Throughput Optimisation in Ad-hoc Networksof Communication-Aware Mobile Robots

Trung Dung Ngo

Universiti Brunei DarussalamFaculty of Science

The More Than One Robotics Laboratorywww.morelab.org

Abstract. We study throughput optimisation of ad-hoc networks ofcommunication-aware mobile robots. The mobile robots equipped withsensing and communication capacities can maintain connectivities andestimate the quality of communication links with their neighbouringpeers. The mobile robots self-organise a wireless ad-hoc network fortransmitting environment exploited data from sources to destinations.Graph-based network model and artificial potential force-based connec-tivity maintenance are integrated in different ways for the control designof mobile robots. We consider throughput optimisation in twofold: (1)routing-aware optimisation and (2) routing-unaware optimisation. TheMonte-Carlo simulation results are comparatively analysed and discussedaccording to the performance metrics.

Keywords: Ad-hoc Networks, Throughput Optimisation, Communication-AwareOptimisation, Route-Aware Optimisation, Mobile Robots, Sensor Networks

1 Introduction

Wireless ad-hoc networks of mobile robots have recently received significantattentions due to their potential applications. This new research field is consid-ered as the intersection of the two fields, wireless sensor networks and multi-robot systems, with an emphasis on diversity of integrating mobility, inter-communication, and routing protocols of robotic sensor nodes in order to improveperformances of wireless ad-hoc networks.

A networked system of mobile robots can be sent into hazardous environ-ments with various tasks such as exploration and rescue, poison detection, vic-tim identification. This kind of ad-hoc networks has a number of advantagesover traditional wireless sensor networks due to controllable mobility of mobilerobots. For examples, a small number of mobile robots can cooperatively navi-gate to explore and cover the large areas, detect and collect environmental databy carrying different types of sensors, and transmit exploited data through thead-hoc network of mobile robotic routers. However, we encounter more chal-lenges of deploying and managing such wireless networks of mobile robots than

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standard wireless sensor networks due to dynamics of mobile robots, e.g., mo-bility of sensor nodes might cause multi-path fading or shadowing affecting thequality of communication links or even the interruption of network routes.

Routing is the conventional problem of selecting the best or feasible commu-nication channels of wireless ad-hoc networks w.r.t link states, network topology,node localisation, quality of services as seen [1], [2], [3], [4]. Using controllablemobility of mobile sensor nodes to improve the communication capacity has beenrecently considered as in [5], [6], [24], [25]. However, combining controllable mo-bility and route awareness on robotic sensor nodes to optimise communicationcapacity/throughput of the wireless ad-hoc network has not been intensivelystudied, to the best of our knowledge.

In this paper we assume that the mobile robots are equipped with sensing andcommunication capacities for mutual interaction and communication with theirneighbouring robots. The control for mobile robots is developed by integratingboth controllable mobility and route awareness for optimising throughput of thead-hoc network. We synthesize the artificial potential force maintaining connec-tivities of the mobile robots and the graph-theoretic network model used formeasuring the quality of communication links for the design of robot control.

The artificial potential field coined out by [7] is the well-known method de-veloping artificial potential force-based control for robot navigation. Artificialpotential force-based robot control composes the attractive force that controlsthe mobile robots to move towards a goal and the repulsive force that keepsthe mobile robots away from obstacles. Synthesis of the attractive and repulsiveforces drives the mobile robots towards the goal without colliding with obstacles.The artificial potential field has been extended for developing decentralised con-trol of multi-robot system in which the artificial potential forces representing thelocal sensing and perception of the mobile robots about their peers and environ-ments. Artificial potential forces used for multi-robot systems are divided intothe three categories: linear function [8], [9], quadratic form [10], [11], [12], andexponential expression [13], [14]. We employ the Artificial Physics-based poten-tial forces as proposed in [10] due to its simplicity of connectivity maintenanceof the mobile robots.

