1. Multi-vehicle Cooperative Control Raffaello D’Andrea Mechanical & Aerospace Engineering Cornell University u Hierarchical Decomposition u Example: RoboCup u Concluding Remarks OUTLINE

2. Hierarchical Decomposition Objective: Develop hierarchy-based tools for designing complex, multi-asset systems in uncertain and adversarial environments MAIN IDEAS: System level decomposition Bottom up design Simplification of models via relaxations and reduction Propagation of uncertainty to higher levels Adoption of heuristics, coupled with verification

3. Example: RoboCup u International competition: cooperation, adversaries, uncertainty –1997: Nagoya Carnegie Mellon –1998: Paris Carnegie Mellon –1999: Stockholm Cornell –2000: Melbourne Cornell –2001: Seattle u Involvement –Universities, Research Labs, Companies Cornell

4. Example

5. Competition Highlights (1999)

6. ROBOT K K INTELLIGENCE AND CONTROL Wheel velocity System Level Decomposition

7. Bottom Up Design Relaxation and Simplified Dynamics: ROBOT K Robust Control Design Restrict possible motions, design low level system to behave like simplified dynamical model

8. Mid-Level Control Trajectory Primitives: minimum time, minimum energy minimum time

9. STRATEGY TRAJECTORY GENERATION LOCAL CONTROL DESIRED FINAL POSITIONS AND VELOCITIES, TIME TO TARGET FEASIBILITY OF REQUESTS DESIRED VELOCITIES Intelligence and Control Current design: finite state machine Obstacle avoidance: Frazzoli, Feron, Dahleh no adaptation no formal methods

11. BACK-PASS PASS-PLAY

12. Example: Goalie

13. Formation Flight Testbed “ satellite” type of applications ( Wolfe, Chichka and Speyer ‘96) MAVs and UAVs, extend range MOTIVATION Use upwash created by neighbouring craft to provide extra lift

14. Formation Flight test bed 5 wings in low speed wind tunnel roll and translation along y axis

15. Concluding Remarks Relaxation, Restriction COMPLEXITY PERFORMANCE 1

16. Robust Control Design... Hierarchical Design

17. Current Activities Propagation of uncertainy/mismatch Randomized Algorithms for planning (MIT) Game Theoretic tools (delayed information) Verification Human in the loop New test-beds