D: Hinge;M: Key point.); (d) Watt mechanism (A, B, C, D: Hinge; M: Key point.).




1Q2Q

3Q



(a) (b) (c) (d)


DC

BA

(a) (b) (c) (d)

Figure 13. Curve track mechanisms. (a) Crank-rocker mechanism (A, B, C, D: Hinge; B: Key point.);(b) disc cam mechanism (A, B, C: Hinge; B: Key point.); (c) moving cam mechanism (A: Hinge; M:Key point.); (d) double-rocker mechanism (A, B, C, D: Hinge; B: Key point.).

The crank–slider mechanism with dead-point self-locking characteristics was selectedto transform the rotating motion of the motor into linear motion by taking into accountthe size of the mechanism, its mechanical properties, and trajectory compliance for thekey points. The moving cam mechanism is used to decompose the linear trajectory intoa linear and curved trajectory as shown in Figure 14. The active end feature point needsstructural support to complete the capture action. The rod QD can support the featurepoint Q to complete the trajectory of the curve segment without affecting the orientation ofthe positioning shaft, and the rod member DC can support the rod member QD to complete

Aerospace 2022, 9, 345 13 of 27

a predetermined trajectory and limit the movement of the positioning axis. This active endcomponent QDC is called a capture hook, and the capture hook vertex Q is a feature point.A cam is installed on the back of the capture hook and forms a moving cam mechanismwith the base arc cam.


Figure 13. Curve track mechanisms. (a) Crank-rocker mechanism (A, B, C, D: Hinge; B: Key point.); (b) disc cam mechanism (A, B, C: Hinge; B: Key point.); (c) moving cam mechanism (A: Hinge; M: Key point.); (d) double-rocker mechanism(A, B, C, D: Hinge; B: Key point.).

The crank–slider mechanism with dead-point self-locking characteristics was se-lected to transform the rotating motion of the motor into linear motion by taking into ac-count the size of the mechanism, its mechanical properties, and trajectory compliance for the key points. The moving cam mechanism is used to decompose the linear trajectory into a linear and curved trajectory as shown in Figure 14. The active end feature point needs structural support to complete the capture action. The rod QD can support the fea-ture point Q to complete the trajectory of the curve segment without affecting the orien-tation of the positioning shaft, and the rod member DC can support the rod member QD to complete a predetermined trajectory and limit the movement of the positioning axis. This active end component QDC is called a capture hook, and the capture hook vertex Q is a feature point. A cam is installed on the back of the capture hook and forms a moving cam mechanism with the base arc cam.

ω

v

Figure 14. Schematic diagram of the capture and lock mechanism.

The movement process of the capture and lock mechanism is as follows: In the initial state, the crank–slider mechanism is unfolded, the slider is at the highest point of the stroke, the capture hook cam in the moving cam mechanism cooperates with the arc cam, and the capture hook vertex is at the highest point. When the capture action starts, the crank drives the slider down, and the capture hook cam continues to cooperate with the arc cam to form a curved track. At the end of the capturing action, the crank continues to drive the slider down, and the capturing hook cam begins to cooperate with the linear cam to form a straight line segment trajectory. When the locking action is completed, the crank reaches the dead center position, the slider is at the lowest point, and the trajectory for the straight line segment of the capture hook vertex ends.

A schematic diagram of the mechanical motion of the capture scheme is shown in Figure 15. The capture process of this scheme is as follows: When the device to be captured enters the ideal capture position with the assistance of the manipulator, the capture hook 5 starts to move. The capture hook vertex Q passes through the capture area of the capture frame (1). As the capture hook vertex moves along the capture trajectory (2), the hook captures the capture frame, and the positioning shaft (3) in the capture frame enters the V-shaped groove (4) to complete capture and positioning. Finally, the capture hook con-tinues to be folded until the catch frame is loaded to complete the locking function.

Figure 14. Schematic diagram of the capture and lock mechanism.

The movement process of the capture and lock mechanism is as follows: In the initialstate, the crank–slider mechanism is unfolded, the slider is at the highest point of the stroke,the capture hook cam in the moving cam mechanism cooperates with the arc cam, andthe capture hook vertex is at the highest point. When the capture action starts, the crankdrives the slider down, and the capture hook cam continues to cooperate with the arc camto form a curved track. At the end of the capturing action, the crank continues to drive theslider down, and the capturing hook cam begins to cooperate with the linear cam to form astraight line segment trajectory. When the locking action is completed, the crank reachesthe dead center position, the slider is at the lowest point, and the trajectory for the straightline segment of the capture hook vertex ends.

A schematic diagram of the mechanical motion of the capture scheme is shown inFigure 15. The capture process of this scheme is as follows: When the device to be capturedenters the ideal capture position with the assistance of the manipulator, the capture hook5 starts to move. The capture hook vertex Q passes through the capture area of the captureframe (1). As the capture hook vertex moves along the capture trajectory (2), the hookcaptures the capture frame, and the positioning shaft (3) in the capture frame enters the V-shaped groove (4) to complete capture and positioning. Finally, the capture hook continuesto be folded until the catch frame is loaded to complete the locking function.


v

ω

pF

NF

(a) (b)

Figure 15. Schematic diagram of the capture scheme (a) Released state; (b) locked state. 1, capture box; 2(the red dotted line), capture hook vertex trajectory; 3, positioning axis; 4, V-groove; 5, capture hook.

A mathematical model was established based on the selected capture and lock mech-anism, and the trajectory for the vertices of the capture hook was parameterized to prepare for the determination and optimization of the subsequent trajectory parameters. The main research object of the mathematical model was the moving cam mechanism, and the model parameters and trajectory formation process are shown in Figure 16. Among them, O1 is the rotation and translation drive center of the capture hook, O2 is the center of the cylindrical roller of the capture hook, O3 is the center of the fixed cylindrical cam of the base, Q is the vertex of the capture hook, and P is the tangent point of the linear cam. The parameters for the size of each structure are defined as follows: a is the stroke of point O1 in the straight-line segment of point Q; b is the distance between O1O2; c is the vertical distance between O1O2; d is the distance between O1O2; e is the horizontal length of the capture hook; f is the vertical height of the capture hook; g is the stroke of point O1 in the curved segment of point Q; R is the cylindrical cam radius of the capture hook; r is the base cylindrical cam radius; and yt is the displacement function of point O1.

1Q

2Q

1Q

2Q

3Q

1Q

pF

ω

NF

(a) (b) (c)

Figure 16. Schematic diagram of model parameters and trajectory formation process. (a) Initial state; (b) end state of curve segment trajectory; (c) locked state.

Figure 15. Schematic diagram of the capture scheme (a) Released state; (b) locked state. 1, capture box;2(the red dotted line), capture hook vertex trajectory; 3, positioning axis; 4, V-groove; 5, capture hook.

A mathematical model was established based on the selected capture and lock mecha-nism, and the trajectory for the vertices of the capture hook was parameterized to preparefor the determination and optimization of the subsequent trajectory parameters. The mainresearch object of the mathematical model was the moving cam mechanism, and the modelparameters and trajectory formation process are shown in Figure 16. Among them, O1is the rotation and translation drive center of the capture hook, O2 is the center of the

Aerospace 2022, 9, 345 14 of 27

cylindrical roller of the capture hook, O3 is the center of the fixed cylindrical cam of thebase, Q is the vertex of the capture hook, and P is the tangent point of the linear cam. Theparameters for the size of each structure are defined as follows: a is the stroke of point O1in the straight-line segment of point Q; b is the distance between O1O2; c is the verticaldistance between O1O2; d is the distance between O1O2; e is the horizontal length of thecapture hook; f is the vertical height of the capture hook; g is the stroke of point O1 in thecurved segment of point Q; R is the cylindrical cam radius of the capture hook; r is the basecylindrical cam radius; and yt is the displacement function of point O1.


v

ω

pF

NF

(a) (b)

Figure 15. Schematic diagram of the capture scheme (a) Released state; (b) locked state. 1, capture box; 2(the red dotted line), capture hook vertex trajectory; 3, positioning axis; 4, V-groove; 5, capture hook.

