Coordination and control of multi agent systems

|T i,j | the number of basis tasks in T i,j;T p the ordered set of high priority tasks; T atv the ordered set of active, but not high priority tasks; T ach the ordered set of archived ta

MULTI-AGENT SYSTEMS

CHENG-HENG FUA

B Eng (Hons.), National University of Singapore

A THESIS SUBMITTEDFOR THE DEGREE OF DOCTOR OF PHILOSOPHYNUS GRADUATE SCHOOL FOR INTEGRATIVE SCIENCES & ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2008

One phase of my life ends and another begins I look upon the road before me withhope and with excitement, and as I face the future that is ahead, I look back upon theway I have come, and am comforted by the fact that I am not alone; that I am blessedwith the great fortune of having the companionship of several distinct individuals LikeFrodo Baggins and the fellowship of the Ring, or Dorothy and her companions in theland of Oz, my own adventures would not have been possible without their support,encouragement, guidance and wisdom, and I would like to take this opportunity toexpress my gratitude to all of them.

To my thesis supervisor, Professor Shuzhi Sam Ge, for his inspiring presence, forhis constant, patient guidance, and for his selfless sharing of experiences in all thingsresearch and more Thanks also go to Professor Khiang Wee Lim, my thesis co-supervisor, for his guidance and help on all matters concerning my research despite hisbusy schedule I would also like to thank Dr Javier-Ibanez Guzman, for his insightfuladvice and guidance on shaping my research direction and goals

To my friends I have been extremely fortunate to have worked with many, manybrilliant people during my study, and who have always been willing and generous withtheir time and friendship Special thanks to Mr Keng Peng Tee and Mr Pey Yuen Tao,

my fellow intrepid adventurers, for the endless hours of discussions and brainstormingthat are always filled with creativity, inspiration and crazy ideas, for their moral sup-port and for always being there to help To Dr Xuecheng Lai, Dr Zhuping Wang and

Dr Feng Guan, for their friendship, help and guidance since the day I first joined theresearch team Thanks also go to Professor Khac Duc Do for his patience, guidanceand wonderful advice in my research on formation control I would also like to thank

To the pillars of my life – my family – I would never be where I am today withouttheir unquestioning trust, support and encouragement They have always been there for

me, stood by me through the good times and the bad, and have always given me theirfull support in whatever choices I made To my inner circle of friends – Mr KonghuiKay, Mr Khiam Boon Png, Mr Keng Chuan Ong and Mr Thian Khoon Ng – who haveshown me what true friendship is, for their unwavering friendship and moral support,and for always being there in times of need

Finally, I am immensely grateful to the Agency of Science, Technology and search (A*STAR), as well as the NUS Graduate School of Integrative Sciences andEngineering (NGS), for their funding and support, without which, this great adventuremight never have taken place

Re-This thesis considers in detail the technical issues associated with the effective trol and coordination of Multi-Agent Systems (MAS), with particular emphasis on tech-niques that increase the robustness of the team of physical agents, when subjected touncertainties, such as malfunctions and imperfect communications For physical agentteams which are to be deployed within uncertain and dynamic environments, it is im-portant for the team to continue functioning even in the event of unforeseen disruptionssuch as single-agent breakdowns and spurious communication losses, and continue be-ing driven toward its collective goals Such abilities are crucial for the success of au-tonomous teams, and would constitute the main motivation for the work presented inthis thesis.

con-The thesis is organized according to the two main decision making levels wherecoordination between members within an agent team can occur, namely on the Macro-and Micro-levels of decision making, following the general flow of decisions, frommission specification, assignment, to actual task accomplishment Agent cooperation

on the macro-level concerns a more general management protocol that, in combinationwith a planning and representation framework, manages the resources (i.e robots) andtries to arrive at a suitable distribution of tasks to either individual robots or sub-teams ofrobots This level of decision making focuses on mission and task representations, andteam organization algorithms Actual task accomplishment by robot sub-teams requirefurther, more explicit, cooperation between individual members, and this falls into therealm of micro-level coordination Such forms of coordination is investigated in thecontext of representing and cooperative accomplishment of multi-agent formations.Under this framework, and with the above objectives in mind, the technical con-

agent systems operating within dynamic, uncertain operating domains The proposedsolutions include:

(i) A general mission/ task representation framework based on the concept of basistasks, that is amenable to analysis, for the efficient portrayal, subdivision, andallocation of tasks to agent teams on-the-fly

(ii) A robust, cooperative task allocation scheme, the Cooperative Back-Off Scheme(COBOS), for instantaneous task (re)distribution between spatially distant tasklocations which are subjected to limited communications

(iii) A representation framework for task allocation schedules over an extended timeperiod, based on the transformation of task schedules into an agent-formationspace, where stable, self-organizing, convergence algorithms are introduced toform a dynamic time-extended allocation

(iv) An efficient formation representation scheme, the Q-structure, to facilitate able and flexible agent formations The Q-structure allows the representation of

scal-a wide vscal-ariety of formscal-ations, scal-and coupled with scal-a behscal-avior bscal-ased scal-algorithms foreach agent, enables decentralized, robust formation tracking with automatic scal-ing

(v) A decentralized and reactive potential field based method is used for stably ing agents into formation based only on local communications, and further subdi-viding the decision making process into the fast and slow time scales Theoreticalanalysis have also been carried out to verify the convergence properties of the nav-igation controls To further improve performance in scenarios involving limitedcommunications, methods for dynamically adapting the short term Q-structurerepresentation are also used

guid-R the field of real numbers;

Rn ×m the set of n × m-dimensional real matrices;

ˆx the unit vector of a vector x;

x (f ) a vector x expressed in the frame f Taken to be in

the world frame if unspecified;

g (f ) (·) a function g(·), expressed in the frame f;

"x" the Euclidean norm of a vector x;

T(f2 )

(f1 ) the transformation matrix from frame f1to f2;

R jk the jk-th element of a matrixR;

|X| the cardinality of a set X;

x k the k-th element of a vector X ∈ R n;

|X| the number of elements in a set X;

n j the number of robots r jhas communication links with;

TSM(j) the Task Utility Matrix compiled by r j;

TSMij (j) the (i, j)-th element of TSM(j);

TSM− (j) a sub-matrix made up of selected rows and columns

ofTSM(j);

B, B the set, or vector form, of Basis Tasks;

b i (! i) (b i ∈ B) the i-th basis task with the list of arguments

it accepts, ! i;

n b the number of basis tasks in B;

L the arguments accepted by basis tasks inB;

L i the physical location associated with T i;

φ i the number of robots required by T i;

T i,k the k-th sub-macro task of T i;

Ti the Task Specification Matrix of T i;

|T i,j | the number of basis tasks in T i,j;

T p the ordered set of high priority tasks;

T atv the ordered set of active, but not high priority tasks;

T ach the ordered set of archived tasks;

T ls the ordered set of all the tasks given to the robots;

n ls the number of tasks given to the robots;

n atv the number of tasks in a subnetwork that can be considered,

given the number of robots in that subnetwork, and the total

number of robots required for each of these tasks;

