1. Path Planning for Multi Agent Systems by Kemal Kaplan

2. Multi Agent Systems (MAS) A multi-agent system is a system in which there are several agents in the same environment which co-operate at least part of the time. A multi-agent system is a system in which there are several agents in the same environment which co-operate at least part of the time. Complexity of the path planning systems for MAS (MASPP) increase exponentially with the number of moving agents. Complexity of the path planning systems for MAS (MASPP) increase exponentially with the number of moving agents.

3. Problems with MASPP Possible problems of applying ordinary PP methods to MAS are, Possible problems of applying ordinary PP methods to MAS are, Collisions, Collisions, Deadlock situations, etc. Deadlock situations, etc. Problems with MASPP are, Problems with MASPP are, Computational overhead, Computational overhead, Information exchange, Information exchange, Communication overhead, etc. Communication overhead, etc.

4. Classification of Obstacles Usually other agents are modelled as unscheduled, non-negotiable, mobile obstacles in MASPPs. Usually other agents are modelled as unscheduled, non-negotiable, mobile obstacles in MASPPs. Category of Obstacles from Arai et. al. (89) Category of Obstacles from Arai et. al. (89)

5. Proposed Techniques Centralised Approaches Centralised Approaches Decoupled Approaches Decoupled Approaches Combined Techniques Combined Techniques

6. Centralised Approaches All robots in one composite system. All robots in one composite system. +Find complete and optimum solution if exists. +Use complete information -Computational complexity is exponential w.r.t the number of robots in the system -Single point of failure

7. Decoupled Approaches First generate paths for robots (independently), then handle interactions. First generate paths for robots (independently), then handle interactions. +Computation time is proportional to the number of neighbor robots. +Robust - Not complete -Deadlocks may occur

8. Combined Techniques Use cumulative information for global path planning, use local information for local planning Use cumulative information for global path planning, use local information for local planning “Think Global Act Local”

9. Utilities For Combined Techniques Global Planning Utilities: Global Planning Utilities: The aim is planning the complete path from current position to goal position. The aim is planning the complete path from current position to goal position. Any global path planner may be used. (e.g. A*, Wavefront, Probabilistic Roadmaps, etc.) Any global path planner may be used. (e.g. A*, Wavefront, Probabilistic Roadmaps, etc.) Requires graph representation achieved by cell decomposition or skeletonization techniques. Requires graph representation achieved by cell decomposition or skeletonization techniques.

10. Utilities For Combined Techniques (II) Local Planning Utilities: Local Planning Utilities: The aim is usally avoid obstacles. However, cooperation should be used also. The aim is usally avoid obstacles. However, cooperation should be used also. Any reactive path planner can be used. (e.g. PFP, VFH, etc.) Any reactive path planner can be used. (e.g. PFP, VFH, etc.) No global information or map representaion required. Decisions are fast and directly executable. No global information or map representaion required. Decisions are fast and directly executable.

11. Improvements for Combined Techniques Priority assignment Priority assignment Aging (e.g. the forces in a PFP varies in case of deadlocks) Aging (e.g. the forces in a PFP varies in case of deadlocks) Rule-Based methods (e.g. left agent first, or turn right first) Rule-Based methods (e.g. left agent first, or turn right first) Resource allocation (leads to suboptimal solutions) Resource allocation (leads to suboptimal solutions)

12. Improvements for Combined Techniques (II) Robot Groups Robot Groups A leader and followers A leader and followers Many leaders (or hierarchy of leaders and experience) Many leaders (or hierarchy of leaders and experience) Virtual leader Virtual leader Virtual dampers and virtual springs Virtual dampers and virtual springs Assigning dynamic information to edges and vertices Assigning dynamic information to edges and vertices

13. Possibe MAS environmets for MASPP Robocup 4-Legged League Robocup 4-Legged League Robocup Rescue Robocup Rescue SIMUROSOT, MIROSOT (?) SIMUROSOT, MIROSOT (?) Games (RTS, FPS) Games (RTS, FPS)......

14. MASPP Example [ARAI & OTA 89] Measures Measures Computational Load Computational Load Total length of the generated trajectories Total length of the generated trajectories The radius of curvature of the generated trajectories The radius of curvature of the generated trajectories Total motion time Total motion time Preferred measure is the first one Preferred measure is the first one

15. MASPP Example [ARAI & OTA 89] Properties of agents Properties of agents

16. MASPP Example [ARAI & OTA 89] Problem 1 Problem 1

17. MASPP Example [ARAI & OTA 89] Problem 2 Problem 2

18. MASPP Example [ARAI & OTA 89] Virtual Impedance Method Virtual Impedance Method

19. MASPP Example [ARAI & OTA 89]

21. Questions?kaplanke@boun.edu.tr