A mathematical model was established based on the selected capture and lock mech-anism, and the trajectory for the vertices of the capture hook was parameterized to prepare for the determination and optimization of the subsequent trajectory parameters. The main research object of the mathematical model was the moving cam mechanism, and the model parameters and trajectory formation process are shown in Figure 16. Among them, O1 is the rotation and translation drive center of the capture hook, O2 is the center of the cylindrical roller of the capture hook, O3 is the center of the fixed cylindrical cam of the base, Q is the vertex of the capture hook, and P is the tangent point of the linear cam. The parameters for the size of each structure are defined as follows: a is the stroke of point O1 in the straight-line segment of point Q; b is the distance between O1O2; c is the vertical distance between O1O2; d is the distance between O1O2; e is the horizontal length of the capture hook; f is the vertical height of the capture hook; g is the stroke of point O1 in the curved segment of point Q; R is the cylindrical cam radius of the capture hook; r is the base cylindrical cam radius; and yt is the displacement function of point O1.

1Q

2Q

1Q

2Q

3Q

1Q

pF

ω

NF

(a) (b) (c)

Figure 16. Schematic diagram of model parameters and trajectory formation process. (a) Initial state; (b) end state of curve segment trajectory; (c) locked state.

Figure 16. Schematic diagram of model parameters and trajectory formation process. (a) Initial state;(b) end state of curve segment trajectory; (c) locked state.

The motion trajectory of the captured hook vertex Q can be expressed as a func-tion related to the displacement yt of O1, and the trajectory of the curve segment can beexpressed as:

x = x0

y = y0 + yt +√

f 2 + e2 sin(arccos (b+R+r)2+(a+c−yt)2+d2−(R+r)2

2d√(b+R+r)2+(a+c−yt)

2

+arctan a+c−ytb+R+r + arctan e

f + arctan bc ) (a ≤ yt ≤ a + g)

z = z0 −√

f 2 + e2 cos(arccos (b+R+r)2+(a+c−yt)2+d2−(R+r)2

2d√(b+R+r)2+(a+c−yt)

2

+arctan a+c−ytb+R+r + arctan e

f + arctan bc ) (a ≤ yt ≤ a + g)

(9)

The trajectory of the straight-line segment can be expressed as:x = x0y = y0 + yt + f (0 ≤ yt ≤ a)z = z0 + e

(10)

2.2.3. Configuration Parameter Optimization for the Capture and Lock System

The established mathematical model for the capture trajectory was graphed in MAT-LAB, and the trajectory of the capture hook vertex Q was obtained. There are manyparameters in the model, and the influence of each parameter on the trajectory curve wasanalyzed as the basis for parameter selection. The parameters in the trajectory modelinclude a, b, c, d, e, f, g, R, and r (see Section 2.2.2 for a definition of each parameter), and by

Aerospace 2022, 9, 345 15 of 27

changing each parameter individually, the effect of each on the trajectory could be observed,as shown in Figure 17.


The motion trajectory of the captured hook vertex Q can be expressed as a function related to the displacement yt of O1, and the trajectory of the curve segment can be ex-pressed as:

( )( )

( )

( )( )

022 2 2

2 20 22

22 2 22 2

0 22

( ) ( )sin(arccos

2 ( )

arctan arctan arctan )

( ) ( )cos(arccos

2 ( )

arctan a

tt

t

tt

t

t

t

x x

b R r a c y d R ry y y f e

d b R r a c y

a c y e b a y a gb R r f c

b R r a c y d R rz z f e

d b R r a c y

a c yb R r

=

+ + + + − + − += + + +

+ + + + −

+ −+ + + ≤ ≤ +

+ +

+ + + + − + − += − +

+ + + + −

+ −+ +

+ +( )rctan arctan ) t

e b a y a gf c

+ ≤ ≤ +

(9)

The trajectory of the straight-line segment can be expressed as:

( )0

0

0

0t t

x xy y y f y az z e

= = + + ≤ ≤ = +

(10)

2.2.3. Configuration Parameter Optimization for the Capture and Lock System The established mathematical model for the capture trajectory was graphed in

MATLAB, and the trajectory of the capture hook vertex Q was obtained. There are many parameters in the model, and the influence of each parameter on the trajectory curve was analyzed as the basis for parameter selection. The parameters in the trajectory model in-clude a, b, c, d, e, f, g, R, and r (see Section 2.2.2 for a definition of each parameter), and by changing each parameter individually, the effect of each on the trajectory could be ob-served, as shown in Figure 17.

(a) (b)


(c) (d)

(e) (f)

(g)

Figure 17. Schematic diagram of the analysis of the influence of the trajectory parameters on the capture hook vertex. (a) Analysis of parameter a; (b) analysis of parameters b, c, d; (c) analysis of parameter e; (d) analysis of parameter f; (e) analysis of parameter g; (f)analysis of parameter R; (g) analysis of parameter r.

After observing the influence of each parameter on the trajectory curve, the following was determined: Parameter a affects the length of the straight-line segment of the trajec-tory curve, where the larger the value, the longer the straight-line segment. Parameters b, c, and d form three sides of a right-angled triangle, so the larger the values, the smaller the curvature and the shorter the length of the curve segment. Parameter e affects the position of the z-axis direction of the trajectory curve, so the larger the value, the closer the curve is to the negative direction of the z-axis. Parameter f affects the position of the y-axis di-rection of the trajectory curve, so as this value increases, the curve moves closer to the positive y-axis. Parameter g affects the length of the curved segment of the trajectory curve, so the larger the value, the longer the length of the curved segment. Parameter R affects the curvature and length of the curved segment of the trajectory curve, so as this

Figure 17. Schematic diagram of the analysis of the influence of the trajectory parameters on thecapture hook vertex. (a) Analysis of parameter a; (b) analysis of parameters b, c, d; (c) analysis ofparameter e; (d) analysis of parameter f ; (e) analysis of parameter g; (f)analysis of parameter R;(g) analysis of parameter r.

Aerospace 2022, 9, 345 16 of 27

After observing the influence of each parameter on the trajectory curve, the followingwas determined: Parameter a affects the length of the straight-line segment of the trajectorycurve, where the larger the value, the longer the straight-line segment. Parameters b, c,and d form three sides of a right-angled triangle, so the larger the values, the smallerthe curvature and the shorter the length of the curve segment. Parameter e affects theposition of the z-axis direction of the trajectory curve, so the larger the value, the closerthe curve is to the negative direction of the z-axis. Parameter f affects the position of they-axis direction of the trajectory curve, so as this value increases, the curve moves closer tothe positive y-axis. Parameter g affects the length of the curved segment of the trajectorycurve, so the larger the value, the longer the length of the curved segment. Parameter Raffects the curvature and length of the curved segment of the trajectory curve, so as thisvalue increases, the curvature becomes smaller and the curved segment becomes shorter.Parameter r also affects the curvature and length of the curved segment of the trajectorycurve with both increasing as this value increases.