Graph theory is widely used as a powerful tool to model networked systems.A networked system is a group of agents interacting and exchanging informationthrough the network. Coordinative and cooperative operations of networked sys-tems can be controlled and optimised in graph theory. Stable flocking of mobileagents in both fixed [15], dynamic or switching topology [16] are proven by al-gebraic graph theory. Formation control of multi-agent systems in [17], [18] isexpressed in terms of the graph Laplacian. Distributed coordination control ofmulti-agent systems in [19] used the graph Laplacian for finding a non-linearfeedback control ensuring the connectedness of mobile agents. In [20], the con-sensus problem of networked agents with capabilities of switching topology andtime delays is modelled by weighted graph.

In the real-world, wireless ad-hoc networks of mobile robots are deployed intwo primary stages: network deployment/installation, and network utilisation.

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In the first stage, the mobile robots sent into the environment automaticallyestablish communication links among them for a wireless ad-hoc network. In thesecond stage, once the ad-hoc network of the mobile robots is established, datastreams are transmitted from sources to destinations. One typical function ofthe network utilisation is how to maximise communication throughput for fasterand more reliable data transmission.

In the scope of this paper, we assume that the first stage of the network de-ployment has been done since the mobile robots have been deployed in the envi-ronment. We consider the second stage of the network utilisation with an empha-sis on throughput optimisation of the wireless ad-hoc network of communication-aware mobile robots in two approaches: (1) route-aware optimisation, and (2)route-unaware optimisation.

The rest of this paper is organised as follows. Optimisation problem is for-mulated by graph theory in section 2. Two methods of throughput optimisationare described in section 3. Monte-Carlo simulation is applied for experimentsand statical results are shown and discussed in section 4. We conclude the paperwith future research directions.

2 Problem Formulation

We consider the kind of wireless ad-hoc networks of mobile robots that commu-nicate in peer-to-peer fashion. The networked robotic system is deployed intounknown environments for exploration, monitoring, patrolling, and data collec-tion. The mobile robots automatically navigate to explore in the environmentwhile maintaining connectivities with their neighbouring peers. They are capa-ble of self-organising a multi-hop wireless network for information exchange. Arobot becomes a source if it transfers environment exploited data through thenetwork of multiple mobile robots - working as mobile routers - to a destina-tion in the network. Data packets are delivered through either single or multiplecommunication channels of the ad-hoc network before reaching the destination.Communication throughput of such channels must be maximised for fast andreliable data transfer.

We employ the graph theory to describe the problem of throughput opti-misation for wireless ad-hoc networks of communication-aware mobile robotsbelow.

2.1 Graph-based Network Model

A graph G(V,E) is employed to describe a multi-hop wireless ad-hoc networkof mobile robotic routers. V is defined as collection of mobile routers while Eis denoted for the set of peer-to-peer communication links between the mobilerobots. V is divided in three groups: sources S - sending the data packets, sinksT - receiving data packets, and routers R - relaying data packets from sourcesto sinks, where S and T must be non-empty.

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In the graph, each edge e(vi, vj) ∈ E represents a communication link witha nonnegative capacity c(vi, vj) ≥ 0. Actual data flow f(vi, vj) between twomobile routers vi and vj must be less than capacity of the communication link,f(vi, vj) ≤ c(vi, vj) for every v ∈ V \{s, t}. On a mobile router r ∈ R, inflowdata must be equal to outflow data, fi(r) = fo(r), where inflow fi(r) is the sumof incoming data into the router while outflow fo(r) is the total data coming outfrom the router.

Data can be transferred from a source s to a sink t through either singleor multiple communication channels. We consider the value of a flow f from asource s, denoted val(f), is the amount of data sending out of a source s to asink t: val(f) =

∑v∈V f(s, t). Hereafter, we define a maximum flow, denoted

fmax, is the network flow satisfying: val(fmax) ≥ val(f),∀f .Considering an wireless ad-hoc network G(V,E) with a group of sources Vs

and a group of sinks Vt, a cut is a group of edges connecting Vs and Vt through anumber of routers Vr ∈ V . Capacity of a cut is the total capacity of communica-tion links on the cut, c(Vs, Vt). Hereafter, we define a minimum cut, cmin(Vs, Vt),of the network as the cut - the set of communication links involved in the cut,with the minimum total capacity.