Aj the vector containing the utility level r jhas with each of

the n b basis tasks;

T rj the task r jis currently performing;

n sn the number of disjoint networks in W ;

Sj (Zn b ×1 ) the Task Success Matrix of r j

t dd,j the time at which task T j must be completed, the task due date;

t sd,j the earliest start time for task T j;

t d,j the approximate task duration for task T j;

A j the set of agents representing the virtual-agent equivalent of task T j;

a jk the agent associated with task T j on robot r k;

n jr the number of robots that can service a task T j;

RS i the Roam-Space on a robot r i;

I jk the area of influence of an agent a jk;

U C i the set of uncovered points in RS i;

F, F N the desired formation consisting of N robots;

Q the set of all the queues in a formation F;

G the set of all the formation vertices;

V j a list of (either one or two) formation vertices

that influences Q j;

S j the set of points describing the shape of Q j;

C j the capacity ∈ [0, 1] of Q j;

E j the encapsulating region of Q j;

O j the set of functions that describe the orientation of agents along Q j

χ i (t) is the queue status of r i at t;

E j excess length (the number of excess robots in Q j);

q i , q tg,i , q t position of robot r i, its target, and team’s target respectively;

v i , v tg,i , v t velocity of robot r i, its target, and team’s target respectively;

κ i , κ tg,i , κ t (topside-vector) vector normal to the plane of robot r i, its target, and team’s target

respectively;

w.r.t r i in frame f;

! j,i,nr the shortest distance between r i and a queue Q j;

N tot the number of robots currently in the team;

N v , N q the number of formation vertices and queues respectively;

ρ sf the safety distance between r iand an obstacle;

ρ adp the distance a deformed queue is from an obstacle;

ρ0 the influence range of an obstacle;

R max the maximum range of r i’s range sensor;

R act (≤ R max), the active range of the Instant Goal behavior;

nR,t the unit vector of the ray from the range readings that is

closest to ˆq (ri),i,t;

(φ, θ) a pair representing the direction of an arbitrary point in the

frame of r i

U b ,Fb the potential function and force derived for a behavior b;

F b the magnitude of the forceFb;

a b the weighting parameter for a behavior b;

δ, δ a the average distance of robots from their queues and

deformed queues (if applicable) respectively;

c ig,on ON(1)/OFF(0) status of Instant Goal Behavior;

v max , ω max the maximum speed and turnrate of a robot respectively

Acknowledgments ii

1.1 Motivation of Research: Multi-Agent Coordination 1

1.2 Macro-Level Planning & Inter-Task Coordination 5

1.2.1 Task Representation & Short Term Allocation 6

1.2.2 Plan Representation & Long Term Allocation 8

1.3 Micro-Level Coordination 10

1.3.1 Formation Representation & Control 10

1.4 Contributions 14

1.5 Thesis Outline 15

2 Task Representation and Short Term Allocation 17 2.1 The Cooperative BackOff Adaptive Scheme 18

2.1.1 Disjoint Broadcast Networks 19

2.1.2 Formal Description of Tasks 20

2.1.3 Task Suitability Matrices (TSM) 26

2.1.4 Fault Tolerance and Coping with Uncertain Task Specifications 28 2.1.5 Adaptation of Internal Robot Model 30

2.2 Task Prioritization and Allocation 32

2.3 Analysis and Comparisons 38

2.3.1 Domain of Operation 39

2.3.2 Communication Complexity 41

2.3.3 Computation Complexity 41

2.3.4 Quality of Solutions 42

2.4 Simulation Experiments 44

2.4.1 Tasks and Mission Statement 44

2.4.2 Tasks in Connected Communication Networks 45

2.4.3 Tasks in Disjoint Communication Networks 50

2.5 Summary 51

3 Plan Representation and Long Term Allocation 54 3.1 Decentralized Task Scheduling 55

3.1.1 Self-Organizing Schedules 55

3.2 Agent Dynamics and Behavior 60

3.3 Simulation Experiments 65

3.3.1 Convergence of Agents with Known Task Durations 65

3.3.2 Tasks with High Degree of Uncertainty 67

3.4 Summary 69

4 Formation Representation with Q-Structures 70 4.1 Queues and Artificial Potential Trenches 71

4.1.1 Assumptions 71

4.1.2 Formations and Queues 72

4.1.3 Changing Queues 75

4.1.4 Potential Trench Functions 77

4.2 Robot Behaviors 80

4.2.1 Target Tracking 80

4.2.2 Instant Goal Behavior 82

4.2.3 Obstacle Avoidance 85

4.2.4 Overall Robot Behavior 86

4.3 Analysis of Parameter Values 86

4.4 Simulation Experiments 89

4.4.1 Convergence to Formations and Scaling 91

4.4.2 Maneuvers in Confined Spaces 93

4.4.3 Reaction of Formations to obstacles 97

4.4.4 Disruption of Wireless Communications 97

4.5 Summary 102

5 Q-Structures and Formation Convergence with Limited Communication 103 5.1 Formation Representation and Dynamic Target Determination 104

5.1.1 Division of Information Flow 105

5.1.2 Properties of the Q-structure 106

5.1.3 Determination of Target on Queue 110

5.2 Navigation of Robots to Positions in Formations 111

5.3 Simulation Studies 121

5.3.1 Formation Convergence and Scaling 121

5.3.2 Moving formations 124

5.3.3 Changing Formations 124

5.3.4 Discussion 126

5.4 Summary 127

6 Q-Structures and Formation Convergence with Motion Limitations 128

6.1 Q-Struture Representation 129

6.1.1 Incorporation of Orientation Information 129

6.2 Target Generation and Determination of Robot Behavior 131

6.2.1 Generation of Target-on-Queue with Limited Communication Ranges 132

6.2.2 Bobber-Agents 136

6.2.3 Convergence of Bobber-Agents towards Minimum Point in the Cast-Zone 139

6.2.4 Generation of Desired Trajectories for Robots 141

6.2.5 Overall Robot Target and Behavior Generation 153

6.3 Simulation Studies 154

6.4 Summary 159

7 Conclusions and Recommendations 161 7.1 Summary and Contributions 161

7.2 Suggestions for Future Work 164

1.1 The three layers of robot decision making according to information

processing requirements The relationship of the Macro- and

Micro-decision making levels for multi-robot teams with these three layers is

also shown 3

1.2 Different Levels of Robot Coordination The coordination mechanisms at each level may either be centralized or decentralized 5

2.1 Existence of subnetworks in workspace due to deep fading and signal attenuation 21

2.2 Elements of each robot’s Internal Models 21

2.3 Components and Phases of the COBOs 29

2.4 Reformulation of the SPP 35

2.5 Closed room (10m × 10m) with a single communication network 46

2.6 Activity Charts of the robots in the presence of a connected network 48

2.7 Evolution of Suitability of r1with the blue find attach(·) and red find attach(·) basis tasks 49

2.8 Robot allocation per task, and robot suitability for basis tasks at the end of mission, for domain with only one network 49