Taking the range of pose error e (±10 mm, ±10 mm, ±10 mm, ±1◦, ±1◦, ±1◦) as anexample, the trajectory of the active end feature point can be designed. The parameterswere selected according to the requirements for the trajectory curve and the results ofthe parameter impact analysis. The requirements for the trajectory curve include: (1) thetrajectory curve of the capture hook vertex must pass through the capture frame to ensurecapture; (2) a smoother trajectory curve is beneficial for capture, but the problem of excessivesmoothness should also be considered; (3) the parameters affecting the size of the structureshould be as small as possible to meet the requirements of structure miniaturization. Thevalues for each parameter were determined according to these requirements, and are shownin Table 3.

Table 3. List of values for the parameters of the capture and lock mechanism.

Parameter a/mm b/mm c/mm d/mm e/mm f /mm g/mm R/mm r/mm

Value 37 15 20 25 33 92 30 10 4

The capture hook vertex trajectory curve was integrated with the error field of thecapture frame, as shown in Figure 18. By comparative observation, it can be judged thatthe capture hook can safely pass through the capture frame during the capture process, andthe capture action can be completed. Thus, the trajectory of the parameterized capture lockmechanism has been completed.


value increases, the curvature becomes smaller and the curved segment becomes shorter. Parameter r also affects the curvature and length of the curved segment of the trajectory curve with both increasing as this value increases.

Taking the range of pose error e (±10 mm, ±10 mm, ±10 mm, ±1°, ±1°, ±1°) as an ex-ample, the trajectory of the active end feature point can be designed. The parameters were selected according to the requirements for the trajectory curve and the results of the pa-rameter impact analysis. The requirements for the trajectory curve include: (1) the trajec-tory curve of the capture hook vertex must pass through the capture frame to ensure cap-ture ; (2) a smoother trajectory curve is beneficial for capture, but the problem of excessive smoothness should also be considered; (3) the parameters affecting the size of the struc-ture should be as small as possible to meet the requirements of structure miniaturization. The values for each parameter were determined according to these requirements, and are shown in Table 3.

Table 3. List of values for the parameters of the capture and lock mechanism.

Parameter a/mm b/mm c/mm d/mm e/mm f/mm g/mm R/mm r/mm Value 37 15 20 25 33 92 30 10 4

The capture hook vertex trajectory curve was integrated with the error field of the capture frame, as shown in Figure 18. By comparative observation, it can be judged that the capture hook can safely pass through the capture frame during the capture process, and the capture action can be completed. Thus, the trajectory of the parameterized capture lock mechanism has been completed.

Figure 18. Schematic diagram of the trajectory passing through the capture frame error field. (A: The top plate center of capture frame; B: The positioning shaft center of capture frame.)

2.3. Capture Hook Layout Design 2.3.1. Analysis of Capture Hook Layout

In the case where the directions of the four positioning shafts are determined, the corresponding direction of each capture hook needs to be further determined. In this scheme, the capture hook can only move in one plane, including rotation and translation, and if it is projected in the plane of the payload base, then it can only move in one direc-tion. In the plane of the payload floor, if the capture hook in group c moves in the negative direction of the x-axis, the hook-frame contact force Fc will cause the payload to rotate counterclockwise around point O, and if the hook moves in the positive direction of the x-axis, the payload will be caused to rotate clockwise. Similarly, if the capture hook in

Figure 18. Schematic diagram of the trajectory passing through the capture frame error field. (A: Thetop plate center of capture frame; B: The positioning shaft center of capture frame.)

Aerospace 2022, 9, 345 17 of 27

2.3. Capture Hook Layout Design2.3.1. Analysis of Capture Hook Layout

In the case where the directions of the four positioning shafts are determined, thecorresponding direction of each capture hook needs to be further determined. In thisscheme, the capture hook can only move in one plane, including rotation and translation,and if it is projected in the plane of the payload base, then it can only move in one direction.In the plane of the payload floor, if the capture hook in group c moves in the negativedirection of the x-axis, the hook-frame contact force Fc will cause the payload to rotatecounterclockwise around point O, and if the hook moves in the positive direction of thex-axis, the payload will be caused to rotate clockwise. Similarly, if the capture hook ingroup b moves in the negative direction of the z-axis, the payload will be forced to rotateclockwise around the point O, and if the hook in the positive direction of the z-axis, thepayload will to rotate counterclockwise, as shown in Figure 19.


group b moves in the negative direction of the z-axis, the payload will be forced to rotate clockwise around the point O, and if the hook in the positive direction of the z-axis, the payload will to rotate counterclockwise, as shown in Figure 19.

1ω

2ω

(a) (b)

cF

0M

2ω

0M

1ω

cF

(c) (d)

Figure 19. Schematic diagram of the direction of the capture hook and the direction of rotation for the payload. (a) Group c capture hooks in the negative x-axis; (b) group c capture hooks in the pos-itive x-axis; (c) group b capture hooks in the negative z-axis; (d) group d capture hooks in the positive z-axis.

According to the influence of the movement direction of the capture hooks on the rotation direction of the payload during the capture process, it can be concluded that: For a set of active and passive catching lock assemblies where the movement direction of the capture hook is perpendicular to the axis of the catching frame, two directions can be se-lected, one of which will force the payload to rotate clockwise, and the other will force the payload to rotate counterclockwise. Since the movement of four sets of capture hooks are different, there are 42 16= =K total movement arrangements. Therefore, to achieve the purpose of adjusting the attitude of the payload during the capture process, two capture hooks on a diagonal line are selected to rotate the payload clockwise, and two capture hooks on the other diagonal line to rotate the payload counterclockwise. Thus, group a cooperates with group c to make the payload rotate counterclockwise, and group b coop-erates with group d to make the payload rotate clockwise, as shown in Figure 20. In this way, four sets of capture hooks work together to achieve the best payload and attitude adjustment effect during the capture process.

0M

2ω 1ωccF

cdF

cbF

caF

Figure 20. Schematic diagram of the orientation layout of the capture hooks.

Figure 19. Schematic diagram of the direction of the capture hook and the direction of rotation for thepayload. (a) Group c capture hooks in the negative x-axis; (b) group c capture hooks in the positivex-axis; (c) group b capture hooks in the negative z-axis; (d) group d capture hooks in the positivez-axis.

According to the influence of the movement direction of the capture hooks on therotation direction of the payload during the capture process, it can be concluded that:For a set of active and passive catching lock assemblies where the movement directionof the capture hook is perpendicular to the axis of the catching frame, two directions canbe selected, one of which will force the payload to rotate clockwise, and the other willforce the payload to rotate counterclockwise. Since the movement of four sets of capturehooks are different, there are K = 24 = 16 total movement arrangements. Therefore, toachieve the purpose of adjusting the attitude of the payload during the capture process,two capture hooks on a diagonal line are selected to rotate the payload clockwise, and twocapture hooks on the other diagonal line to rotate the payload counterclockwise. Thus,group a cooperates with group c to make the payload rotate counterclockwise, and group bcooperates with group d to make the payload rotate clockwise, as shown in Figure 20. Inthis way, four sets of capture hooks work together to achieve the best payload and attitudeadjustment effect during the capture process.

Aerospace 2022, 9, 345 18 of 27


group b moves in the negative direction of the z-axis, the payload will be forced to rotate clockwise around the point O, and if the hook in the positive direction of the z-axis, the payload will to rotate counterclockwise, as shown in Figure 19.

