Development of a Bionic Hexapod Robot for Walking on Unstructured Terrain

Journal of Bionic Engineering 11 (2014) 176–187

Development of a Bionic Hexapod Robot for Walking on Unstructured Terrain

He Zhang, Yubin Liu, Jie Zhao, Jie Chen, Jihong Yan State Key Lab of Robotics and System, Harbin Institute of Technology, Harbin 150080, P. R. China

Abstract This paper reports the design methodology and control strategy in the development of a novel hexapod robot HITCR-II that

is suitable for walking on unstructured terrain. First, the entire sensor system is designed to equip the robot with the perception of external environment and its internal states. The structure parameters are optimized for improving the dexterity of the robot. Second, a foot-force distribution model and a compensation model are built to achieve posture control. The two models are capable of effectively improving the stability of hexapod walking on unstructured terrain. Finally, the Posture Control strategy based on Force Distribution and Compensation (PCFDC) is applied to the HITCR-II hexapod robot. The experimental results show that the robot can effectively restrain the vibration of trunk and keep stable while walking and crossing over the un-structured terrains.

Keywords: hexapod robot, structure optimization, posture control, force distribution, force compensation Copyright © 2014, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(14)60041-X

1 Introduction

The locomotion of a multi-legged robot is highly complex[1,2]. The hexapod robot which is typically multi-legged is characterized by its climbing capability and fault-tolerance for walking on unstructured terrain. It is particularly suitable for tasks in complex environ-ment[3], such as exploration (SpaceClimber)[4] or trans-portation (Athlete)[5] in outer space, detection in the wild (Dylema)[6,7] and for operation in extreme environment (Lemur)[8] where high reliability is essential. Thus the development of a hexapod robot capable of walking on unstructured terrain is of practical importance.

Much research work has been devoted to the generation method of free gait. This includes the method based on Central Pattern Generators (CPG)[9,10,11] applied in robot Scorpion[12] and Cruse′s Walknet[13–15] which is used in the design of several robots[16]. The free gait brings autonomic coordination between the legs into effect. The research efforts have been expanded to improve the stability of hexapod walking on unstructured terrain since the compliance control of the legs was proposed. This strategy is

successfully applied in robots LAURON[17] and DLR-Crawler[18] that is based on the force sensors in locating their legs. Under the compliance control, the disturbance due to state transition between swing and stance is restrained and the stability of walking is im-proved. The purpose of research on hexapod robot is to achieve its autonomous and stable walking on un-structured terrain. A large stability margin is necessary for its broad adaption to unstructured terrain. The posture adjustment is an effective approach to achieve this. The technique for posture prediction, applied in robot RHex[19] and Robot III[20], adjusts the posture by computing the position of projection of Center of Gravity (COG) in Support Polygon (SP). The kine-matic calculation is complex as the structure is se-ries-parallel and there are 18 degrees of freedom (DOFs). The problem of foot-force distribution of hexapod robot during locomotion on a vertical surface has been discussed in Ref. [21]. This paper proposes a strategy called Posture Control strategy based on Force Distribution and Compensation (PCFDC). The dis-tributed foot-force is used as a feedback for posture control to avoid computing the position of COG, and

Corresponding author: Jie Zhao E-mail: [email protected]

Zhang et al.: Development of a bionic hexapod robot for walking on unstructured terrain 177

also is combined with compensative foot-force to re-strain the vibration of trunk.

The hexapod robot HITCR-II is developed for walking in complex environment. The vision, force and other sensors are designed for the robot to realize the perception of environment and its own state for suc-cessfully crossing over unstructured terrain. The walk-ing of hexapod with free gait on flat terrain is successful for the first generation robot, HITCR-I[22]. The compli-ance control based on 3-DOF force sensor on a leg of the second generation hexapod robot HITCR-II[23] is also investigated. The free gait provides the robot inde-pendent walking ability, and the compliance control of leg improves robot’s adaptability to slightly rough ter-rain. The work reported in this paper is to enhance the stability margin of walking of the robot by posture con-trol strategy, which is a key technology for crossing over unstructured terrain and even for climbing over the ob-stacles.