2.9 Activity Charts of the robots with one connected network and no un-certain task specifications 50

2.10 Activity Charts of the robots in the presence of multiple subnetworks The small kinks in the graphs, characterized by slightly raised lines, indicate that the robot is in recruitment phase for the associated task 52

2.11 Robot allocation per task, and robot suitability for basis tasks at the end of mission, for domain with multiple subnetworks 53

3.1 Elements concerning an agent, in a Roam-Space with two agents a jk and a j1k1 57

3.2 The Dandelion Formation and connected graph for agents within and between six Roam-Spaces 59

3.3 Agent Clusters and Uncovered Spaces in a Roam-Space 63

3.4 Gannt Chart and Convergence of Agents on Roam-Spaces when tasks may end before the expected time or be prematurely removed from the system 66

3.5 Maximum completion date on each Roam Space 68

3.6 The number of tasks successfully completed 69

4.1 Vectorsqi,vi and κ i of r iin the world coordinate system 71

4.2 Examples of queues, and formation vertices (circles), where x t and y t are the axes of the coordinate frame of the target centered at V1 Open queues are drawn with solid (and dashed) lines, indicating that they extend indefinitely from the vertex 75

4.3 Forces acting on a robot (r i) when it enters a queue A robot is attracted to the point on Q j (at q (vj),nr) that is nearest to it 78

4.4 Instead of the original queue (that passes through the obstacle), the pres-ence of the obstacle causes the robots (triangles) to be attracted to the deformed queue that hugs the obstacle at a distance of ρ adp 81

4.5 3D view of the potential trench function of Q4 in the (x,y)-coordinate space of the vertex, V3 81

4.6 Representation of the direction (nq,i,a)of a point in the coordinate frame of r i by the pair (φ a , θ a) 85

4.7 Attractive & Repulsive forces on an robot joining an established queue 89 4.8 Convergence of team to desired formation Solid: Wedge, Dashed: Col-umn, Dash-dot: Double ColCol-umn, Dotted: Circle 92

4.9 Scaling of formations Solid: Wedge, Dashed: Column, Dash-dot: Double Column, Dotted: Circle 92

4.10 Snapshots of the team of nine robots forming the wedge formation 93

4.11 Snapshot of corridor and waypoints 94

4.12 Team Maneuver through a confined corridor Solid: δ, Dashed: δ a 95

4.13 Formation deformation during a turn 95

4.14 Team Maneuver through a confined corridor Solid: δ, Dashed: δ a 96

4.15 Snapshot of wedge deformed into a column in a narrow corridor 96

4.16 Snapshot of environment with Type I and II obstacles 98

4.17 Plot of δ vs time for team traversal through obstacle fields 98

4.18 Plot of δ vs time for disruption to a maximum of half the communica-tions links 100

4.19 Queue status of the robots for I loss = 0.50, P txloss = 0.05 101

4.20 Effect of different degrees of communication breakdown on the forma-tion Circle (•): I loss = 1.00 , Cross (×): I loss = 0.50, Triangle (!): I loss = 0.25 101

5.1 Graphical Representation of Q-structures Dotted circles represent vir-tual vertices 107

5.2 The triangular formation represented using connectivity graphs 108

5.3 Robot convergence to formation with robot deactivation/removal at t = 10s 122

5.4 Robot Separation and Control Forces 122

5.5 Distance of robots from related queue’s encapsulating area 123

5.6 Formation convergence with a moving target 124

5.7 Robot Separation and Control Forces 125

5.8 Robot convergence to formation with formation switching Wedge: t =

[0s, 15s), Column: t = [15s, 30s), Line: t = [30s, 45s) 125

5.9 Robot Separation and Control Forces 126

6.1 Examples of queues, and formation vertices (V1 to V5) in 3-D space 131

6.2 Robots are attracted to their associated queues based on the potential trenches in the 3-dimensional space The potential trenches experienced by each robot, given their positions, are also shown 132

6.3 Decision Flow within the system, as well as the different levels of com-munications and decision making 133

6.4 Cast-zone of a robot located at q i 137

6.5 The attractive potential (U tcast,i) in the cast-zone 141

6.6 Constellation agents around a robot 144

6.7 Convergence of formation with 9 robots 156

6.8 Inter-robot collision avoidance and robot directional changes 156

6.9 Convergence of formation with 6 robots changing between formations 157 6.10 Inter-robot separation as the team changes between formations 157

6.11 Convergence of formation with 6 robots 158

6.12 Inter-robot collision avoidance and robot directional changes 158

6.13 Convergence of formation with 6 robots through an obstacle field 159

6.14 Distance between different robots, and the distance between robots and obstacles 160

2.1 Comparison between different Task Allocation Architectures For

sim-plicity, r = n r and n = n ls for this table The figures pertaining toALLIANCE, BLE, M+, and Dynamic Role Assignment are based onthe work presented in [1] 392.2 Robot Capabilities and suitability levels for basis tasks and Tasks B:Blue, R: Red Tasks are prioritized using their subscript (Note: Infor-mation regarding Task 4 is presented here for convenience It is, in fact,introduced only at runtime as a new task.) 463.1 Robot Capabilities and Task Requirements/ Specifications (R: Red, G:Green, B: Blue) 674.1 Parameter Values for simulations 90

This chapter presents a broad overview of the motivation and background for carryingout the research work on collaborative mobile robot teams that is presented in this thesis.The research objectives and scope of this research as well as the outline of this thesis isalso presented

1.1 Motivation of Research: Multi-Agent CoordinationMulti-Agent Systems, consisting of huge numbers of interacting agents, linked to-gether in complex networks, are becoming increasingly prevalent in the everyday con-text Such agents manifest themselves in the form of virtual robots, operating factoryprocesses, humans and embodied mobile robots The advancement of technology inrobotics, control, computer science and communications, has made possible the deploy-ment of large teams of mobile robots in real life scenarios These systems have beenapplied to a wide variety of areas, from manufacturing and warehouse automation, con-struction and shipping industries, to autonomous robot humanitarian demining, surveil-lance and urban search-and-rescue A comprehensive overview of issues in multi-robotcooperation may be found in [2]

In light of the growing autonomy of singular mobile robots and the great potential ofcollaborative teams, this thesis focuses on the efficient coordination of embodied robots,with the main aim of improving the autonomy of robot teams operating in dynamic

and unknown environments Embodied robot systems are significantly different fromtypical multi-agent technologies employed in Distributed Artificial Intelligence (DAI)approaches [3] that considers software agents.