1ω

2ω

(a) (b)

cF

0M

2ω

0M

1ω

cF

(c) (d)

Figure 19. Schematic diagram of the direction of the capture hook and the direction of rotation for the payload. (a) Group c capture hooks in the negative x-axis; (b) group c capture hooks in the pos-itive x-axis; (c) group b capture hooks in the negative z-axis; (d) group d capture hooks in the positive z-axis.

According to the influence of the movement direction of the capture hooks on the rotation direction of the payload during the capture process, it can be concluded that: For a set of active and passive catching lock assemblies where the movement direction of the capture hook is perpendicular to the axis of the catching frame, two directions can be se-lected, one of which will force the payload to rotate clockwise, and the other will force the payload to rotate counterclockwise. Since the movement of four sets of capture hooks are different, there are 42 16= =K total movement arrangements. Therefore, to achieve the purpose of adjusting the attitude of the payload during the capture process, two capture hooks on a diagonal line are selected to rotate the payload clockwise, and two capture hooks on the other diagonal line to rotate the payload counterclockwise. Thus, group a cooperates with group c to make the payload rotate counterclockwise, and group b coop-erates with group d to make the payload rotate clockwise, as shown in Figure 20. In this way, four sets of capture hooks work together to achieve the best payload and attitude adjustment effect during the capture process.

0M

2ω 1ωccF

cdF

cbF

caF

Figure 20. Schematic diagram of the orientation layout of the capture hooks. Figure 20. Schematic diagram of the orientation layout of the capture hooks.

The positioning shaft of each passive end has two layout directions, parallel to eitherthe x-axis or the z-axis. Thus, there are Kp = 24 = 16 possible layouts for the fourpositioning shafts. Since the locking hook of each active end can only move along thepositive and negative directions of the x-axis and the z-axis during capture, it will causethe payload to rotate after generating torque Mi. The number of possible layouts for thehooks also amounts to Kd = 24 = 16, and if all possible combinations for the hooksand positioning shafts are considered, 256 layouts would need to be analyzed. However,the classification can be simplified to reduce unnecessary work and improve simulationefficiency. The payload base plate has square symmetry, so the layout of the positioningshafts can be simplified into Kp

′ = 4 layouts, as shown in Figure 21.


The positioning shaft of each passive end has two layout directions, parallel to either the x-axis or the z-axis. Thus, there are 4

p 2 16= =K possible layouts for the four posi-tioning shafts. Since the locking hook of each active end can only move along the positive and negative directions of the x-axis and the z-axis during capture, it will cause the pay-load to rotate after generating torque Mi. The number of possible layouts for the hooks also amounts to 4

d 2 16K = = , and if all possible combinations for the hooks and posi-tioning shafts are considered, 256 layouts would need to be analyzed. However, the clas-sification can be simplified to reduce unnecessary work and improve simulation effi-ciency. The payload base plate has square symmetry, so the layout of the positioning shafts can be simplified into 4pK ′ = layouts, as shown in Figure 21.

(a) (b) (c) (d)

Figure 21. Simplified classification layout of the positioning axis. (a) Three-one orthogonal layout; (b) two-two diagonal orthogonal layout; (c) two-two unilateral orthogonal layout; (d) parallel lay-out.

The movement direction of the capture hook is perpendicular to the axial direction of the positioning shaft. When the positioning shaft is arranged in a certain direction, the direction of the contact torque ( )oM i for each group of hook frames is determined by the movement direction of the capture hook. If the contact force Fi for each group of hook frames is equal during capture, the contact torque for each group of hook frames is

( ) 2o iM i F l= ⋅ , and the magnitude of the torque has nothing to do with the arrangement direction of the positioning shafts or the movement direction of the capture hook. Thus,

the movement direction of the capture hooks can also be simplified into 4dK ′ = layouts, as shown in Figure 22.

0M

12ω 1-2ω( )0M c

( )0M d ( )0M a

( )0M b

0M

22ω 2-2ω( )0M c

( )0M d ( )0M a

( )0M b

0M

3ω 3-3ω( )0M c

( )0M d ( )0M a

( )0M b

0M

4-4ω( )0M c

( )0M d ( )0M a

( )0M b

(a) (b) (c) (d)

Figure 22. Simplified classification of capture hook motion direction (a) Two−two moments unilat-eral balance; (b) Two−two moments diagonal balance; (c) Three−one moments reversal; (d) Four moments equal.

Figure 21. Simplified classification layout of the positioning axis. (a) Three-one orthogonal layout;(b) two-two diagonal orthogonal layout; (c) two-two unilateral orthogonal layout; (d) parallel layout.

The movement direction of the capture hook is perpendicular to the axial directionof the positioning shaft. When the positioning shaft is arranged in a certain direction,the direction of the contact torque Mo(i) for each group of hook frames is determinedby the movement direction of the capture hook. If the contact force Fi for each group ofhook frames is equal during capture, the contact torque for each group of hook frames isMo(i) = Fi·l/2, and the magnitude of the torque has nothing to do with the arrangementdirection of the positioning shafts or the movement direction of the capture hook. Thus,the movement direction of the capture hooks can also be simplified into Kd

′ = 4 layouts, asshown in Figure 22.

Aerospace 2022, 9, 345 19 of 27


The positioning shaft of each passive end has two layout directions, parallel to either the x-axis or the z-axis. Thus, there are 4

p 2 16= =K possible layouts for the four posi-tioning shafts. Since the locking hook of each active end can only move along the positive and negative directions of the x-axis and the z-axis during capture, it will cause the pay-load to rotate after generating torque Mi. The number of possible layouts for the hooks also amounts to 4

d 2 16K = = , and if all possible combinations for the hooks and posi-tioning shafts are considered, 256 layouts would need to be analyzed. However, the clas-sification can be simplified to reduce unnecessary work and improve simulation effi-ciency. The payload base plate has square symmetry, so the layout of the positioning shafts can be simplified into 4pK ′ = layouts, as shown in Figure 21.

(a) (b) (c) (d)

Figure 21. Simplified classification layout of the positioning axis. (a) Three-one orthogonal layout; (b) two-two diagonal orthogonal layout; (c) two-two unilateral orthogonal layout; (d) parallel lay-out.

The movement direction of the capture hook is perpendicular to the axial direction of the positioning shaft. When the positioning shaft is arranged in a certain direction, the direction of the contact torque ( )oM i for each group of hook frames is determined by the movement direction of the capture hook. If the contact force Fi for each group of hook frames is equal during capture, the contact torque for each group of hook frames is

( ) 2o iM i F l= ⋅ , and the magnitude of the torque has nothing to do with the arrangement direction of the positioning shafts or the movement direction of the capture hook. Thus,

the movement direction of the capture hooks can also be simplified into 4dK ′ = layouts, as shown in Figure 22.

0M

12ω 1-2ω( )0M c

( )0M d ( )0M a

( )0M b

0M

22ω 2-2ω( )0M c

( )0M d ( )0M a

( )0M b

0M

3ω 3-3ω( )0M c

( )0M d ( )0M a

( )0M b

0M

4-4ω( )0M c

( )0M d ( )0M a

( )0M b

(a) (b) (c) (d)

Figure 22. Simplified classification of capture hook motion direction (a) Two−two moments unilat-eral balance; (b) Two−two moments diagonal balance; (c) Three−one moments reversal; (d) Four moments equal.