In this paper, a novel hexapod robot HITCR-II suitable for walking on unstructured terrain is proposed (as shown in Fig. 1). It is characterized by high-integration and control with multi-sensors. An objective function is formulated to optimize the pa-rameters of structure to improve the dexterity. Using the sensing information of the force sensors and pose sensor, the PCFDC strategy is proposed to improve the stability margin of hexapod walking. Firstly, the foot-force dis-tribution model is developed to obtain the desired dis-tributed foot-force of all stance legs in any gait pattern. Secondly, the foot-force compensation model is created to obtain the compensation value of foot force, with the aim to restrain the vibration of trunk while the robot walks on unstructured terrain. The method proposed in this paper is verified by comparing the simulation and experimental results.

Fig. 1 The hexapod robot HITCR-II walking on unstructured terrain.

2 Design of the hexapod robot HITCR-II

The design of HITCR-II is based on three objec-tives. The first objective is to provide enough mo-tion-promoting force for its walking, and to realize a small-scale highly-integrated structure. The second ob-jective is to design complete sensor system within the structure of robot so that the robot has the perception of environment and its own state. The third objective is to improve motion dexterity by optimizing its structural parameters.

2.1 Structure, sensors and transmission agent of

HITCR-II The outline of the body of HITCR-II and the dis-

tribution of its six limbs are designed as oval-shaped to improve the stability of walking as well as to reduce the possibility of interference between the legs during movement. As shown in Fig. 2, the length of trunk is 320 mm, and the width of anterior and posterior parts are 136 mm and 196 mm respectively. Binocular stereo vision is developed to select the route and the support point of the foot. The pose sensor is installed at the geometric center, which is equidistant to all the six foot-ends to perceive the posture on-line.

Pinboard Leg control module

Motor driver

Core controller320 mm

196 mm

Binocular stereo vision

Main control board

Pose sensor

Fig. 2 Structure of HITCR-II’s trunk.

Journal of Bionic Engineering (2014) Vol.11 No.2 178

The hexapod robot is characterized by

multi-sensors and multi-DOF of series-parallel hybrid. The hardware of control system of the robot is designed as layered distributed architecture to enhance computing performance. The embedded ARM based main control board executes the coordination of six legs and transfers the information between PC-based host computer and embedded system, and communicates with the host computer via Ethernet. All the devices in robot com-municate by a single CAN bus, except the binocular stereo vision which connects to PC directly. Each leg is considered as a modularized isolated system controlled by DSP based control module. It consists of pinboard, core controller and three motor drivers, and processes all the tasks of each leg.

The leg of HITCR-II is designed as a uniform modular structure for easy interchangeability. As shown in Fig. 3, the leg consists of coxa, femur, and tibia. It has three independent DOFs comprising the three joints and a passive DOF based on the spring mechanism along the direction of tibia axes.

As shown in Fig. 3, the joint position sensors are designed into the structure of all joints. The sensor comprises a Hall Effect chip and magnet and it per-ceives the absolute angle of the joint directly. In com-bination with the Hall Effect sensor in the motor, ac-curate control of joint position can be achieved by the double-loop control structure. There are 3-DOF force sensors in the tibia; joint torque sensors in the coxa and coxa-femur joints, to provide legs to have the percep-tion of omnidirectional force. Several force/torque sensors have been designed in the past, such as the one-DOF force sensor used in the tendon-driven system of mechanical hand and multi-DOF force/torque sensor based on Stewart platform. Considering the size of leg and the DOFs of the perceptive force, all force sensors of HITCR-II are designed as elastomers into the struc-ture of leg and bonded with strain gages. The Printed Circuit Board (PCB) of sensor information processing module is designed in the femur. It processes the in-formation of all the force sensors as a node of CANopen bus and sends the data to central controller of the leg.

The typical joint is shown in Fig. 3, and all the joints have similar transmission mode. A flat DC brushless motor with large power to volume ratio is used to minimize volume of the joint. The synchronous belt

drive mode is designed to reduce the lateral dimensions of the joint, so that the possibility of interference during movement is reduced and the dexterity is enhanced. A harmonic reducer with a reduction ratio of 100 is em-ployed in the transmission organ. In combination with the speed ratio of large and small synchronous pulleys, the total speed reduction ratio is 230. The actual nominal speed and torque of the joint is 24 rpm and 1.9 Nm re-spectively. The structure parameters of HITCR-II’s joints are shown in Table 1.