One major difference is that embodied robots respond and interact directly withother entities in the environment Virtual agents, on the other hand, perform tasks thatare mostly informational [4] Furthermore, the constraints faced by software agents aredifferent from those faced by mobile robots, which also influences the type of solutiontechniques available for each type of agents (virtual or embodied) For instance, therange of capabilities each robot may be equipped with correspondingly affects the set

of feasible coordination mechanisms In addition, disembodied agents are given theopportunity to modify their intrinsic capabilities and even replicate themselves to copewith the uncertain virtual environment in which they exist, while embodied robots have

to make the most out of whatever equipment each possesses and react in appropriateways to cope with malfunctions and highly uncertain sensor readings

It is highly impractical, and even impossible, to require a single robot to be equippedwith a myriad of capabilities that can handle every possible scenario that may arise.Moreover, such systems are extremely prone to malfunctions that cripple and jeopar-dize the success of robot missions The use of multi-robot teams removes the need forevery robot to be capable of performing complex missions single-handedly Instead,individuals cooperate with each other, volunteer their expertise for tasks, and utilize thecollective capabilities of the team to accomplish missions This greatly improves therobustness of robots against malfunctions

However, the use of multiple robots for missions is not without problems cially for mobile robots operating in unknown and highly dynamic environments, it isimportant for the team to be able to react suitably, given their limited capabilities, tofully utilize expertise afforded by individuals, to ensure that the mission may be accom-plished as much as possible

Espe-The decision making process of each autonomous robot can generally be dividedinto three interacting layers According to the work in [5], the these are: (i) the Reactive,(ii) the Routine, and (iii) the Reflective, layers shown in the right side of Fig 1.1 As

the name implies, the reactive layer consists solely of behaviors that can be furthergeneralized into attractive and repulsive forces This is the most primitive layer, wherethe amount of information processing is the bare minimal On a higher level, is theroutine layer, where case-based reasoning occurs Classical conditioning also results inthe generation of behaviors in this layer, where responses are more “automated” (andyet, not as primitive as the reactive layer behaviors) The largest amount of informationprocessing occurs on the reflective layer, where counter-factual reasoning and high leveldeliberation can occur The layer does not directly influence the robot’s actions, butinstead produces biases to the lower levels that in turn, affects the resultant actions.

Figure 1.1: The three layers of robot decision making according to information ing requirements The relationship of the Macro- and Micro-decision making levels formulti-robot teams with these three layers is also shown

process-Specifically, this thesis examines decision making within the routine and reactivelayers, and further sub-divides these layers into the macro- and micro-decision levels toreflect the degree of coordination required for different processes within a multi-agentteam The relationship of these two forms of multi-robot decision making with Ortony’sthree layers are also shown in Fig 1.1 The two forms of multi-robot decision makingare further described as follows

(i) Mission level planning and inter-task coordination This involves planning the job

assignments to each robot (or robot sub-team), taking into account their ties and the requirements of each job Such mechanisms may be centralized andperformed by a single leader robot, or decentralized, in which robots reach a suit-able arrangement through a series of observations and self-organizing inter-robotnegotiations The allocation and planning mechanism acts as a top level man-agement scheme that should manage the available resources to ensure missionaccomplishment As mentioned earlier, it is important for such a mechanism to

capabili-be fault tolerant and able to cope suitably well with changes to team compositionand any uncertainties that may be present in the system

(ii) Coordination for single task accomplishment The resource management schemes

typically do not specify exact behavioral and interaction rules for individual robots.These are lower level coordination mechanisms that explicitly plans the actions ofindividual robots in relation to those of others After going through mission levelplanning and arriving at the actual task(s) to perform, a sub-team of robots need

to plan their motions and paths (thus coordinating amongst the members of thesub-team) to ensure that the task can be completed For instance, a transportationtask may require the sub-team to encircle the object and move in a tight formationbetween two points in space As with higher level planning, the issues of faulttolerance and adaptability resurfaces, and must be considered

Coordination mechanisms on both levels mentioned above are critical for the able operation of autonomous mobile robot teams The relationships between them areshown in Fig 1.2 In this research, coordination mechanisms on both levels of planningwill be presented in detail, with the overarching theme of increasing the robustness ofrobot teams in uncertain environments and allowing them to produce desirable resultseven in the face of adversity, on both the macro and micro levels The following sec-tions will present the background literature and introduction to the main chapters of thisthesis

reli-Macro Level Coordination Mechanism

Task Dissemination and Allocation Formation of Sub-Teams

Mission/ Task Specifications Robot Team

Micro Level Coordination

Action Coordination

Robot Sub-Team

Micro Level Coordination

Action Coordination

Robot Sub-Team

Micro Level Coordination

Action Coordination

Robot Sub-Team

…

Individual Robot Actions

Individual Robot Actions

Individual Robot Actions

as where information regarding each task is incomplete or insufficient to derive accurateestimates of quantities such as task durations, the team is only able to perform alloca-tions instantaneously based on information it has at each time On the other hand, whenthe team has sufficient information regarding their mission – when future tasks are ex-pected to occur, the duration of tasks, the lifespan of each team member – allocationefficiency can be increased through planning over a extended time scale

1.2.1 Task Representation & Short Term Allocation

Much work has been done in recent years with regards to the coordination of robotteams Coordination architectures such as ALLIANCE [6], MURDOCH [4] and, morerecently, BOAs/COBOS [7, 8], with a focus on instantaneous allocations, have beenproposed for cooperating mobile robots in unstructured environments The use of suchmulti-robot teams removes the need for every robot to be capable of performing com-plex missions single-handedly Instead, individuals cooperate with each other, volunteertheir expertise for tasks, and utilize the collective capabilities of the team to accomplishmissions set in highly dynamic environments where information may be incomplete oruncertain

When robot teams operate in unknown environments (e.g exploring/surveying anunknown territory), it is difficult to predict all the challenges and tasks that robot teamsmay face A number of schemes have been proposed to deal with this problem A well

known fault tolerant architecture is ALLIANCE [6], which integrates impatience and

acquiescence into each robot The L-ALLIANCE [9] extends ALLIANCE by adding

parameter adaptivity into the architecture Another approach is the Broadcast of LocalEligibility (BLE) technique [10] It uses cross inhibition of behaviors between robots in

a team, based on a calculated task eligibility measure that robots compute individuallyand broadcast to the team A decision theoretic technique based on Markov decisionprocesses is used for collaboration in persistent teams [11], of which embodied multi-robot teams considered here are a part of A task assignment architecture that usestask templates and the prioritization of task instances in a task assignment planner hadalso been proposed [12] for transportation applications in unknown, but static, environ-ments The M+ protocol [13] has a task allocation layer, and the negotiation processused is based on the Contract Net Protocol These schemes typically consider robotoperation in ST-SR-IA1domains As opposed to SR-tasks, MR-tasks require more thanone robot to perform, and where the tasks cannot be decomposed into independent SR-

Multi-Robot tasks, Instantaneous Assignment systems; SR: Single-Multi-Robot tasks; TA: Time-extended ment).