Figure 22. Simplified classification of capture hook motion direction (a) Two−two moments unilat-eral balance; (b) Two−two moments diagonal balance; (c) Three−one moments reversal; (d) Fourmoments equal.

After simplification of the arrangement of the active and passive ends, the numberof layouts for the capture and lock system can be simplified into K′ = Kp

′·Kd′ = 16

possible arrangements.

2.3.2. Simulation Verification of Tolerance Capability for the Layout of Capture andLock System

With the aim of determining the working characteristics of the distributed capture andlock system, a method for analyzing and verifying the tolerance capability of the captureand lock system is proposed, which is shown in Figure 23. The key steps are as follows:

1. According to the boundary conditions of the structure size of the space payload andthe working requirements of the capture and lock system, determine the simplestlayout for the capture and lock system that will fully reflect the working conditions ofthe system;

2. Determine the initial tolerance T0 and increase the tolerance by ∆T, then the systemtolerance will be Tm = T0 + n∆T(n = 1, 2, 3 . . .);

3. Convert the tolerance index Tm into a limit boundary pose that can be tested;4. Carry out the capture judgments for the limit boundary pose, and if all poses are

successfully captured, set n = n+1, and continuously increase the tolerance for capture.If not all captures are successful, the system tolerance will be Tm = T0 + (n− 1)∆T.

According to the boundary conditions for the shape and size of the payload and theworking requirements of the capture and lock system, the initial tolerance was determinedas T0 = (±1mm,±1mm,±1mm,±0.1◦,±0.1◦,±0.1◦) and the incremental tolerance was∆T = (±1mm,±1mm,±1mm,±0.1◦,±0.1◦,±0.1◦). The iterative simulation tolerancecapability analysis was carried out on K′ = 16 system layouts, and the results are shown inTable 4.

Table 4. Layout tolerance capability of 16 capture and lock systems (measured in mm).

Three-OneOrthogonal Layout

Two-Two DiagonalOrthogonal Layout

Two-Two UnilateralOrthogonal Layout Parallel Layout

Two-two momentsunilateral balance

±9mm,±9mm,±9mm,±0.9◦,±0.9◦,±0.9◦

±10mm,±10mm,±10mm,±1◦,±1◦,±1◦

±5mm,±5mm,±5mm,±0.5◦,±0.5◦,±0.5◦

±8mm,±8mm,±8mm,±0.8◦,±0.8◦,±0.8◦

Two-two momentsdiagonal balance

±5mm,±5mm,±5mm,±0.5◦,±0.5◦,±0.5◦

0mm, 0mm, 0mm,0◦, 0◦, 0◦

±9mm,±9mm,±9mm,±0.9◦,±0.9◦,±0.9◦

±5mm,±5mm,±5mm,±0.5◦,±0.5◦,±0.5◦

Three-onemoments reversal

±4mm,±4mm,±4mm,±0.4◦,±0.4◦,±0.4◦

±9mm,±9mm,±9mm,±0.9◦,±0.9◦,±0.9◦

±5mm,±5mm,±5mm,±0.5◦,±0.5◦,±0.5◦

±5mm,±5mm,±5mm,±0.5◦,±0.5◦,±0.5◦

Four moments equal ±5mm,±5mm,±5mm,±0.5◦,±0.5◦,±0.5◦

±7mm,±7mm,±7mm,±0.7◦,±0.7◦,±0.7◦

±3mm,±3mm,±3mm,±0.3◦,±0.3◦,±0.3◦

±4mm,±4mm,±4mm,±0.4◦,±0.4◦,±0.4◦

Aerospace 2022, 9, 345 20 of 27


After simplification of the arrangement of the active and passive ends, the number of layouts for the capture and lock system can be simplified into 16p dK K K′ ′′ = ⋅ = possible arrangements.

2.3.2. Simulation Verification of Tolerance Capability for the Layout of Capture and Lock System

With the aim of determining the working characteristics of the distributed capture and lock system, a method for analyzing and verifying the tolerance capability of the cap-ture and lock system is proposed, which is shown in Figure 23. The key steps are as fol-lows: 1. According to the boundary conditions of the structure size of the space payload and

the working requirements of the capture and lock system, determine the simplest layout for the capture and lock system that will fully reflect the working conditions of the system;

2. Determine the initial tolerance T0 and increase the tolerance by ΔT , then the system tolerance will be 0 1,2,3mT T n T n= + Δ = ⋅⋅⋅（）;

3. Convert the tolerance index Tm into a limit boundary pose that can be tested; 4. Carry out the capture judgments for the limit boundary pose, and if all poses are

successfully captured, set n = n+1, and continuously increase the tolerance for capture . If not all captures are successful, the system tolerance will be 0 ( 1)= + − ΔmT T n T .

0mT T n T= + Δ

256 16K K ′= → =

1n n= +

0 ( 1)mT T n T= + − Δ

0T1T nΔ =，

mT

Figure 23. Tolerance capability analysis process for the capture and lock system.

According to the boundary conditions for the shape and size of the payload and the working requirements of the capture and lock system, the initial tolerance was determined

Figure 23. Tolerance capability analysis process for the capture and lock system.

Among the 16 system layouts, the combination of a two-two diagonal orthogonal layoutfor the positioning shafts with a two-two moments unilateral balance for the movementdirection of the capture hooks had a maximum tolerance of Tm = (±10mm,±10mm,±10mm,±1◦,±1◦,±1◦). The position change curve for the payload center of mass under the limitpose of this layout is shown in Figure 24.


as 0 ( 1mm, 1mm, 1mm 0.1 0.1 0.1 )T = ± ± ± ± ° ± ° ± °，，， and the incremental tolerance was ( 1mm, 1mm, 1mm 0.1 0.1 0.1 )TΔ = ± ± ± ± ° ± ° ± °，，， . The iterative simulation tolerance capa-

bility analysis was carried out on 16′ =K system layouts, and the results are shown in Table 4.

Table 4. Layout tolerance capability of 16 capture and lock systems (measured in mm).

Three-One Orthogonal Layout

Two-Two Diagonal Or-thogonal Layout

Two-Two Unilateral Or-thogonal Layout

Parallel Layout

Two-two mo-ments unilat-eral balance

9mm, 9mm, 9mm,0.9 , 0.9 , 0.9

± ± ±± ° ± ° ± °

± ± ±

± ° ± ° ± °mm, mm, mm,

, ,10 10 10

1 1 1

5mm, 5mm, 5mm,0.5 , 0.5 , 0.5

± ± ±± ° ± ° ± °

8mm, 8mm, 8mm,

0.8 , 0.8 , 0.8± ± ±

± ° ± ° ± °

Two-two mo-ments diago-nal balance

5mm, 5mm, 5mm,0.5 , 0.5 , 0.5

± ± ±± ° ± ° ± °

0mm,0mm,0mm,

0 ,0 ,0° ° °

9mm, 9mm, 9mm,0.9 , 0.9 , 0.9

± ± ±± ° ± ° ± °

5mm, 5mm, 5mm,

0.5 , 0.5 , 0.5± ± ±

± ° ± ° ± °

Three-one mo-ments reversal

4mm, 4mm, 4mm,0.4 , 0.4 , 0.4

± ± ±± ° ± ° ± °

9mm, 9mm, 9mm,

0.9 , 0.9 , 0.9± ± ±

± ° ± ° ± °

5mm, 5mm, 5mm,0.5 , 0.5 , 0.5

± ± ±± ° ± ° ± °

5mm, 5mm, 5mm,

0.5 , 0.5 , 0.5± ± ±

± ° ± ° ± °

Four moments equal

5mm, 5mm, 5mm,0.5 , 0.5 , 0.5

± ± ±± ° ± ° ± °

7mm, 7mm, 7mm,

0.7 , 0.7 , 0.7± ± ±

± ° ± ° ± °

3mm, 3mm, 3mm,0.3 , 0.3 , 0.3

± ± ±± ° ± ° ± °

4mm, 4mm, 4mm,0.4 , 0.4 , 0.4

± ± ±± ° ± ° ± °

Among the 16 system layouts, the combination of a two-two diagonal orthogonal layout for the positioning shafts with a two-two moments unilateral balance for the move-ment direction of the capture hooks had a maximum tolerance of

( 10mm, 10mm, 10mm, 1 , 1 , 1 )mT = ± ± ± ± ° ± ° ± ° . The position change curve for the payload center of mass under the limit pose of this layout is shown in Figure 24.