Fig. 3 Structure of HITCR-II’s leg.

Table 1 Structure parameters of HITCR-II’s joint

Structure parameters

Length(mm)

Width (mm)

Thickness (mm)

Weight (kg)

Dimension 58.5 42 28 0.118

2.2 Optimization of structure parameters The posture of the hexapod robot is expressed by

six parameters, {X, Y, Z, α, β, γ}, which respectively represent the displacement and angular rotation of trunk coordinates relative to X′, Y′, Z′ axes of the ground co-ordinate system. For the restraint of multi-loop parallel mechanism, the parameters of posture will vary within a certain extent. It is described by the dexterity parameter derived from the equation


f 1 2 3 4 5 6

r 1 2 3

d 4 5 6

16 2 2 2

13

13 2 2 2

,

y yx z x z

yx z

yx z

SS Sk k k k k k

L L L

k k k

SS Sk k k

L L L

θθ θδ

π π π

θθ θδ

π π π

δ

= ⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅

= ⋅ + ⋅ + ⋅

= ⋅ + ⋅ + ⋅

⎧ ⎛ ⎞⎜ ⎟⎪⎝ ⎠⎪

⎪ ⎛ ⎞⎪⎨ ⎜ ⎟

⎝ ⎠⎪⎪ ⎛ ⎞⎪ ⎜ ⎟⎪ ⎝ ⎠⎩

(1)

where, δf, δr, δd stand for dexterity ratio, rotation ratio and displacement ratio respectively, L stands for the length of robot’s leg, θx, θy, θz are the values of maxi-mum difference of angular rotation and Sx, Sy, Sz are the values of maximum difference of displacement along X′, Y′, Z′ axes, as shown in Eq. (2), and ki is weighting co-efficient (0 ≤ ki ≤ 1, ki ∈ R, 0 ≤ i ≤ 6, i ∈ Z). By setting the value of ki the proportion of components in the ob-jective function of dexterity is adjusted.

max min max min max min

max min max min max min

, ,

, ,x y z

x y zS X X S Y Y S Z Z

θ α α θ β β θ γ γ= − = − = −

= − = − = −

⎧⎪⎨⎪⎩

(2)

According to the performance of motion and the structural character of HITCR-II, the range of each joint angle during walking process is set as α, β, γ in Table 2. Using the general-motion command in the software ADAMS, the robot’s trunk is controlled to accomplish translation and rotation along X′, Y′, Z′ axes. During the process of motion, the Point-Measure and Meas-ure/Orientation are set as the measuring points to record

every extreme position. The purpose of optimizing the dexterity ratio is to obtain the robot’s comprehensive capability of motion, constituting the translation and rotation in the space, specified by the six components θx, θy, θz, Sx, Sy, Sz and these affect the δf on average. Hence the weighting coefficient, ki is set as ki = 1. The values of dexterity ratio, rotation ratio and displacement ratio are recorded under specified conditions that include different orientation of axis of the coxa to trunk, different lengths of coxa, femur and tibia in proportion to the length of the leg. The results obtained are shown in Fig. 4.

Table 2 Motion ranges of HITCR-II’s joints

Joint angles Angle of coxa joint

Angle of coxa-femur joint

Angle of femur-tibia joint

Joints rotation ranges −45° ≤α ≤ 45° −90° ≤ β ≤ 60° 0° ≤ γ ≤ 120°

Fig. 4b shows that the value of dexterity ratio de-

creases as the length of coxa joint increases. But the minimum length of coxa is limited for the constraint conditions of motor scale and structure. Fig.4a shows that the value of dexterity ratio first increases and then decreases as the angle between axis of coxa joint and plane of trunk increases. Figs.4b and 4c show that the value of dexterity ratio first increases and then decreases as the ratio of length of femur and tibia to length of leg increases. In addition, when the range of angle between axis of coax and plane of trunk is [20, 50], the range of