Assign-tasks Coalitions may be formed [14] for such situations However, uncertain (and/orincomplete) task specifications have not been considered although it greatly impacts al-locations, especially in ST-MR-IA domains where the evaluation of team effectiveness

is impaired This problem is especially true in environments where domain knowledge

is incomplete Consider the task of clearing an obstructing rock detected during a sion It is difficult for a remote user to determine, using only sensor information (e.g.video images), the exact weight of the rock, and the number of robots required, whichmay vary greatly across different teams

mis-Auctioning schemes, utilizing explicit communications have been used in variousforms in allocation schemes Robust multi-robot cooperation may be achieved throughthe use of market-based approaches [15] Similarly, ‘Hoplites’ [16] have been proposedfor robots to execute tightly coupled tasks Market-driven software agents [17] are alsoused in electronic negotiations, and which is able to adapt their strategies depending onthe prevailing conditions A dynamic role assignment scheme that represents roles ascontrol modes in hybrid automatons has also been proposed [18, 19] The MURDOCHscheme [4] also uses an auctioning approach with a publish/subscribe communicationmodel A role assignment strategy based on multi-threaded computer programming wasused to resolve any risks and conflicts that may arise during dynamic role swapping[20] In cases where communication losses are considered (e.g in MURDOCH [4]), it

is often assumed that persistent communication losses imply the failure of a robot, andanother robot will be activated to take over the task This does not account for the factthat the robot may still be performing the task adequately In the absence of team-widecommunications, robots should be able to respond appropriately to achieve suitableallocations For instance, if a team of robot is deployed to survey separate regions, due

to security and practical issues, robots in one region would not be able to communicatewith those in other regions

While a number of papers (such as [4,21,22]) have considered the issue of adapting

to robot malfunctions, there is very little attempt to use a robot’s history of failures

in completing certain tasks to assess the operability of its onboard capabilities (and

to determine which capability is the most likely cause of failures), and to make use

of these information for making future decisions Although the work in [22] is able

to detect and adapt to partial robot malfunctions, it does not attempt to identify themalfunctioning resource unless the malfunction can be directly assessed based on aloss of access to the resource This may not be applicable in certain scenarios, such aswhen a resource only suffers from diminished capability (e.g wear and tear of hardwarecomponents on a gripper that reduces its ability to carry heavy loads) and the robot stillhas continued access to the resource Therefore, with regards to instantaneous planningand task allocations, the work presented in this thesis will focus on:

(i) Improving the autonomy of robot teams by having robots decide independently

on a suitable allocation under uncertain operating conditions and with gradedvariations in competencies between individuals

(ii) Cooperation between robots in different spatial domains with disconnected cast networks, in addition to uncertain task specifications

broad-(iii) Improving the team’s robustness via the automatic identification of problematicresources, and a review of an individual’s task achievement history, to adapt thetask allocation on-the-fly

1.2.2 Plan Representation & Long Term Allocation

As mentioned in the previous section, a large amount of work has focused on neous task allocation in embodied multi-robot teams used for missions such as recon-naissance, surveillance, disaster search and rescue and toxic waste disposal However,

instanta-in many cases, estimated values of task durations and earliest start times are available

as rough guides for allocation schemes Thus, longer term scheduling of tasks can bebeneficial

(Re)Scheduling problems have been typically examined in the domain of operationsresearch In a more structured environment where conditions are less dynamic, by tak-ing certain time constraints into consideration, scheduling of allocations and actionsmay be performed The availability of such information, however, does not diminish

the need for systems to be fault tolerant, since unexpected events do occur on a lar basis When this happens, scheduling systems must be able to react appropriatelyand perform re-scheduling The application of different scheduling approaches to thescheduling problem in supply chains is investigated in [23] In addition to obtaining aschedule before commencement of an operation, schedule repairs and rescheduling may

regu-be required for the system to cope with changes in operating conditions (e.g demandchanges) This problem has been partly addressed in the work by Jenson [24], whichfocuses on choosing a schedule based on a robustness measure The GA has also beenused to evolve a population of agents based on an artificial immune system [25] Sched-ules may also be modified according to the algorithm proposed in [26] that is based on

an Activity-on-Node network flow model The Polite Rescheduler (PRIAM) has beenproposed in [27] to minimize the propagation of disruptions through the network ofinterconnected manufacturing cells A rescheduling mechanism (applied to the prob-lem of system maintenance) that takes into account the communication times betweendifferent decision centers is proposed in [28] The efficiency of rescheduling processes

is studied in [29], in which the Segment-Based Reactive Rescheduling (SBR) approachwas proposed, for structured environments where the user has a more or less accu-rate description of processes and conditions The Self-Adjusting Dynamic Scheduling(SADS) technique is presented in [30] for the scheduling of parallel processors andwith one processor dedicated to scheduling Similarly, a process that transits betweenexecution and reconciliation phases for dynamic rescheduling is proposed in [31] AHolonic architecture is proposed in [32] and a negotiation protocol, based on the con-cepts in the Contract Net Protocol, is used between various components of the systemfor the allocation tasks to resource holons Viera et al [33] provided a survey of severalexisting approaches and issues involved in rescheduling, and proposed a general frame-work within which rescheduling may be studied These approaches, however, typicallyinvolve large scale, long term (re)planning procedures which are computationally inten-sive These methods are therefore not directly applicable to autonomous mobile robotteams which require fast reaction times when operating in uncertain environments, andwhere the planning horizon is significantly shorter than that encountered in large scale

logistics, manufacturing or supply chain scenarios Nonetheless, the ability to utilizetask information can significantly improve the current allocation derived from instan-taneous allocation mechanisms, by allowing robots to make better plans (e.g., motionpaths) In light of this, the thesis will consider:

(i) Single-Task Robots, Single-Robot Tasks, Time-Extended Assignment TA) [1], with hard earliest start time constraints and relaxed due date constraints.For example, if a robot’s current task is nearing completion, it can perform a pre-liminary evaluation of the required capabilities for the next task to detect possiblehardware failures2

(ST-SR-(ii) A flexible plan representation method and self-organizing framework that allowsfast and stable generation of feasible plans over time

1.3 Micro-Level Coordination

Coordination within agent teams do not stop at the more abstract task and mission ning stage For successful implementation of tasks that have been assigned to individu-als or sub-teams, there is a need for additional, finer coordination, at the level of agentactions This often involves the explicit collaboration of movements and positioning ofindividual robots for specific applications such as surveillance, scouting and coverage.With respect to micro-level coordination, this thesis therefore focuses upon multi-robotformation control as a representative domain within which lower level motion/behaviorcoordination within an agent team can be examined

plan-1.3.1 Formation Representation & Control

Robust multi-robot formations in dynamic and uncertain environments has been

inten-sively studied in recent years For instance, the approach adopted by Olfati-Saber et

by right-shifts to ensure that the earliest start time constraints are satisfied (e.g the technique described

in [34]) However, this can create unnecessary idle times between tasks, which should be reduced with additional mechanisms.

al [35] uses centralized control, with a central unit processing collected data, and

pass-ing instructions to the rest of the robots For large multi-robot teams in dynamic anduncertain environments (e.g., field applications), where communications can be limitedand unreliable, decentralized approaches are generally favored

