COORDINATION and NETWORKING of GROUPS OF MOBILE AUTONOMOUS AGENTS

1. COORDINATION and NETWORKING of GROUPS OF MOBILE AUTONOMOUS AGENTS

2. COOPERATIVE CONTROL Yale is the lead institution on a cross-disciplinary NSF project {with Harvard, Princeton, U. of Washington} aimed at understanding how various animal groups such as fish schools and bird flocks coordinate their collective motions and how groups of mobile autonomous agents such as AUVs might use these biological principles to collectively perform useful tasks such as data gathering, search and rescue, in a safe, cooperative, and coordinated manner. A FISH WHORL The Grouper

3. ROADMAP 1. Rigid Graph Theory “Maintaining Vehicle Formations Using Rigid GraphTheory” “Sensor Localization in Large Ad Hoc Communication Networks” 2. Emergent Behavior The “Flocking Problem” The “Multi-Agent Rendezvous Problem”

4. Maintaining Vehicle Formations Using Rigid Graph Theory By an nvehicleformation is meant collection of n mobile autonomous agents {i.e., robots} moving through real 2 or 3 space. Maintaining a formation means making sure that the distance between each pair of agents remains {nominally} unchanged over time. Formation maintenance is typically achieved by requiring some, but not all agent pairs to maintain fixed distances between them. We’ve developed a framework based on the theory of “rigid graphs” from classical mechanics {Cayley, Maxwell,…} for devising provably correct procedures for so maintaining very large formations.

5. Sensor Localization in Large Ad Hoc Communication Networks sensors Each Sensor: Does there exist a unique solution to the problem? 1. is fixed in position. 2. can communicate with neighbors. 500m 3. knows distance from each neighbor. Some sensors know their positions in world coordinates. Localization problem is for each sensor to determine its position in world coordinates by communicating with its neighbors.

6. Sensor Localization in Large Ad Hoc Communication Networks Does there exist a unique solution to the problem? Answer is central to: • determining required • topology of the network. 2. the devising of provable correct distributed localization algorithms. We introduced rigid graph theory to the networking community and settled the uniqueness question. Localization problem is for each sensor to determine its position in world coordinates by communicating with its neighbors.

7. THE FLOCKING PROBLEM i i= heading s = speed s In a recent Phy. Rev. Letters paper Vicsek et al. simulated a flock of n agents {particles} all moving in the plane at the same speed s, but with different headings1, 2, …, n Each agent’s heading is updated using a local rule based on the average of its own current heading plus the headings of its “neighbors.” Vicsek’s simulations demonstrate that these nearest neighbor rules can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent’s set of neighbors changes with time. Using graph theory and the theory of non-homogeneous Markov chains we have provided a complete theoretical explanation for this observed behavior.

8. Bifrucation Vicsek’s Leader’s Neighbors Yellow Following Red Leader

9. r sensing region The Multi-agent Rendezvous Problem deals with set of n mobile autonomous agents which can all move in the plane. Each agent is able to continuously sense the relative positions of all other agents in its “sensing region” where by agent i’s a sensing region is meant a closed disk of radius r centered at agent i’s current position. Problem: Devise local control strategies, one for each agent, which without active communication between agents, cause all members of the group to eventually rendezvous at a single unspecified point. We have devised a provably correct solution to this problem which provides a framework for the development of a wide range of group maneuvers {e.g., forming Yale Marching Band formations} using decentralized control.

10. connected disconnected trapping

11. Concluding Remarks New data structures, models, etc.are needed to represent large groups of mobile autonomous agents at various degrees of granularity, for pur- poses of simulations, management, analysis, communication and control. Such representations will exploit tools from both graph theory and from thetheory of dynamical systems At least initially, individual agent descriptions usingsimple kinematic and dynamic models will suffice. System complexitywill stem more from thenumber of agent models being studied than from the detailed properties of the individual agent models. New concepts ofrobustness, stability, etc. are needed to understand such systems – to address issues such ascascade failure, security, reliability, coordination, etc.