Dexterity ratioDisplacement ratioRotation ratio




Direction of axes (°)

Proportion of femur

Proportion of coxa

Proportion of tibia

20 30 40 50 60 70 80

0.3 0.4 0.5 0.6 0.7 0.3 0.4 0.5 0.6 0.7

0.1 0.15 0.2

0.2

0.30

0.250.20

0.15

0.100.05

0.30

0.260.22

0.18

0.140.10

0.260.22

0.18

0.140.10

0.30

0.30

0.250.20

0.15

0.100.05

0.2

(c)

(a) (b)

(d)

10

Fig. 4 Values of dexterity ratio (blue curves), displacement ratio (red curves) and rotation ratio (green ratio) under different structure parameters: (a) axis orientation of the coxa to trunk; (b) length proportion of coxa to leg; (c) length proportion of femur to leg; (d) length proportion of tibia to leg.


ratio of length of femur to length of leg is [0.45, 0.55], and the range of ratio of length of tibia to length of leg is [0.30, 0.45], the dexterity ratio attains larger values, and both the displacement ratio and rotation ratio as well at the same time. On the basis of above results and realistic structure constraints, the structure parameters of the legs of HITCR-II are designed. The details are given in Table 3. The coax angle is 30°, the lengths of femur and tibia are 140 mm and 122 mm respectively. The proportion of length of femur and tibia are 0.45 and 0.39 respectively. All the structure parameters are within the optimal ranges that make the robot have a better dexterity ratio.

Table 3 Structure parameters of each leg Values Total Coxa Tibia Femur

Length (mm) 310 48 140 122

Mass of leg (kg) 0.428

Coax angle (°) 30

3 Analysis of relationship between stability margin and dexterity

In the process of design, the structure parameters are optimized to improve the dexterity at utmost. How-ever, when robot is walking, the support positions of stance legs and the gait pattern have great influence on dexterity as well as the stability margin. It is desired that the robot has a better dexterity while satisfying the ut-most stability margin. The analysis is as follows.

As shown in Fig. 5, robot is assumed to stand on a flat terrain, the vertical projection of COG is taken as the origin of the reference, X, Y, Z are coordinate axis, the locations of each stance foot are shown as the points P1 to P6. The stability margin Rsm is defined as the shortest perpendicular distance from the vertical projection of-COG to each side of SP. The value of stability margin is relevant to the position of COG relative to the support

P6 (231, 216, 0)

P2 (−266, 0, 0)

P6 (231, 216, 0)

P2 (−266, 0, 0) P5 (266, 0, 0)

P3 (−231, −216, 0) P4 (231, −216, 0)P4 (231, −216, 0)

P6 (231, 216, 0)

P5 (266, 0, 0)P2 (−266, 0, 0)

P4 (231, −216, 0)P3 (−231, −216, 0)

P2 (−246, 0, 0)

P3 (−200, −200, 0) P4 (200, −200, 0)

P6 (200, 200, 0)

300250200150100400200 0−200−400−400−200 0

200

400

X/mm

300250200150100400 200 0−200−400−400−2000 200 400

X/mmY/mm Y/mm

300250200150100400200 0−200−400−400−200 0 200 400

X/mmY/mm

300250200150100400200 0−200−400−400−2000 200 400

X/mmY/mm

(a)

(b)

SP SP

SP SP

Rsm Rsm

Rsm Rsm

COG COG

COG COG

X

Y

X

Y

X

Y

X

Y

Fig. 5 Comparision of dexterity of trunk: (a) different number of stance-legs while homologous support points are same; (b) different support points while the number of stance-legs is same.


points of the stance-legs. The dexterity is indicated by the workspace of the trunk. The workspaces of trunk for different number of stance legs and different support positions of stance-legs are calculated using MATLAB. The range of rotation of each joint angle for the simula-tion is shown in Table 2. Taking relationship between each foot-end and terrain as a spherical pair, and the range of rolling angle is [−70°, 70°]. The vertices of each blue polygon stand for the support points of stance-legs, and the number of stance-legs is the same as the vertices. The results are shown in Fig. 5.