We have to search for bottlenecks - so-called minimum cut according to theMax-Flow Min-Cut graph theorem [23] - of the network if we wish to improveits communication throughput. Controllable mobility is employed to relocatethe communication aware mobile robots to appropriate positions in the networktopology where they contribute better to the overall communication capacity ofthe network. In short, throughput optimisation is a sequent procedure of search-ing for the mobile robotic routers contributing the bottlenecks of the network,and then controlling such routers to relocate to the appropriate positions toenable improvement of the communication links.

3 Throughput Optimisation

We aims to optimise communication throughput of the wireless ad-hoc networkof mobile robots by two methods: (1) routing-aware optimisation and (2) routing-unaware optimisation. In the network, we state that the mobile robots are onlycapable of communicating with their neighbouring robots within the commu-nication range. Without loss of generality, we assume that the communicationrange is typically longer than the sensing range for every mobile robots, thus themobile robots successfully establish communication links among them if they aremutually within their sensing range.

Capacity of a communication link established by two mobile robots is in-versely proportional to their relative distance according to the general principleof path-loss without considering effectiveness of multi-path fading or shadowingas explained in [21], [22]. Therefore, capacity of the communication link increasesif the mobile robots move closer to each other.

In general, relative localisation of the mobile robots can be identified throughestimation of relative distance and relative bearing extracted by their sensing ca-

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pacity. The Artificial Physics-based potential force [10] is the well-known methodthat preserves connectivities of mobile robots using their relative distance andrelative bearing.

Capacity of communication links can be estimated without the relative lo-calisation. The mobile robots are not aware of communication links using onlytheir sensing capacity while they are not able to estimate the relative local-isation using only measurement of communication links due to unidirectionalsignal propagation. As a result, we have to combine the sensing-based relativelocalisation and measurement of communication links to design a control of themobile robots that governs their mobility for improvement of communicationlink capacity.

We propose that the mobile robots are capable of preserving connectivi-ties with their neighbouring robots using the Artificial Physics-based potentialforces. The mobile robots are also capable of measuring the capacity and infor-mation flow of communication links made with their neighbouring robots. Wepresent different ways of combining relative localisation managed by the ArtificialPhysics-based potential forces and maximisation of capacity of communicationlinks governed by the graph theory-based network representation.

3.1 Routing-Aware Optimisation (RAO)

In the Max-Flow-Min-Cut graph theorem [23], the value of a maximum flow isequal to the capacity of a minimum cut, so-called min-cutfmax(Vs, Vt) = cmin(Vs, Vt) in a network. That is, to find maximum flow ina multi-hop wireless ad-hoc network of mobile routers, we can find min-cut thatis also recognised as bottlenecks of the communication network.

In the routing-aware optimisation, the Edmonds-Karp algorithm - an ex-tended version of Max-Flow Min-Cut theorem - is employed to search for thecommunication route between sources and sinks, and then identifying min− cutwhere the mobile robots are controlled to optimise communication throughputof the network. To use the breath-first search in the Edmonds-Karps algorithmto find optimal routes between sources and sinks, we assume that all the mo-bile robots exchange capacity of communication links through the entire networksuch that capacities of communication links are used to search for the best routeswith the highest capacities between sources and sinks.

We develop the routing-aware optimisation that searches for min-cuts be-tween sources and sinks, and then control the mobile robots to find the ap-propriate positions in the network topology where capacities of communicationlinks are improved. The control of the mobile robots synthesizes the ArtificialPhysics-based potential force and capacity of communication links as seen in (1):

−−→Frao(vi) = nAP ∗

−−→FAP (vi, vj) + nMC ∗

−−→FAP (vi, vj)

‖ −−→FAP (vi, vj) ‖∗ FMC(vi, vj) (1)

where,

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−−→FAP (vi, vj) =

∑vj∈MC(vi)

G∗m(vi)∗m(vj)r2 is the Artificial-Physics-based po-

tential force synthesised by the sum of the artificial potential forces between therobot vi and its neighbouring robots involved in the min-cuts, vj ∈ MC(vi), inwhich r is the relative distance between vi and vj and the gravitational constantG is arbitrarily chosen.