(a) (b) (c)

Figure 24. Variation curve for the position of the payload center of mass. (a) Variation curve for the position along the x-axis of the payload center of mass; (b) Variation curve for the position along the y-axis of the payload center of mass; (c) Variation curve for the position along the z-axis of the payload center of mass.

3. Results 3.1. Development of a Space Payload Ground Capture Test System

Combined with the orthogonal distributed capture and lock system studied in this paper, a space payload ground capture test system was designed and developed. The cap-ture test platform consists of an attitude adjustment system with six degrees of freedom, a simulated manipulator with seven degrees of freedom, a counterweight centering sys-tem with three degrees of freedom, a simulated payload, a six-dimensional force sensor, an orthogonally distributed capture and lock system, a motion capture system, and data acquisition. The composition of the control system is shown in Figure 25.

Figure 24. Variation curve for the position of the payload center of mass. (a) Variation curve for theposition along the x-axis of the payload center of mass; (b) Variation curve for the position alongthe y-axis of the payload center of mass; (c) Variation curve for the position along the z-axis of thepayload center of mass.

Aerospace 2022, 9, 345 21 of 27

3. Results3.1. Development of a Space Payload Ground Capture Test System

Combined with the orthogonal distributed capture and lock system studied in thispaper, a space payload ground capture test system was designed and developed. Thecapture test platform consists of an attitude adjustment system with six degrees of freedom,a simulated manipulator with seven degrees of freedom, a counterweight centering systemwith three degrees of freedom, a simulated payload, a six-dimensional force sensor, anorthogonally distributed capture and lock system, a motion capture system, and dataacquisition. The composition of the control system is shown in Figure 25.


After the attitude adjustment system and the payload handle are connected and fixed by the spigot, the captured initial pose error [ , , , , , ]e x y z α β γ= Δ Δ Δ Δ Δ Δ for the simulated payload can be adjusted with the Oe point as the origin of the pose error. The simulated manipulator is composed of a simulated arm and a joint damper. During the capture pro-cess, the damper can generate damping that is inversely proportional to the motion speed, effectively simulating the manipulator in the follow-up damping control mode during the actual capture process. The counterweight centering system can change the spatial posi-tion of the suspension point by adjusting the bolts and can be used to accurately find the center of mass for the simulated payload when there is an error in the process of simulated payload processing and assembly. The counterweight method was used to simulate the microgravity environment in space, and the floating state of the payload in space was effectively simulated by suspension at the center of mass of the payload. To reduce the counterweight load and make test operation easy, a simulated payload was developed. The envelope size of the simulated payload is exactly the same as an actual payload, but the mass is smaller. The three-dimensional force sensor was installed at the end of the simulated manipulator. When the capture hook is in contact with the capture frame, the sensor will sense the force signal and feed it back to the control system, providing a basis for the selection of control strategies. The data acquisition and control system consisted of an upper computer, lower computer, and a control cabinet. The system was developed based on the xPC Target control module in MATLAB. The control cabinet is directly con-nected to the test system, collecting capture contact force, capture time, and other param-eters to provide the basis for capture strategy selection, and sends out signals, such as capture hook speed, start and stop, etc., to execute the selected capture strategy.

0M

yΔ

xΔzΔ

myΔ

mxΔmzΔ

0G

0

2G

1dc

2dc3dc

4dc

5dc6dc 7dc

1T 2T

HaV

HbV

HcV

HdV

cF

it

lXlV

βΔ

γΔ αΔeO

0

2G

Figure 25. Schematic diagram of the space payload ground capture test system.

During the capture test, a motion capture system was used to detect the pose of the payload. The motion capture system uses four cameras to monitor positional changes in the four targets, measure motion speed and track the centroid of the simulated payload. The test platform, camera layout, and target capture positions are shown in Figure 26. Before the motion capture system can be used, system calibration must be carried out. Through the calibration of the relative position of the camera, calibration of the horizontal

Figure 25. Schematic diagram of the space payload ground capture test system.

After the attitude adjustment system and the payload handle are connected and fixedby the spigot, the captured initial pose error e = [∆x, ∆y, ∆z, ∆α, ∆β, ∆γ] for the simulatedpayload can be adjusted with the Oe point as the origin of the pose error. The simulatedmanipulator is composed of a simulated arm and a joint damper. During the captureprocess, the damper can generate damping that is inversely proportional to the motionspeed, effectively simulating the manipulator in the follow-up damping control modeduring the actual capture process. The counterweight centering system can change thespatial position of the suspension point by adjusting the bolts and can be used to accuratelyfind the center of mass for the simulated payload when there is an error in the processof simulated payload processing and assembly. The counterweight method was used tosimulate the microgravity environment in space, and the floating state of the payloadin space was effectively simulated by suspension at the center of mass of the payload.To reduce the counterweight load and make test operation easy, a simulated payloadwas developed. The envelope size of the simulated payload is exactly the same as anactual payload, but the mass is smaller. The three-dimensional force sensor was installedat the end of the simulated manipulator. When the capture hook is in contact with thecapture frame, the sensor will sense the force signal and feed it back to the control system,providing a basis for the selection of control strategies. The data acquisition and controlsystem consisted of an upper computer, lower computer, and a control cabinet. The systemwas developed based on the xPC Target control module in MATLAB. The control cabinet isdirectly connected to the test system, collecting capture contact force, capture time, and

Aerospace 2022, 9, 345 22 of 27

other parameters to provide the basis for capture strategy selection, and sends out signals,such as capture hook speed, start and stop, etc., to execute the selected capture strategy.