Fig. 5a is the comparison of dexterity of trunk with three stance-legs and six stance-legs while the ho-mologous legs have the same support positions. It can be inferred that dexterity decreases with the increase in the number of stance legs, and the stability margin in-creases. Fig. 5b is the comparison of dexterity of trunk with different support positions of homologous legs for the same number of stance legs. It can be deduced that the dexterity increases with the decrease in the support polygon, and the stability margin decreases simultane-ously. Through above analysis, it is realized that the stability margin and dexterity of the hexapod robot are a couple of incompatible factors that fail to reach their optimal values at the same time. Accordingly, when the robot is at rest, more care to the dexterity should be taken to prepare the following movement. When the robot is walking on unstructured terrain, the posture control must be employed for improving the stability margin on-line.

4 Strategy of the PCFDC

4.1 Structure of the control system of HITCR-II The movements of legs are composed of swing

phase and stance phase. The swing legs work just in the free space, accordingly the desired foot-end trajectory can be achieved through simple position control strate-gies. When touching terrains, legs change from swing state into stance phase, which falls into the constraint space. Therefore, the adaptability to the terrain must be improved through force perception. Fig. 6 is the struc-ture of control system of HITCR-II. In the position control loop of a single leg (It is the control loop indi-cated by black arrows), the foot-end tracks the desired trajectory and the joint angles of this leg are calculated by inverse kinematics algorithm. Then the PD controller

is employed to realize the precise position control of each joint with the feedback of truth value of joint angle from the position sensor. As shown in green frame with dashed line, the posture control module consists of foot-force distribution unit, foot-force compensation unit and the posture adjusting unit. The foot-force dis-tribution unit calculates the desired foot-force of all stance-legs for any gait pattern. The foot-force com-pensation unit computes the variation in foot-force due to unstructured terrain to compensate the calculated foot -force distribution. In the control loop indicated by the red arrows, the posture adjusting unit corrects the de-sired foot-end position of each leg by the corrected foot-force and real posture. In this manner, adapting to terrain is achieved by the posture control.

The mathematical models of PCFDC, the foot-force distribution model and foot-force compensa-tion model, will now be developed.

Fig. 6 Structure of control system of HITCR-II.

4.2 Foot-force distribution model of the hexapod robot

Locomotion mode of hexapod robot is crawl, which is in stable state of motion and has a low velocity. Therefore the acceleration can be ignored. The purpose of analyzing mechanical model of hexapod robot is to obtain the relationship of foot-forces between the stance legs when the robot has a larger stability margin and the pos-ture of the hexapod robot is adjusted by tracking the foot-force.

Fig. 7 shows the mechanical model of the hexapod robot. The O-XYZ coordinate system is global. The coor-dinate system [xG, yG, zG] is barycentric. The coordinate system of trunk is [XCG, YCG, ZCG]. The trunk is in the plane of XCGYCG. The contact point between foot and terrain of leg i, is given by Pi = [xi, yi, zi]. The external force and torque on the whole robot are F = [Fx, Fy, Fz] and M = [Mx, My, Mz] respectively. The foot-force of the


leg i is fi = [fix, fiy, fiz]. ZCG

YCGXCG

Leg 4Leg 5

Leg 6

Leg 1Leg 2

Leg 3

f1z

(x1, y1, z1)f1yf1x

CZ

Pitch angle

Y KZ

KPCP

CR KR

Vertical direction

X

Z Roll angle

O

ZG

YGXG

Fig. 7 Mechanical model of hexapod robot.

Considering the balance of the hexapod robot, the

main factors that affect posture are the fluctuation in vertical direction, rotation around pitch direction and roll direction. These factors are directly related to the vertical component of foot-force fiz. Thereby the vertical component Fz of F = [Fx, Fy, Fz], the pitch torque MP of M = [Mx, My, Mz] and the roll torque MR are mainly considered. The model takes the following form

1

1

1

( ) ,

( )

n

iz zi

n

i G iz Ri

n

i G iz Pi

f F mg

x x f M

y y f M

=

=

=

⎧ = +⎪⎪⎪

− =⎨⎪⎪

− =⎪⎩

∑

∑

∑

(3)

where 1 ≤ n ≤ 6. The matrix equation of Eq. (3) is ex-pressed as

iz .× =A F M (4)