FMC(vi) =∑

vj∈MC(vi)1

c(vi,vj)is min-cut strength synthesised by the sum

of capacity of communication links involved in min-cut, MC(vi), of the mobilerobot vi. Because this min-cut strength is unidirectional, it is converted to the

min-cut force by the normalised Artificial Physics force,−−→FAP (vi,vj)

‖−−→FAP (vi,vj)‖

.

Two numerical factors, nMC and nAP are used to normalise the trade-offs ofthe min-cut force and the Artificial Physics-based potential force.

3.2 Routing-Unaware Optimisation (RUO)

Shortcomings of the route-aware optimisation using the Max-Flow Min-Cutgraph theorem to search for the routes between sources and destinations include:

– The breath-first search algorithm requires the full table of communicationlink capacities to search for the optimal routes. This condition is not alwaysachievable in scalable networks where number of deployed mobile robots areunpredictable due to conditions of unknown environments.

– The multi-commondity flow with virtual super-sinks [23] is requested to mea-sure the network flows when there exist more than one source or one sink inthe network.

Without using the Edmonds-Karp algorithm, we can not exactly find min-cuts - bottlenecks of the network - in order to design the control of the mo-bile robots for improvement of communication throughput. On the other hand,the mobile robots with only the sensing-based potential forces can not directlyimprove the communication link capacities since they are not aware of commu-nication links, although the communication link capacities might be implicitlyimproved because the artificial potential forces tend to drive the mobile robotsto the equilibrium point among their neighbouring robots. The mobile robotscan only measure capacities and information flows of the communication linksestablished with their neighbouring robots, which are used to estimate possiblemin-cut corresponding to saturated communication links, c(vi, vj) = f(vi, vj).Communication link capacities and information flows are synthesised to developthe control of the mobile robots as seen in (2):

Fruo(vi) =

∑

vj∈N(vi)

f(vi, vj)

ε + (c(vi, vj)− f(vi, vj))∗−−→FAP (vi, vj)

‖ −−→FAP (vi, vj) ‖if f(vi, vj) 6= 0∑

vj∈N(vi)

−−→FAP (vi, vj) if f(vi, vj) = 0

(2)

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where∑vj∈N(vi)

c(vi, vj) is the sum of capacities of communication links made by

the robot vi with its neighbouring robots, vj ∈ N(vi), and∑

vj∈N(vi)f(vi, vj) is

the sum of information flows of such communication links.−−→FAP (vi, vj) =

∑vj∈MC(vi)

G∗m(vi)∗m(vj)r2 is the Artificial-Physics-based po-

tential force synthesised by the sum of the artificial potential forces betweenthe robot vi and its neighbouring robots, vj ∈ N(vi), in which r is the relativedistance between vi and vj and the gravitational constant G is arbitrarily chosen.

ε is arbitrarily chosen as small as possible, ε �∑

vj∈N(vi)c(vi, vj) to avoid

min− cut saturated where∑

vj∈N(vi)c(vi, vj) =

∑vj∈N(vi)

f(vi, vj)

The mobile robots with the control described in (2) operate in two modes:

– If no information flow is detected by the mobile robots, they only use theArtificial Physics-based potential forces to maintain connectivities with theirneighbouring robots, which might indirectly affect to the communication linkcapacities.

– If information flows are detected by the mobile robots, they drive towardstheir neighbouring robots obtaining the most saturated communication links,that is the highly potential candidate of min-cut.

4 Simulations and Results

4.1 Simulation Setups and Performance Metrics

The Monte-Carlo simulation is applied to generate experimental scenarios. Atypical scenario with three stationary base stations operated as sources and sinksare created as in Fig 1(a). We have applied the Gaussian random distribution toplace the mobile robots into the experimental scenario as seen in Fig 1(b). Thegenerated scenarios are selected for experiments if three base stations are wellconnected through an ad-hoc network of mobile robots and all mobile robotscontribute to the network. For each experiment, we executed 10000 simulationsteps to measure communication throughput. Statistical results of communica-tion throughput are averaged from 100 simulations.

