A GENERAL FRAMEWORK FOR MULTI-AGENT TASK SELECTION JAMES FU GUO MING B. Eng (Second Upper) National University of Singapore A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2012 Declaration I hereby declare that the thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. James Fu Guo Ming 27 July 2012 i Summary Multi-agent (or multi-robot) systems have many advantages over single agent systems, which include greater robustness, reliability, scalability and economy. Having multiple agents allow the use of simple agents. The lack of sophistication and capabilities of individual agents is more than made up for by numbers. Together, working in coordination and cooperation, multi-agent systems can solve problems that are difficult or impossible for an individual agent. Multiplicity also adds a layer of redundancy to the system. While it has its advantages, there are many challenges to making the agents work in coordination and cooperation to achieve an effective multi-agent system. One of these challenges is task allocation or how each agent should select and execute its task to maximize overall effectiveness of the whole multi-agent system. Here, we propose a general framework, making use of the idea of Voronoi Tessellations, for multi-agents to distributively perform task selection. Agents make decisions based only on local information. Agents dynamically determine their mutually exclusive local Region of Influence before task selection in their region. As such, the proposed framework is applicable to a dynamic environment. A Utility Function, based on the heterogeneity of the multi-agent system, task replicability, and agent specialization, is developed as a task performance measure for agents to use during task selection. The general framework was applied to two common problems - exploration and patrolling. While exploration requires a single instance of information discovery, patrolling is the continuous process of information update. An example of the former is a search and rescue mission to locate all persons in distress while the mission of detecting intruders in a strategic area will require a round-the-clock patrolling of that area. A proposed Local Voronoi Decomposition (LVD) Algorithm, adapted from the proposed general framework, was implemented for the exploration of an unknown environment. Agents are able to perform online distributive task selection based purely on local ii information. The Voronoi regions eliminate the occurrence of agents selecting the same area for exploration at the same time. The results show an interesting emergence of cooperative behaviours, such as an overall systematic exploration of the free space by the multiple agents, thereby minimizing exploration path overlaps. As the LVD Algorithm does not require a pre-processing of the map, it is able to work well in a dynamically changing map with changing number of agents. Benchmarked against two other wellknown algorithms, the Ants Algorithm and the Brick&Mortar Algorithm, on various test maps, the performance of LVD is clearly superior and is close to the theoretical best. A proposed Probabilistic Ants (PAnts) Algorithm, based on the proposed general framework, was implemented in the patrolling of an unknown environment. The proposed strategy makes use of virtual pheromone traces, which act as potential fields, to guide agents toward regions which have not been visited for a long time. Decision making is done distributively in a probabilistic manner based on an agent’s local pheromone information. Benchmarked against the traditional Ant Algorithm as well as our proposed variant of this for various test maps, PAnts showed a clearly better performance. Keywords: Multi-Agent System, Task Allocation, Task Selection, Local Voronoi Decomposition, Utility Function, Exploration, Patrolling. iii Acknowledgements I thank God for the completion of this thesis. I thank everyone, including family and friends, who have been instrumental to the course of my research. While I have learnt much from a technical standpoint, many more life-lessons have been learnt along the way. I am deeply grateful to my advisor, Prof. Marcelo H. Ang. Jr, for his personal guidance and mentorship, as well as being very patient with my progress over the years. I am thankful for the many profitable discussion sessions, especially on occasions where my work was apparently stuck in some local minima and he was there to provide the much needed perturbation. It is also a most wonderful experience to have some of the discussions at his home and to have the occasional meal with his family, Carol, Mark, Kyle and Ivan. I dedicate this thesis to my parents. They have undoubtedly showed their love and remained supportive throughout the course of my studies. I thank my Dad for the much given advice and even helping to brainstorm in certain areas of my research work. I thank my Mom for showing much concern throughout the years. With the completion of this thesis, I am glad she now has one less thing to worry about. I thank my friends in the Control and Mechatronics Lab for invaluable discussions, sharing of ideas, and just being really good friends to make this whole journey a much more pleasant one, and in particular, Gim Hee, Niak Wu, Mana, Tomek, Weiwei, and Huan. It is always comforting to know that there is someone to have dinner with when I am working late in the lab! A special shout-out goes to Tirtha. A simple question of ”James, are you familiar with Voronois?” one day sparked off a whole series of my research work. Last, but most certainly not the least, I thank my wife, Angeline, for the emotional and spiritual support, and the much needed companionship over the years. I am very iv glad that even through all these years, I don’t recall her asking me the most dreaded question any Ph.D. student could be asked, ”how’s your research going?”