Herein,

1 2

1 G 2

1 1 1,G G n G

G n G

y y y y y yx x x x x x

⋅ ⋅ ⋅⎛ ⎞⎜ ⎟= − − ⋅ ⋅ ⋅ −⎜ ⎟− − ⋅ ⋅ ⋅ −⎝ ⎠

A (5)

[ ]T1 2 ,iz z z nzf f f= ⋅ ⋅ ⋅F (6)

[ ]Tz ,R Pmg F= +M M M (7)

where xi, yi are coordinates of tip of leg i in trunk co-ordinate system; xG, yG are coordinates of COG of robot in trunk coordinate system; Fiz is external force at tip of leg i in vertical direction; mg is the total weight

of robot. When the hexapod robot walks with tripod gait, a

unique solution can be obtained from Eq. (4), and it is shown in Eq. (8)

.iz−= ⋅F A M (8)

But when the hexapod robot walks with wave gait which occurs when the number of stance legs is more than three, Eq. (8) cannot be solved as the system is non-deterministic. Therefore additional constraint con-ditions should be set up. While the stance-legs carry weight of the robot on average, the hexapod robot has better stability margin, high load capacity and low en-ergy consumption. On these considerations, the least mean square error of the foot force is set as the objective function

( ) 2( )= ( ) min,n

iz izi

D f n f μ− →∑1/ (9)

where, (1 / ) ( ) /n

iz zi

n f F mg nμ = = +∑ , and n is the number of stance legs. According to Eqs. (4) and (9) the distributed foot-force in tripod gait and the four-legged gait pattern can be obtained directly. When five legs are in the stance state, Eq. (4) is substituted in Eq. (9). Then the objective function is converted to a binary quadratic polynomial,

2 2( ) ( , )= 2 ,izD f f x y ax bxy cy dx ey g= + + + + + (10)

( , ) min , ,izf x y x y f→ ∈ ( ) (11)

where a, b, c, d, e, g are the coefficients of objective function. Similarly, when the hexapod robot has six stance-legs the objective function is converted to ternary quadratic polynomial,

2 2 2( ) ( , , ),

izD f f x y z hx my nz rxy pyzqxz ux vy wz l

= = + + + ++ + + + +

(12)

( , , ) min , , ,izf x y z x y z f→ ∈ ( ) (13)

where h, m, n, r, p, q, u, v, w, and l are the coefficients of objective function. The equation representing the rela-tionship between x, y or x, y, z can be obtained by seeking the minimum value of this polynomial. Based on above analysis, the optimal foot-force distribution can be determined for the hexapod robot under arbitrary gait pattern. 4.3 Model of foot-force compensation


Using the foot-force distribution model developed above, the desired distributed foot-force can be obtained when perturbation is absent. Next, the foot-force com-pensation model will be formulated to restrain the vi-brations caused by the changing terrain to enable the robot to adapt to unstructured terrain. The force and pose sensors equipped in the HITCR-II facilitate this aspect of control.

As shown in Fig. 7, the ground is assumed to be rigid, suspension models with virtual spring and damper are designed in the vertical direction which is the direc-tion of the pitch angle and the direction of roll angle. Here, θP, θR and Δz are defined as variations in the di-rections of pitch angle, roll angle and the vertical direc-tion respectively. The torques and force required to correct the deviation are ΔMP, ΔMR and ΔFz respec-tively. The objective model can be represented as

z z z

,P P P P P P P

R R R R R R R

F mz K z C z

M I K C

M I K C

θ θ θ

θ θ θ

Δ = = − Δ − Δ⎧⎪Δ = = − −⎨⎪Δ = = − −⎩

(13)

where Kz, KP and KR are stiffness of virtual springs, Cz, CP and CR are damping coefficients of virtual damping, m is the mass of robot, IP and IR are moments of inertia about the Y axis and X axis respectively, z , Pθ , Rθ are the external disturbance variables in vertical direction, the directions of pitch angle and roll angle respectively.