We propose three key performance metrics to evaluate characteristics andproperties of the two throughput optimisation algorithms:

– Optimality: how much is communication throughout of the ad-hoc networkimproved over time?

– Adaptability: does communication throughput of the ad-hoc network adapt-ably improve if more mobile robots are added into the ad-hoc network?

– Convergence: how fast does communication throughput of the ad-hoc net-work converge to a steady state?

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(a) Three stationary base stations (b) 15 randomly placed mobile robots

Fig. 1. The experimental scenario with three stationary base stations: (LHS) Station-ary base stations, (RHS) Randomly placed mobile robots

4.2 Simulation Results and Discussions

Communication throughput of the ad-hoc network of communication aware mo-bile robots is improved over time in both the routing-aware optimisation andthe routing-unaware optimisation. However, the RAO provided significant im-provement of communication throughput, approximately 200%, while the RUOenables communication throughput increase in the range of 15%-50%. As a re-sult, both the RAO and the RUO are capable of optimising communicationthroughput of the ad-hoc network of communication-aware mobile robots.

The RAO algorithm is extremely consistent in optimising communicationthroughput by retaining 200% improvement when more robots are added intothe scenario. Communication throughput of the RUO algorithm dramaticallyincreases from 15% for 10 robots, 30% for 15 robots, to 50% for 20 robots roughly.Both the RAO and RUO can adaptively improve communication throughput ofthe ad-hoc network when more mobile robots contribute the communicationnetwork although the RAO performs significantly better than the RUO does.The RAO method provides a consistent solution for utilisation of the ad-hocnetwork of communication-aware mobile robots but this algorithm is more timeconsuming for the network setting due to searching the optimal route using thebreath-first search algorithm. The RAO algorithm is, therefore, more suitable forless dynamic environments allowing the mobile robots to search for the optimalroutes in the self-organised network before performing throughput optimisationof such routes for data transmission. In contrast, the RUO issues a promisingsolution for utilisation of the ad-hoc network of communication-aware mobilerobots in more dynamic environments where communication routes might notlast for long due to dynamical mobility of the mobile robots and unpredictablechanges of the environments.

Looking into the statistical results of communication throughput in Fig 2,only communication throughput of the RUO algorithm converges to a steady

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(a) RAO - 10 mobile robots (b) RUO - 10 mobile robots

(c) RAO - 15 mobile robots (d) RUO - 15 mobile robots

(e) RAO - 20 mobile robots (f) RUO - 20 mobile robots

Fig. 2. The Monte-Carlo simulations results with the route-aware optimisation (RAO)and the route-unaware optimisation (RUO)

state, i.e., after 5000 running steps approximately, while communication through-put of the RAO still tends to increase over time. The RAO forces the mobilerobots to keep updating of successfully searched routes of which they are re-

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served to contribute to improvement of communication throughput. Meanwhile,the mobile robots still have to reserve a part of their communication capacitiesfor updating the routes, and consume energy for their mobility for through-put optimization. In contrast, although the RUO does not improve quality ofcommunication as much as the RAO does, but the RUO makes communicationthroughput converge to a steady state quickly, which guarantees that the mobilerobots are not longer consuming energy for their mobility for throughput opti-misation, and the communication channels are fully reserved for transmission ofenvironment exploited data.

5 Conclusions

We have shown the two methods of throughput optimisation for ad-hoc networksof communication-aware mobile robots. The graph-based network model and theArtificial Physics-based potential forces are integrated in different ways for de-signing the control of the mobile robots. The Monte-Carlo simulation method isapplied for experiments and statistical results are used to evaluate the perfor-mances of both the route-aware optimisation and the route-unaware performedaccording to the three performance metrics. We have discussed characteristicsand properties of the developed optimisation algorithms to point out their us-abilities.

In the future, we are going to work towards more accurate models of commu-nication links including multi-path fading and shadowing as stated in [21] [22]before we recall the two optimisation methods for throughput maximisation ofad-hoc networks of communication-aware mobile robots.

Acknowledgement: This research was supported in part by the UniversityResearch Grant at the University of Brunei Darrusalam (UBD/PNC2/2/RG/1(259)).

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