. I also thank my two daughters, Olivia and Chloe, for bringing much colour and laughter into my life. Daddy is going to have more time to play with you now! v Contents Declaration i Summary ii Acknowledgments iv Table of Contents vi List of Tables x List of Figures xi Systems with Multiple Robots 1.1 Challenges of Multi-Agent Systems . . . . . . . . . . . . . . . . . . . 1.1.1 Communications . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Heterogeneity vs. Homogeneity . . . . . . . . . . . . . . . . . 1.1.3 Coordination and Cooperation . . . . . . . . . . . . . . . . . . 1.1.4 Task Allocation and Execution . . . . . . . . . . . . . . . . . . 1.1.5 Dynamic Reconfigurability . . . . . . . . . . . . . . . . . . . . Applications of Multi-Agent Systems . . . . . . . . . . . . . . . . . . 1.2.1 The Exploration Problem . . . . . . . . . . . . . . . . . . . . . 1.2.2 The Patrolling Problem . . . . . . . . . . . . . . . . . . . . . . 1.3 Scope of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 vi Contents Literature Survey 10 2.1 Self-Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Multi-Agent Task Selection . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.2 Swarm Intelligence . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.3 Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . 15 The Exploration Problem . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.1 Frontier-Based Approach . . . . . . . . . . . . . . . . . . . . . 17 2.3.2 Potential Field Approach . . . . . . . . . . . . . . . . . . . . . 18 2.3.3 Ants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 The Patrolling Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.1 Watchman Route Problem (WRP) . . . . . . . . . . . . . . . . 20 2.4.2 Cyclic Strategies . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.3 Partition-Based Strategies . . . . . . . . . . . . . . . . . . . . 26 2.4.4 Reinforcement Learning . . . . . . . . . . . . . . . . . . . . . 26 2.4.5 Heuristic Agents . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4.6 Ant Colony Optimization . . . . . . . . . . . . . . . . . . . . . 27 2.3 2.4 Dynamic Local Voronoi Decomposition for Multi-Agent Task Selection 29 3.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.1.1 The Task Environment . . . . . . . . . . . . . . . . . . . . . . 31 3.1.2 The Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 The General Framework . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.1 Voronoi Tessellations . . . . . . . . . . . . . . . . . . . . . . . 36 3.2.2 The Agent Architecture . . . . . . . . . . . . . . . . . . . . . . 36 3.2.3 Region of Influence . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.4 Defining Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2.5 Task Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.6 Local Voronoi Decomposition Algorithm . . . . . . . . . . . . 46 Utility Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2 3.3 vii Contents 3.4 Time, tˆ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.3.2 Resources, rˆ . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.3 Appropriateness, a ˆ . . . . . . . . . . . . . . . . . . . . . . . . 57 3.3.4 Priority, pˆ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.3.5 Feasibility, fˆ . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Local Voronoi Decomposition for Multi-Agent Exploration 64 4.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.2 Existing Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2.1 Ants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2.2 Brick&Mortar . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.3 3.3.1 Local Voronoi Decomposition (LVD) Algorithm for Multi-Agent Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3.1 Local Voronoi Decomposition (LVD) . . . . . . . . . . . . . . 69 4.3.2 The Search Mode . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.3.3 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.3.4 Emergent Cooperative Behaviour . . . . . . . . . . . . . . . . 74 4.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Dynamic Local Voronoi Decomposition for Multi-Agent Patrolling 82 5.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.2 Limitations of Currently Used Strategies . . . . . . . . . . . . . . . . . 