The variation of posture can be detected by the posture sensor installed in trunk. The force/torque re-quired for correcting the deviation can be obtained from Eq. (13), and they are substituted in Eq. (3), so the fol-lowing equation is obtained

' ,iz−Δ = ⋅F A M (14)

where,

[ ]T'z P R .mg F M M= + Δ Δ ΔM (15)

A compensating value is used to correct the initial dis-tributed force, and on-line control of posture is achieved by tracking the corrected distributed foot-force.

5 Results and analysis

5.1 Simulation results

In pro/E the 3D model of HITCR-II is directly in-putted into ADAMS by MECH/Pro, and the

co-simulation system of ADAMS and MATLAB is built up by ADAMS_Sub.

A flat terrain with obstacles is built to simulate un-structured terrain. The robot is made to walk with tri-pod-gait and the simulation is done to observe and ana-lyze the motion state only under the position control and with PCFDC. As shown in Fig. 8, when leg R1 touches the obstacle, elevation angle Δθ of trunk from pitch and roll angle is obvious in case of only under the position control (shown as red dotted straight line). By contrast, there is no visible elevation angle of trunk under PCFDC. In addition, in case of only under position control, it is usual for the robot to miss its steps as some of stance-legs shoot off the terrain unexpectedly, and a drop in height Δh of the step-missed leg occurs (indicated as leg L1 by red dotted circle line). This results in a sharp reduction of the stability margin. According to Zero Moment Point (ZMP) theory[27], from the relative posi-tion of COG and SP shown in Fig. 8, the accident of instability is likely to happen only under position control. In contrast, in case with PCFDC strategy the accident of instability is clearly prevented.

Fig. 8 Comparison of stability margin intuitively.

The walking period cycle is set at 5 s for HITCR-II

to walk over the unstructured terrain. As shown in Fig. 9, the blue curves and the red curves represent walkings with and without PCFDC respectively. The curves rep-resent the variation of pitch angle, roll angle and sta-bility margin during the process of walking. In the first walking cycle from 0 s to 5 s, leg R1, R3 and L2 are in swing state and the legs R2, L1 and L3 are in stance state. At the instant of 1.3 s as the leg R1 touches an obstacle, both pitch angle and roll angle change sharply. The peak values of pitch angle and roll angle reach 2.6° and 2.8° respectively only under the position control. Moreover,


the values of these angles stay large all along. But when combined with PCFDC, the peak values of pitch angle and roll angle decreased to 1.2° and 1.3° or they are reduced by 54% and 53% respectively. Furthermore the angles are readjusted to zero quickly and the fluctuation remains small. In the following three walking cycles (C2: 5 s –10 s, C3: 10 s –15 s, C4: 15 s –20 s, C1LC4: Cycle 1 to Cycle 4), the legs R2 and R3 touch the obstacle orderly until entire HITCR-II steps across obstacle finally. As hexapod robot is characterized by high stability margin for its redundancy of legs, it can also step over the ob-stacle only under position control. But the walking is not stable, and especially the trunk of robot vibrates heavily. The PCFDC can effectively inhibit the varia-tion of pitch angle and roll angle caused by the un-structured terrain and make the robot to step across the obstacle more stable. Next the stability margin is ana-lyzed directly.

As shown in Fig. 9, in walking cycle C2, the distur-bances from terrain are the most complex and the stability margin in this period is typical. So the stability margin is analyzed in C2. From the last segment of Fig. 9, it can be seen that the stability margin undergoes a marked change only under the position control and that its minimumvalue even drops to 106 mm. When combining with PCFDC the stability margin keeps above 138 mm throughout the walking process. It is enhanced by 39% at the point of maximum value of difference and is without sharp wave. So it is seenthat the PCFDC can effectively improve the stability margin of hexapod walking, which makes the hexapod robot adapt largely to the unstructured terrain. 5.2 Experiment results

In order to evaluate the effectiveness of the pre-sented algorithm, experiments are conducted with robot HITCR-II on artificial and irregular terrain. The robot is made to walk with free gait based on local rules between the legs[28]. The Xsens-MTi-28A53G35 is installed at the geometric center of robot’s trunk to measure the posture in real time. It is a complete miniature inertial meas-urement unit, with an embedded processor capable of calculating the roll and pitch data. The foot force is measured by the 3-DOF force sensor. As shown in Fig. 10, the obstacles of height 50 mm are set irregularly. The HITCR-II can walk over the terrain either with or without the PCFDC, but the stability of posture in the process of walking is quite different. Following are the

results from experiments.