During the capture test, a motion capture system was used to detect the pose of thepayload. The motion capture system uses four cameras to monitor positional changes in thefour targets, measure motion speed and track the centroid of the simulated payload. Thetest platform, camera layout, and target capture positions are shown in Figure 26. Beforethe motion capture system can be used, system calibration must be carried out. Throughthe calibration of the relative position of the camera, calibration of the horizontal plane,and calibration of the global coordinate system, position information can be collected. Atarget is pasted on key positions of the model, the surface of the target is then coveredwith a photosensitive material, and the camera determines the position of the target afterreceiving reflected light from the target. In fact, a single target point is identified as a linepassing through the target point and perpendicular to the mirror of a single camera. If thetarget point pt coordinates are (xt, yt, zt), the normal vector perpendicular to the mirror ofcamera 1 is nt1 (ut1, vt1, wt1), then camera 1 identifies the target point pt as a straight line lt1:

x− xt

ut1=

y− yt

vt1=

z− zt

wt1(11)


plane, and calibration of the global coordinate system, position information can be col-lected. A target is pasted on key positions of the model, the surface of the target is then covered with a photosensitive material, and the camera determines the position of the target after receiving reflected light from the target. In fact, a single target point is identi-fied as a line passing through the target point and perpendicular to the mirror of a single camera. If the target point pt coordinates are (xt, yt, zt), the normal vector perpendicular to the mirror of camera 1 is nt1 (ut1, vt1, wt1), then camera 1 identifies the target point pt as a straight line lt1:

1 1 1

t t t

t t t

x x y y z zu v w− − −

= = (11)

The normal vector perpendicular to the mirror of camera 2 is nt2 (ut2, vt2, wt2), and camera 2 recognizes the target point pt as the straight line lt2:

2 2 2

t t t

t t t

x x y y z zu v w− − −

= = (12)

The pt coordinates of the target points can be obtained by combining Equations (11) and (12), which is the principle for a motion capture system to identify the coordinates of a target point. To obtain the position data for the center of mass Ct of a rigid body, at least three target points that are not on the same line need to be pasted on the rigid body: pt1(xt1,yt1,zt1), pt2(xt2,yt2,zt2), and pt3(xt3,yt3,zt3). If the distances from the three target points to the centroid are dt1, dt2, and dt3, respectively, the Ct coordinates for the centroid of a rigid body can be obtained by solving the following equation:

2 2 21 1 1 1

2 2 22 2 2 2

2 2 23 3 3 3

( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )

t t t

t t t

t t t

x x y y z z dx x y y z z dx x y y z z d

− + − + − =

− + − + − = − + − + − =

(13)

By calculating the coordinates of the target point, the attitude data for a rigid body can be obtained, and the change in the position and attitude of the point of interest, such as the center of mass of a rigid body, can also be calculated.

Figure 26. Space payload ground capture test system. 1, attitude adjustment system with six degrees of freedom; 2, six-dimensional force sensor; 3, simulated payload; 4, counterweight centering system

Figure 26. Space payload ground capture test system. 1, attitude adjustment system with six de-grees of freedom; 2, six-dimensional force sensor; 3, simulated payload; 4, counterweight centeringsystem with three degrees of freedom; 5, orthogonal distributed capture and lock system; 6, sim-ulated manipulator with seven degrees of freedom; 7, target; 8, camera; 9, data acquisition andcontrol system.

The normal vector perpendicular to the mirror of camera 2 is nt2 (ut2, vt2, wt2), andcamera 2 recognizes the target point pt as the straight line lt2:

x− xt

ut2=

y− yt

vt2=

z− zt

wt2(12)

The pt coordinates of the target points can be obtained by combining Equations (11)and (12), which is the principle for a motion capture system to identify the coordinates

Aerospace 2022, 9, 345 23 of 27

of a target point. To obtain the position data for the center of mass Ct of a rigid body,at least three target points that are not on the same line need to be pasted on the rigidbody: pt1(xt1,yt1,zt1), pt2(xt2,yt2,zt2), and pt3(xt3,yt3,zt3). If the distances from the three targetpoints to the centroid are dt1, dt2, and dt3, respectively, the Ct coordinates for the centroidof a rigid body can be obtained by solving the following equation:

(x− xt1)2 + (y− yt1)

2 + (z− zt1)2 = d1

(x− xt2)2 + (y− yt2)

2 + (z− zt2)2 = d2

(x− xt3)2 + (y− yt3)

2 + (z− zt3)2 = d3

(13)

By calculating the coordinates of the target point, the attitude data for a rigid bodycan be obtained, and the change in the position and attitude of the point of interest, such asthe center of mass of a rigid body, can also be calculated.

In the space payload ground capture test system, it was necessary to measure changesin the position and attitude trajectory of the simulated payload center of mass. In theory,at least three target points and two cameras are required. To avoid the phenomenon ofmissing target images caused by the occlusion of platform components during the shootingprocess, four target points and four cameras were used. The target images captured by thefour cameras and the positions of the four cameras are shown in Figure 27.


with three degrees of freedom; 5, orthogonal distributed capture and lock system; 6, simulated ma-nipulator with seven degrees of freedom; 7, target; 8, camera; 9, data acquisition and control system.

In the space payload ground capture test system, it was necessary to measure changes in the position and attitude trajectory of the simulated payload center of mass. In theory, at least three target points and two cameras are required. To avoid the phenome-non of missing target images caused by the occlusion of platform components during the shooting process, four target points and four cameras were used. The target images cap-tured by the four cameras and the positions of the four cameras are shown in Figure 27.

Figure 27. Target image and the positions of four camera in the space payload ground capture test system.

3.2. Experimental Verification of Capturing Tolerance Capability To verify the synchronous capture tolerance capability of the developed orthogonal

distributed capture and lock system, the space payload ground capture test system was used to perform tolerance capability tests on the boundary poses of four types of typical boundary errors, as shown in Table 5.

Table 5. Four types of typical boundary pose errors.

Boundary Pose x/mm y/mm z/mm /α ° /γ ° /β ° P1 10 −10 10 1 −1 −1 P2 −10 10 10 1 1 −1 P3 10 10 −10 −1 −1 1 P4 10 10 10 −1 1 −1

Using the space payload ground capture test system and the motion capture system to carry out the synchronous capture tests, the trajectories for the center of mass of the simulated payload in the four groups are shown in Figures 28–31. It was found that the displacement curves obtained by the synchronous capture test were constantly approach-ing the theoretical end position for the displacement of the center of mass, which proves

that the tolerance capability of the capture and lock system had reached mT ′ .

Figure 27. Target image and the positions of four camera in the space payload ground capturetest system.

3.2. Experimental Verification of Capturing Tolerance Capability

To verify the synchronous capture tolerance capability of the developed orthogonaldistributed capture and lock system, the space payload ground capture test system wasused to perform tolerance capability tests on the boundary poses of four types of typicalboundary errors, as shown in Table 5.

Table 5. Four types of typical boundary pose errors.

Boundary Pose x/mm y/mm z/mm α/◦ γ/◦ β/◦

P1 10 −10 10 1 −1 −1P2 −10 10 10 1 1 −1P3 10 10 −10 −1 −1 1P4 10 10 10 −1 1 −1

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Using the space payload ground capture test system and the motion capture systemto carry out the synchronous capture tests, the trajectories for the center of mass of thesimulated payload in the four groups are shown in Figures 28–31. It was found that thedisplacement curves obtained by the synchronous capture test were constantly approachingthe theoretical end position for the displacement of the center of mass, which proves thatthe tolerance capability of the capture and lock system had reached Tm

′.


(a) (b) (c)

Figure 28. The displacement of the center of mass of the captured test payload in the first boundary pose (see Table 5 for details). (a) The x-axis displacement of the center of mass of the captured test payload in the first boundary pose; (b) The y-axis displacement of the center of mass of the captured test payload in the first boundary pose; (c) The z-axis displacement of the center of mass of the captured test payload in the first boundary pose.

(a) (b) (c)

Figure 29. The displacement of the center of mass of the captured test payload in the second bound-ary pose (see Table 5 for details). (a) The x-axis displacement of the center of mass of the captured test payload in the second boundary pose; (b) The y-axis displacement of the center of mass of the captured test payload in the second boundary pose; (c) The z-axis displacement of the center of mass of the captured test payload in the second boundary pose.