To guide robots into formations, virtual leaders are proposed and used by Leonard

and Fiorelli [36] Balch and Arkin [37], Das et al [38] and Desai et al [39] allocated

specific identification to individual robots with each robot required to maintain a

pre-defined position in the formation Das et al [38] also proposed an algorithm for stable

switching between formations Egerstedt and Hu [40] made use of a formation strained function to determine the formation of a group of robots, each moving along

con-a trcon-ajectory determined with respect to con-a virtucon-al lecon-ader Ren con-and Becon-ard [41] proposed

a decentralized scheme that is based upon the virtual structure approach for effectiveformation maintenance A method for calculating the virtual center of a team of space-

crafts in formation flight is presented by Tillerson et al [42], which improves

coordina-tion and fuel use amongst members of the team Robots using the algorithm proposed

by Yun et al [43] allows robots to follow line and circle formations that have no quirements on the formations’ orientations Eren et al [44] describes the establishment

re-and removal of links as robots are added or removed from the team It is concerned withthe maintenance of formation rigidity during robot team movements along trajectories,instead of any particular geometric formation

There are several issues that must be tackled while considering multi-agent tions Improved robot autonomy leads (potentially) to an increase in team size, whichalso faces possible changes during operations in highly unstructured environments (e.g.,during an incursion of robotic scouts into enemy territory) It is, therefore, important

forma-to consider the issues of formation scalability and flexibility This problem is tigated by Balch and Hybinette [45] who used the concept of social potentials whichallow robots to ‘snap’ into the correct relative positions, based on a predetermined set

inves-of ‘attachment sites’ around each robot This method however inves-offers no control overthe geometry of the formation, and more dispersed formations, like the wedge and di-amond formations, cannot be achieved Carpin and Parker [46] described a distributed

approach, based on explicit communication between robots, for coordinated motion in

a linear pattern The framework is also able to handle the emergence of unexpected

obstacles within the formation Kostelnik et al [47] solve the problem by using a

com-munication network between the robots, so that each robot may be assigned social roles

by a dynamically chosen leader Kang et al [48, 49] proposed general methods for the

controller design for the formation maintenance of multiple vehicles tracking a desiredpath It was assumed that the desired trajectories are known, and each robot is asso-ciated with a specific node in the formation The formation controllers can be easilyaltered by the designer when vehicles are added or removed from the system

Most of the seminal works described above use a formation representation based

on connectivity graphs where each robot tracks a specific node as a target (e.g., invirtual structure approaches [41]) Such representation is also implicit in more reactiveapproaches, such as those that require a robot to choose and follow a neighbor at aspecified distance and orientation (for instance in [38, 50]) When team size changes,the graph representation will change, which can become difficult to track dynamically.There is therefore the need for formation schemes to be amenable to dynamic scaling.Another pressing concern in formation control is that of ensuring convergence andstability within the proposed schemes Several work have focused on this aspect, andhave derived provably stable convergent algorithms for formation control In the work

by Song and Kumar [51], specific artificial potential fields for each robot relative to theother robots are calculated to produce stable formations in equilibrium The concept ofLeader-to-Formation Stability is introduced in [52], and the paper examined how errorspropagate from the leader and influences the stability of formations (those based onleader following) Navigation functions, first proposed in [53], have also been used forcentralized control of formations [54] The problem of ensuring formation stability in arobot team while it moves in formation through an obstacle field between two points isinvestigated in [55]

For practical implementation of formation control schemes, communications tween controllers and mobile robots, or between mobile robots, are indispensable forthe transmission of crucial information required for meaningful coordination to occur

be-Indeed, wireless data transmission is the most common form of information transferemployed in mobile robot teams Agent cohesion and collective behavior when delaysare present in sensing and communication networks are examined in [56] Khoo andHorswill [57] proposed the HIVEMind, a tagged behavior based architecture for smallteams of robots, enabling the utilization other agents in the team as remote sensors

connected via wireless links Bay et al [58] assumes communication in the form of

a common ‘road map’ that is constantly updated by all the robots in a flock, enablingimproved robot navigation in complex environments Fredslund and Matari´c [59] al-lows individual robots to broadcast periodic ‘heart-beat’ messages about itself and eachrobot is given specific IDs As with any form of sensing, wireless communications aresusceptible to attenuation, disturbances and losses It is therefore imperative for anycoordination scheme to be able to adequately cope with intermittent information lossessuch that the overall performance of the team is not compromised

With these issues in mind, this section of the thesis focuses on developing:

(i) A feasible formation representation that is flexible and scalable with respect toagent team changes, and which will support both centralized and decentralizedformation schemes

(ii) Provably stable and convergent decentralized formation schemes

(iii) Robust formation schemes that can cope well and maintain stability under tions with limitations in communication and sensing ranges, as well as in teamswith movement constraints

condi-Remark 1 The thesis mainly deals with coordination between embodied agents, which

are referred to collectively as robots In addition, several methods described in the chapters of this thesis utilizes a separate layer of virtual agents to facilitate decision making and planning by the robots These will be referred to as agents, to distinguish them from the embodied robots.

1.4 Contributions

Based on the overall framework under which the various aspects of multi-agent oration are organized, the research presented in this thesis focuses upon the overarchingtheme of developing frameworks, representation, and coordination schemes that im-proves the robustness of multi-agent teams in uncertain operating domains The maincontributions of this research are briefly listed as follows:

collab-(i) A general mission/ task representation framework, based on the concept of basistasks, that is amenable to analysis for the efficient portrayal, subdivision, andallocation of tasks to agent teams on-the-fly

(ii) A robust, cooperative task allocation scheme, the Cooperative Back-Off Scheme(COBOS), for instantaneous task (re)distribution between spatially distant tasklocations which are subjected to limited communications

(iii) A representation framework for task allocation schedules over an extended timeperiod, based on the transformation of task schedules into an agent-formationspace, where stable, self-organizing, convergence algorithms are introduced toform a dynamic time-extended allocation

(iv) An efficient formation representation scheme, the Q-structure, to facilitate able and flexible agent formations The Q-structure allows the representation of

scal-a wide vscal-ariety of formscal-ations, scal-and coupled with scal-a behscal-avior bscal-ased scal-algorithms foreach agent, enables decentralized, robust formation tracking with automatic scal-ing

(v) A decentralized and reactive potential field based method is used for stably ing agents into formation based only on local communications, and further subdi-viding the decision making process into the fast and slow time scales Theoreticalanalysis have also been carried out to verify the convergence properties of thenavigation controls

guid-1.5 Thesis Outline

Following this chapter, the remainder of this thesis is organized as follows:

Chapter 2 examines the task allocation layer of macro-level decision making in bile robot teams, with an emphasis on a flexible deliberative task specification schemeand fault tolerant instantaneous task allocation between heterogenous team members Amatrix-based approach is presented for the composition and specification of tasks usingbasic task achieving behaviors The chapter then examines fault tolerant task alloca-tion using the Cooperative Back-Off Adaptive Scheme (COBOs), designed to improve

mo-robot autonomy in the ST- MR-IA domains with uncertain task specifications, and with

isolated pockets of communication networks

Chapter 3 presents a self-organizing framework for time-extended decision ing by mobile robot teams The presented approach focuses on the organization of tasksinto a feasible work plan or schedule The chapter first examines the representation ofallocations in the framework of self-organizing virtual agents, with the use of a Dande-lion network/graph that defines agent neighborhood relationships Next, algorithms thatgovern agent interactions and produce clustering behavior are presented The agentsself organize to produce a feasible and flexible schedule (respecting constraints), whileequalizing work loads (as far as possible) between robots based on the latest expectedcompletion date of all the tasks each robot is handling

mak-Chapter 4 presents the concept of queues, instead of nodes, as a novel and flexibleformation representation framework to define and support a large variety of formations

A decentralized redistribution algorithm is used, which enables the robots to redistributethemselves dynamically and efficiently amongst queues in response to changes in theformation or in the number of robots in the team The concept of Artificial PotentialTrenches, each associated with a queue, are then presented

Chapter 5 extends the Q-structure to reduce its reliance on global tions In particular, the Q-structure is first extended by considering finite communi-cation ranges, and separating the decision making process into two time scales – afast time scale for reactive decision making based only on local communications, and

communica-a slower time sccommunica-ale which communica-allows less time criticcommunica-al informcommunica-ation to propcommunica-agcommunica-ate through

a weakly connected network Next, a rigorous proof of convergence for a ized control law that guides robots into formations represented by the Q-structure ispresented Lastly, an improved dynamic target determination algorithm is proposed toincrementally guide robots into their queues

decentral-Chapter 6 presents a further extension to the Q-structure to allow adaptation of thecommunication structure itself, by leveraging on the fact that the Q-structure provides aconvenient high level organization of the agent team in terms of short term informationflow In addition, the Q-formation scheme is extended into the 3-D space and orienta-tion information is incorporated into the representation The chapter also considers thelimitations on the amount of direction changes each robot is capable of making at eachinstant, preferring to make gradual directional changes instead of abrupt turns

Chapter 7 summarizes the work presented in this thesis It concludes this thesisand highlights the major contributions It also discusses the limitations of this thesisand suggests future research directions that can be extended from the current researchresults

Task Representation and Short Term Allocation

This chapter presents a first look into the task allocation layer of Macro-level decisionmaking in mobile robot teams, with an emphasis on a flexible task specification schemeand fault tolerant instantaneous task allocation between heterogenous team members

Deliberative cooperation between heterogeneous members [60] of embodied robotic

teams is the main concern in this chapter This is different from reactive and

swarm-ing [61] approaches where cooperation emerges as a byproduct of inter-agent tions, which is more suitable for very large teams of homogeneous robots Lower levelbehaviors for the robots (e.g formation control [62–64]) to carry out their allocatedtasks are presented in the later chapters of this thesis

interac-In particular, for this chapter, a matrix-based approach is employed for the position and specification of tasks using basic task achieving behaviors It accountsfor alternative methods of performing the tasks as well as task dependencies, and im-proves the portability of tasks across different robot teams and allows robots to makeuse of task success/failure histories to detect, isolate and adapt to device imperfectionsand malfunctions Following the representation of a mission and associated tasks tothe robot team, the chapter then examines fault tolerant task allocation using the Coop-erative Back-Off Adaptive Scheme (COBOs), designed to improve robot autonomy in

com-the ST- MR-IA domains with uncertain task specifications, and with isolated pockets of

communication networks.

2.1 The Cooperative BackOff Adaptive Scheme

The COBOs is implemented on each robot in the team Each robot makes use of theinformation it obtains from its sensors to construct, and adapt, its internal models ofthe team and the tasks Information that the robots receive from the broadcast channel

is treated as another form of sensor input Note that the robots do not participate innegotiation and direct communication, in which they ‘discuss’ and make arrangementsfor their own and others’ task allocation The following assumptions are made

Assumption 1 All robots are equipped with wireless communication abilities, and do

not deliberately distort any information they transmit.

Assumption 2 Through explicit communications between robots, a robot determines

the task statuses of tasks handled by robots it currently has contact with A task’s status indicates whether (i) one of the robot has started the task, or (ii) has been completed The current activities of robots are broadcasted for this purpose The broadcasting range of each robot is limited and finite Due to imperfect communications, if a robot loses contact with another, and is unable to ascertain a task’s current status, the robot will keep the associated task status unchanged, until the robots come into range of each other again.

Assumption 3 The generation of tasks is entirely random and no a priori planning is

possible This is true for robot operation in unstructured and dynamic environments,

Remark 2 ‘Backing off’ that is used in communications and networks (e.g IEEE

802.11 networks) is competitive [66, 67] In contrast, COBOs explicitly synthesizes

scheduling problems [1], e.g manufacturing systems [65] Scheduling involves the allocation of a set

of jobs to the set of machines, over time – which is a time-extended task allocation problem It uses available knowledge (e.g task due dates) for planning This is beyond the scope of the chapter, where

we assume robots and users have minimal task information and no a priori task models In such cases,

only instantaneous assignment is possible, and the scheduling problem becomes an assignment problem.

cooperation into the system Conventional ‘backing off’ cannot solve the problem we are concerned with, e.g Consider a system with one task (or resource) Success in

‘accessing’ the resource occurs when the task shows progress A robot that fails at the task will first back off, and continue attempting the task after each random back off period The robot that first claims the task after robot 1 backs off will attempt the task.

If this robot is still unable to complete it, this second robot will eventually back off as well This causes an ‘infinite loop’ where the robots continuously vie for the task, but never attempting to perform it cooperatively COBOs avoids this by ensuring sufficient cooperation between the robots to accomplish the given tasks.

2.1.1 Disjoint Broadcast Networks

For deliberative cooperation, communication is indispensable The impact of nication on the performance of agent societies have been studied [68, 69] Broadcastmessaging, instead of unicast messaging, is employed in COBOs For unicasting, a to-

commu-tal of n j (n j −1) (O(n2

j)) channels must be used, entailing high bandwidth requirementsdue to the inefficient transmission of identical data to a large number of other locationsvia different channels On the other hand, a smaller bandwidth is needed for broadcast-

ing Information is put on a common channel that is known to all robots and only a total

of O(n j)channels is required For this reason, broadcasting is commonly used for thetransfer of information in multi-robot teams [4, 6]

In general, there are two types of communication imperfections The first typeoccurs when signal strength (and thus, broadcasting range) is limited as stated in As-

sumption 2 This is justified in real life scenarios where communications may face

per-sistent losses because of deep fading, large interferences from other strong signal/noise

sources, or when robots are given tasks that are very far apart This causes some robots

to lose complete contact with others over an extended time period This is the

com-munication problem that COBOs is concerned with This should be distinguished fromthe second case when robots are within the same broadcast region, but suffers from

spurious and temporary packet losses Such problems can be solved through the use

of standard communications protocols Most work dealing with communications perfections deal with the second type, which may also be solved through more frequentauctioning (e.g in [22]) and monitoring communications connectivity.