86 5.3 Existing Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.3.1 Ants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.3.2 Biased Ants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.4 Probabilistic Ants (PAnts) Algorithm for the Multi-Agent Patrolling Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.4.1 90 Pheromone Deposit and Decay . . . . . . . . . . . . . . . . . . viii Contents 5.4.2 Probabilistic Decision Making . . . . . . . . . . . . . . . . . . 91 5.4.3 The PAnts Algorithm . . . . . . . . . . . . . . . . . . . . . . . 91 5.4.4 Selection of Parameters . . . . . . . . . . . . . . . . . . . . . . 94 5.4.5 Robustness and Adaptability . . . . . . . . . . . . . . . . . . . 95 5.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Conclusion 105 6.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Bibliography 112 ix Bibliography [68] A. 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Ant Task Allocation (ATA) algorithm proposed by Du et el [76], agents probabilistically determine their tasks and update their thresholds upon task completion Unlike ACO, ATA allows for dynamic task allocation where new tasks may arise and agents using ATA keeps its own response 14 2.3 The Exploration Problem threshold records as opposed to ACO using a central database 2.2.3 Machine Learning Machine... term task can encapsulate the idea of a ”role”, as ultimately, it boils down to the agent performing tasks A ”role” can be seen as a collection of subtasks 2.2.1 Negotiation Most multi- agent systems make use of intentional cooperation [45] where multi- agents cooperate explicitly through communication and negotiation [46] In the centralised multi- agent negotiation approach for collaborative air traffic... Thesis of these challenges, namely that of task allocation Task allocation is a fundamental issue in every multi- agent system and significantly affects the overall effectiveness of the system Many task allocation strategies are mission specific One strategy may work well in a specific case, but not so in others This thesis thus focuses on developing a general framework for multi- agent task allocation which... used for the Patrolling Problem 1.4 Contributions A general framework, utilising the concept of Local Voronoi Decomposition (LVD) and a Utility Function, has been developed for multi- agent task selection This framework allows agents to make decisions on task selection, based on local information, in a completely distributed manner This framework is robust to changes and adaptable to a dynamically changing... allocation” can refer to a supervisor or some authority having the final say on all agents’ allocated tasks In other cases, task allocation” can refer to the individual agent s cognition of self-allocation of tasks This thesis focuses on the case where the decision making for task allocation is carried out distributively, i.e., each agent determines for itself which task it should perform next To avoid... able to have the tasks performed in a highly coordinated manner with minimal reliance on communications 1.1 Challenges of Multi- Agent Systems While the use of multi- agents has many advantages over their single agent counterpart, managing and coordinating a whole team of robots to execute tasks efficiently, effectively and successfully can be very challenging as there are many factors and variables which... varying functions and capabilities) A homogeneous multi- agent system is generally easier to manage and to be catered for because it is easier to model such a system In practical cases, multi- agent systems are rarely homogeneous especially in environments where the tasks that are required to be performed are different In such environments, having agents all identical to one another would mean that each... Blackboard architecture and the CNP According to Msoteo and Montano [54], the first robot implementation of the auctionbased scheme was MURDOCH [55] MURDOCH has been demonstrated in a loosely coupled task allocation scenario where all available tasks can be performed by single agents, as well as in a coordinated box-pushing scenario The Cooperative Assignment of Simultaneous Tasks (CAST) auction is a. .. obstacles 2.2 Multi- Agent Task Selection A task can be defined as a subgoal which is required to ba achieved to accomplish the overall mission required in the environment To have good self-organisation in a multiagent system, ensuring efficient task selection by individual agents becomes a challenging problem in a distributed setting because of the dynamic nature of the environment 11 2.2 Multi- Agent Task . some cases, task allocation” can refer to a supervisor or some authority having the final say on all agents’ allocated tasks. In other cases, task allocation” can refer to the individual agent s. challenges, namely that of task allocation. Task allocation is a fundamental issue in every multi- agent system and significantly affects the overall effectiveness of the system. Many task allocation. in a probabilistic manner based on an agent s local pheromone information. Benchmarked against the traditional Ant Algorithm as well as our proposed variant of this for various test maps, PAnts