(a) (b) (c)

Figure 30. The displacement of the center of mass of the captured test payload in the third boundary pose (see Table 5 for details). (a) The x-axis displacement of the center of mass of the captured test payload in the third boundary pose; (b) The y-axis displacement of the center of mass of the captured

Figure 28. The displacement of the center of mass of the captured test payload in the first boundarypose (see Table 5 for details). (a) The x-axis displacement of the center of mass of the captured testpayload in the first boundary pose; (b) The y-axis displacement of the center of mass of the capturedtest payload in the first boundary pose; (c) The z-axis displacement of the center of mass of thecaptured test payload in the first boundary pose.


(a) (b) (c)


(a) (b) (c)


(a) (b) (c)


Figure 29. The displacement of the center of mass of the captured test payload in the second boundarypose (see Table 5 for details). (a) The x-axis displacement of the center of mass of the captured testpayload in the second boundary pose; (b) The y-axis displacement of the center of mass of thecaptured test payload in the second boundary pose; (c) The z-axis displacement of the center of massof the captured test payload in the second boundary pose.

Aerospace 2022, 9, 345 25 of 27


(a) (b) (c)


(a) (b) (c)


(a) (b) (c)


Figure 30. The displacement of the center of mass of the captured test payload in the third boundarypose (see Table 5 for details). (a) The x-axis displacement of the center of mass of the captured testpayload in the third boundary pose; (b) The y-axis displacement of the center of mass of the capturedtest payload in the third boundary pose; (c) The z-axis displacement of the center of mass of thecaptured test payload in the third boundary pose.


test payload in the third boundary pose; (c) The z-axis displacement of the center of mass of the captured test payload in the third boundary pose.

(a) (b) (c)

Figure 31. The displacement of the center of mass of the captured test payload in the fourth bound-ary pose (see Table 5 for details). (a) The x-axis displacement of the center of mass of the captured test payload in the fourth boundary pose; (b) The y-axis displacement of the center of mass of the captured test payload in the fourth boundary pose; (c) The z-axis displacement of the center of mass of the captured test payload in the fourth boundary pose.

4. Discussion In this paper, modular parameter design and analysis of a capture and lock mecha-

nism was carried out, and a parameterized capture and lock mechanism unit with strong versatility and adaptability and a highly reliable capture and lock system layout was ob-tained. The system layout was simulated and verified by experiments, and the large-tol-erance capturing capability of the system layout was verified, which is briefly summa-rized as follows: 1 A multi-point over-positioning evaluation model was established, the positioning de-

sign of the capture and lock mechanism was carried out, and a positioning mechanism with an orthogonal layout was obtained, which created a foundation for designing the configuration of the capture and lock mechanism;

2 Through the analysis of the payload attitude and the error domain for the passive end, the planning and design of the capture trajectory of the active end was completed, and the configuration of the passive end was obtained by comprehensively consider-ing the optimal dynamic performance of the system. A mathematical model for the capture and lock mechanism was established, and the ideal trajectory parameters for the active end were obtained. Through the analysis of the capture trajectory curve, optimization of the configuration parameters for the capture lock system was com-pleted;

3 To improve payload attitude adjustment, the system positioning method was com-prehensively considered, the layout design of the active end was carried out, and the system layout with the largest tolerance capacity and optimal attitude adjustment was obtained;

4 A simulation was used to verify the layout tolerance capability of the capture lock system, a space payload ground capture test system was developed, and a system layout tolerance capability test was carried out to verify the large-tolerance capability of the developed capture system.

Author Contributions: Conceptualization, G.W.; methodology, Y.Y. and G.W.; software, J.W. and Y.Y.; validation, W.H.; formal analysis, G.X.; investigation, X.H.; resources, G.W.; data curation, Y.Y. and G.W.; writing—original draft preparation, Y.Y.; writing—review and editing, G.W. and Y.Y.;

Figure 31. The displacement of the center of mass of the captured test payload in the fourth boundarypose (see Table 5 for details). (a) The x-axis displacement of the center of mass of the captured testpayload in the fourth boundary pose; (b) The y-axis displacement of the center of mass of the capturedtest payload in the fourth boundary pose; (c) The z-axis displacement of the center of mass of thecaptured test payload in the fourth boundary pose.

4. Discussion

In this paper, modular parameter design and analysis of a capture and lock mechanismwas carried out, and a parameterized capture and lock mechanism unit with strong versatil-ity and adaptability and a highly reliable capture and lock system layout was obtained. Thesystem layout was simulated and verified by experiments, and the large-tolerance capturingcapability of the system layout was verified, which is briefly summarized as follows:

1. A multi-point over-positioning evaluation model was established, the positioning de-sign of the capture and lock mechanism was carried out, and a positioning mechanismwith an orthogonal layout was obtained, which created a foundation for designingthe configuration of the capture and lock mechanism;

2. Through the analysis of the payload attitude and the error domain for the passive end,the planning and design of the capture trajectory of the active end was completed, andthe configuration of the passive end was obtained by comprehensively considering theoptimal dynamic performance of the system. A mathematical model for the captureand lock mechanism was established, and the ideal trajectory parameters for the active

Aerospace 2022, 9, 345 26 of 27

end were obtained. Through the analysis of the capture trajectory curve, optimizationof the configuration parameters for the capture lock system was completed;

3. To improve payload attitude adjustment, the system positioning method was com-prehensively considered, the layout design of the active end was carried out, and thesystem layout with the largest tolerance capacity and optimal attitude adjustmentwas obtained;

4. A simulation was used to verify the layout tolerance capability of the capture locksystem, a space payload ground capture test system was developed, and a systemlayout tolerance capability test was carried out to verify the large-tolerance capabilityof the developed capture system.

Author Contributions: Conceptualization, G.W.; methodology, Y.Y. and G.W.; software, J.W. andY.Y.; validation, W.H.; formal analysis, G.X.; investigation, X.H.; resources, G.W.; data curation, Y.Y.and G.W.; writing—original draft preparation, Y.Y.; writing—review and editing, G.W. and Y.Y.;visualization, Y.Y.; supervision, G.W.; project administration, G.W.; funding acquisition, G.W. Allauthors have read and agreed to the published version of the manuscript.

Funding: This research was funded by the Youth Natural Science Foundation of Hebei Province,grant number E2021409025; the S & T Program of Hebei, grant number 21375414D; Scientific ResearchProject of Higher Education Institutions of Hebei Province, grant number QN2022123; and theCentral Guidance on Local Science and Technology Development Fund of Hebei Province, grantnumber 226Z1803G.

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement: Not applicable.

Acknowledgments: The authors gratefully acknowledge the full support of the Langfang MunicipalScience and Technology Program Self-financing Project, grant number 2021011068; the PhD researchstartup foundation of North China Institute of Aerospace Engineering, grant number BKY-2021-11;the Postgraduate Innovation Funding Project of North China Institute of Aerospace Engineering,grant numbers YKY-2021-22, YKY-2021-23; and Hebei Education Department innovative abilitytraining support project for postgraduate students, CXZZSS2022133.

Conflicts of Interest: The authors declare no conflict of interest.

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http://doi.org/10.1007/BF03256532

http://doi.org/10.3182/20110828-6-IT-1002.00827

http://doi.org/10.1017/S0263574711001007

http://doi.org/10.1016/j.robot.2006.07.003

http://doi.org/10.1016/j.actaastro.2009.05.015

http://doi.org/10.1177/0954410018786615

http://doi.org/10.1007/s11071-018-4498-1

http://doi.org/10.1163/156855304322758015

Layout Design and Verification of a Space Payload Distributed ...

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