im-Let N = {N i sn | N i sn ∈ W, for i sn = 0, 1, , n sn }, be disjoint subnetworks of

the entire workspace W Each N i sn may be treated as a separate network resulting from

the separation of robots from the main broadcasting network Let n snbe the number ofsubnetworks Since the subnetworks arise chiefly due to the locations of each task (forsystems with real, embodied robots), these locations are related to one of the subspaces,

i.e L i ⊆ N i sn , where L i is the location where T iis to be conducted (shown in Fig 2.1).Furthermore, information regarding a new task may be obtained only when a robot is

in N0, where the user is located For instance, if T5 is introduced only after all the

other tasks are underway, only robots in N0 would be aware of the new task Robots

in the other locations (i.e N1 and N2) will only be aware of T5 if they reenter N0,

or another robot that has claimed T5 enters their subnetwork For subnetworks whichoverlap, simple rebroadcasting of information by robots may be done to ensure a betterspread of information This increases the communications range of robots, resultingfrom the merger of several small subnetworks into a larger one However, disjointsubnetworks may still exist at different locations due to reasons cited earlier, and thecurrent formulation still holds

2.1.2 Formal Description of Tasks

A robot’s task model consists of the properties of tasks (as perceived by the robot) it iscurrently aware of The task model is used to calculate the robot’s own suitability levelfor each of the tasks Task suitability is defined as follows

Definition 1 (Task Suitability) The suitability of a robot for performing a certain task,

based on the set of intrinsic capabilities it possesses and the abilities required for cessful execution of that task The computation of suitability levels will be detailed in the subsequent parts of this section.

suc-By combining information in the broadcast channel with its own suitability levels

Updated Online All tasks in range Recruiting tasks

Suitabilities of other robots from communications

Internal Model

Information a robot broadcasts

Figure 2.2: Elements of each robot’s Internal Models

for the tasks, a robot r j forms its team model (Task Suitability Matrix (TSM(j))) This

is used by r j to decide the task that it should perform The elements of a robot’s internalmodels are shown in Fig 2.2 These elements and COBOs will be described in theremainder of the chapter

Remark 3 Although task suitability may be construed as a form of utility measure, it

is slightly different from how utility is normally used Instead of predicting the expected solution quality a robot-to-task allocation yields, suitability reflects how qualified a robot is in performing a certain task, based on the qualities it possess.

The proposed task description aims to make the information regarding basic taskachieving behaviors required for individual tasks, readily available to robots.2 Although

similar to task abstractions [15] (where subtasks with AND relations can be executed

by different robots) and atom tasks [70], the proposed approach allows explicit

specifi-cation of the capabilities that a robot must possess to be eligible for a task This would

mean the further decomposition of each primitive/atom task into even smaller subtasks(capabilities), with the constraint that they must all be achievable by one robot Theproposed representation thus improves the handling of information regarding robot ca-pabilities, alternative ways of performing tasks, and task dependencies, that have notbeen considered in [70]

Definition 2 (Basis Tasks) Basic high level tasks (or behaviors) out of which other,

more complex tasks may be composed Basis tasks may also be seen as basic abilities, motor schemas [71] or resources [4].

Definition 3 (Macro Tasks) Complex tasks that are composed from basis tasks These

will be referred to as ‘tasks’ for the remainder of the chapter.

A task, T i, is defined as a quadruplet, (Ti ,Li , T i,dp , E i (t)), and the individual

ele-ments are described as follows

Operator ‘(’

Let B be the known set of n b basis tasks, each accepting its own list of arguments %

(which may be sets of coordinates, areas to explore, etc.), available for task specification

such that b1(%1), b2(%2), , b n b (% n b) ∈ B It may not reflect only the capabilities of

current members of the team (which is its minimum size), and can encompass a largerset of basis tasks The basis tasks and the corresponding list of arguments is cast invector form asB = [b1, b2, , b n b]T andL = [%1, %2, , % n b]T respectively A task, T i,

to ontologies in artificial intelligence However, for our purposes here, we are mainly interested in the problem of allocating a set of tasks (already specified) to a team of robots As such, what is proposed here acts to constrain the type of information required, and is a general structure that users may follow when specifying tasks for the robot team.

is composed of a combination of basis tasks, i.e T i ⊂ B, and is written as

Equation (2.1) may be interpreted as: T i , under (‘*’) B, requires all the basis tasks

b j for which Ti (j) = 1 and accepts % j as arguments The entries of L are ignored

for the basis tasks that are not required For simplicity, ‘* B’ will be omitted from task specifications The operator ‘(’ acts like the matrix multiplication, except that the result is a set of basis tasks required for the task This allows tasks to be represented

by matrices, facilitating the manipulation and use of task information through normalmatrix operations

The ‘nature’ of a task refers to the generic type of task that it belongs to, and therelated abilities (though perhaps in varying degrees) required of robots that wants toperform it For instance, two separate tasks involving grasping and lifting an object (ofdifferent weights, thus requiring different strengths), are of the same nature, i.e bothare ‘picking’-type tasks Tasks are decomposed into two main parts (i) the nature, and(ii) the details of the task, characterized byT and L respectively A more general task

is stated as

T i,k =Ti,k ( L i,k , for k = 1, 2, , n

T i,j +⊆ T i,k , for j, k = 1, 2, , n and j += k (2.4)

and T i,dp is the set of tasks that must be performed before T i can be activated On two

the resulting n × 1 vector is obtained by using ‘(’ on the k-th row and column of the

is given byTi,k ( L i,k Precedence relationships are indicated within the parentheses

of ‘&(·)’ The sign ‘|’ means that T i may be satisfactorily described by any one of theset of basis tasks Ti,k for k = 1, 2, , |T i | Any robot possessing all the capabilities

specified in any of the sets,Ti,k , will be able to handle T i These tasks will be referred

to as ‘sub-macro tasks’.

For illustration, consider a mission that requires a land-based gathering task to bringobjects to a point A, and the transportation of these objects from point A to B across abody of water These two tasks may be specified as

Task dependence of T2 on the completion of T1 is also reflected by the dependence setafter ‘&’ in its specification.

Expected Maximum Task Durations

The expected maximum duration of a task, t d,i, is specified by the user When the task

is not completed after t d,i, it is an indicator to the robots that either (i) the sub-teamassigned to the task may have encountered some problems and have possibly failed, or

(ii) none of the robots are doing the task Such tasks will be referred to as lapsed tasks.

This triggers a reallocation, either replacing the current sub-team completely with anew team, or enlarging the sub-team After the reorganization of the robot team, the

deadline will be reset, and the new team will be given t d,i to complete the task

Expressiveness of Representation

As mentioned previously, the representation presented in this section aims to streamlinethe task specification process from the human user to the robot team, in situations whereinformation may be severely lacking Therefore, this knowledge constraint limits thedescription of overly complex tasks that can involve finer, more detailed task specifi-cations In exchange, the representation used here allows for faster and more efficientrepresentation, and (as will be described in the later sections) easier use by the robotsfor fault diagnosis and evaluation