Pitc

h an

gle

(deg

)

−1.5

0.0

1.5

3.0

0.0 5.0 10.0 15.0 20.0−3.0

Pitch angle

Roll angle

5.0 10.0 15.0 20.0

Stability margin from 5.0 s to 10.0 s

Time (s)R

oll a

ngle

(deg

)

0.0

1.0

2.0

3.0

−1.00.0

6.25 7.5 8.75 10.0Time (s)

Rol

l ang

le (d

eg)

5.0

Without PCFDCWith PCFDC



100.0

120.0

140.0

160.0

Fig. 9 Comparison of stability margin.

Fig. 10 Experiment of HITCR-II walking on artificial irregular terrain.

Fig. 11 shows the foot force of leg L1 during the

experiment. In the process of walking, the actual motion state of the robot is different from that of pre-designed due to the disturbance from obstacles. In the first ex-periment without PCFDC, some large fluctuations of the


foot force are found and the reason is the change in robot postures. In contrast, in the second experiment which integrated the proposed PCFDC, the foot force changes regularly with the variation of leg motion, and it is al-ways around the desired value of 6.8 N. As demonstrated by the experimental results, the proposed PCFDC con-troller effectively controls the robot’s posture by ad-justing the foot forces, which is of critical importance to the walking stability on rough terrain.

Ver

tical

com

pone

nt o

f foo

t-for

ce (N

)V

ertic

al c

ompo

nent

of f

oot-f

orce

(N)

Fig. 11 Comparison of foot-force of leg L1, (a) without PCFDC controller; (b) with PCFDC controller.

Fig 12 and Fig. 13 show the recorded data of pitch

angle and roll angle in the process of walking over arti-ficial irregular terrain. The blue curves and red curves represent the angles of trunk controlled with and without PCFDC respectively. The results show that the proposed method of PCFDC is able to effectively reduce the variation of pitch and roll angles, thereby restrain the vibration of trunk and adjust the robot posture to a more balanced state. The experiment also verifies the walking capability of HITCR-II in practice.


2552 3552 4552 5552 6552 7552 8552 9552 10482Counter

10

5

0

−15

−10

−5

Rol

l ang

le (d

eg)

Fig. 12 Comparison of pitch angle of trunk.


2552 3552 4552 5552 6552 7552 8552 9552 10482Counter

8

6

4

2

0

−8

−6

−4

−2

Fig. 13 Comparison of roll angle of trunk.

6 Conclusion

In this work, a hexapod robot HITCR-II with novel structures and highly integrated sensor systems is de-veloped. A complete sensor system is designed to make the robot have the perception of environment and its own state. In addition, the foot-force distribution model and the foot-force compensation model are developed to realize PCFDC, which effectively restrains the vibration of trunk and improves the stability margin of hexapod walking on unstructured terrain. The simulation results show that with the proposed method the pitch angle and roll angle of trunk are reduced by 54% and 53% respec-tively, and that the stability margin is enhanced by 39%. The experimental results confirm the walking capability of HITCR-II on unstructured terrain, and demonstrate that the PCFDC controller can effectively improve the stability of walking by adjusting the foot force. All the results are promising for future implementation.

Future research will be focused on developing


methods to improve implementation of PCFDC strategy over highly unstructured terrain and to use binocular stereo vision system for selecting safe footholds. These improvements should further enhance the HITCR-II’s performance in crossing over impassable obstacles.

Acknowledgment

This work is supported by the National Natural Science Foundation (Grant No. 51105101), and the Self-Planned Task of State Key Laboratory of Robotics and System (Grant Nos. SKLRS200901A01 and SKLRS200901A03.

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Development of a Bionic Hexapod Robot for Walking on Unstructured Terrain

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