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Modeling and Planning with Robust Hybrid Automata

Modeling and Planning with Robust Hybrid Automata. Cooperative Control of Distributed Autonomous Vehicles in Adversarial Environments 2001 MURI: UCLA, CalTech, Cornell, MIT Dahleh/Feron/Williams May 14, 2001 UCLA. Investigators Dahleh Feron Massaquoi Williams. Students Z.-H. Mao (PhD)

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Modeling and Planning with Robust Hybrid Automata

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  1. Modeling and Planning with Robust Hybrid Automata Cooperative Control of Distributed Autonomous Vehicles in Adversarial Environments2001 MURI: UCLA, CalTech, Cornell, MIT Dahleh/Feron/Williams May 14, 2001 UCLA

  2. Investigators Dahleh Feron Massaquoi Williams Students Z.-H. Mao (PhD) G. Kotsalis (PhD) K. Santarelli (PhD) T. Schouwenaars (PhD) M. Valenti (PhD) A. Walcott (PhD) Brief update on MIT status

  3. Outline • Robust Hybrid Automaton concepts • Model-Based Programming of autonomous explorers • Game-theoretic concepts

  4. Problem Formulation • Basic problem for autonomous vehicles/robots: • Generate and execute a (sub)-optimal motion plan, satisfying given boundary conditions, flight envelope and obstacle avoidance constraints, in a dynamic and uncertain environment • Nonlinear control • Steering of underactuated, non-holonomic systems • Stabilization/tracking for nonlinear systems • Flight envelope protection • Robotics/Artificial Intelligence • Path planning (obstacle avoidance) for non-holonomic dynamical systems • Computer science/Software Engineering • Hard real-time constraints • Research supported by AFOSR, Draper, ONR

  5. Hierarchical decomposition • Need to introduce a hierarchical structure to achieve computational tractability, e.g. (Stengel, 93): • “Strategic layer”:Task scheduling, goal planning • “Tactical layer”:Guidance, navigation • “Reflexive layer”: Tracking, control, estimation • General hierarchical systems, derived from arbitrary decompositions, can be extremely hard to analyze and verify • Design a hierarchicalsystem such that it offers safety and performance guarantees by construction • Analysis and verification: robustness analysisproblem • Consistent hierarchical system

  6. System Quantization • Quantization of feasible trajectories into trajectory primitives • formalization of the concept of “maneuver” • Consistent abstraction of the system dynamics • Hierarchical decomposition of the control tasks: • Maneuver sequencing (guidance, trajectory planning) • Maneuver execution (control, trajectory tracking) • Control synthesis: • Build a “maneuver library” (with feedback control) • Behavioral programming: Solve a mixed-integer program on a “small” space • Hybrid control system with performance and safety guarantees by design.

  7. Maneuver Automaton • Two classes of trajectory primitives ( trim trajectories + maneuvers ) • Construct a “Maneuver Library”, with a finite number of primitives • Generate trajectories by sequencing such primitives • All generated trajectories are solutions of the system’s diff. equations • All generated trajectories satisfy the flight envelope constraints (assuming F(x,u)=F(Yhx,u)) Steady left turn Hover Forward flight Steady right turn

  8. actual position actual velocity commanded position "maneuver switch" Example of planning in a free environment 400 300 200 100 0 -100 -200 -300 0 5 10 15 20 25 30 35 40

  9. Model-based Autonomy • How do we program explorers that reason quickly and extensively from commonsense models? • How do we coordinate heterogeneous teams of robots -- in space, air and land -- to perform complex exploration? • How do we couple reasoning, adaptivity and learning to create robust agents? • How do we incorporate model-based autonomy into every day, ubiquitous computing devices?

  10. Model-based Autonomy Programmers generate breadth of functions from commonsense models in light of mission goals. • Model-based Reactive Programming • Programmer guides state evolution at strategic levels. • Commonsense Modeling • Programmer specifies commonsense, compositional models of spacecraft behavior. • Model-based Execution Kernel • Reason through system interactions on the fly,performing significant search & deduction • within the reactive control loop.

  11. Model-based Programming ofCooperating Explorers

  12. Managing Interactions for Cooperation Programmers and operators must reason through system-wide interactions to : • select among redundant procedures • Evaluate outcomes • Plan contingencies • select deadlines • select timing constraints • allocate resources

  13. c • If c next A • Unless c next A • A, B • Always A • Choose reward • A in time [t-,t+] Decision-theoretic Temporal Planner Model-based Cooperative Programming • Model-based Programs • Specify team behaviors as concurrent programs. • Specify options using decision theoretic choice. • Specify timing constraints between activities. • Model-based Execution • Achieves correctness and economy • Pre-plans threads of execution that are optimal and temporally consistent. • Responds at reactive timescales • Perform planning as graph search

  14. Mission Scenario TWO ONE HOME Enroute RENDEZVOUS RESCUEAREA Station: ABC Diverge Station: XYZ RESCUE LOCATION MEETING POINT

  15. Enroute Activity: Enroute Corridor 2 Rendezvous Rescue Area Corridor 1 Corridor 3

  16. Enroute Activity: • Least cost threads of execution generated by extended auction algorithm price = 425 price = 0 1 [450,540] 2 0 0 Extend Path 4 425 5 9 30 10 0 0 0 0 price = 425 price = 0 price = 30 price = 0 8 13 3 price = 0 price = 0 price = 425 0 0 0 0 6 440 7 11 1 12 price = 440 price = 0 price = 1 price = 0 9  10   13  2 Path P = 1  3  4  5  8   11  12 Start Node : 1 End Node: 2

  17. Temporal planning is combined with randomized path planning to find a collision free corridor Path 1 xinit xgoal Xobs 4 5

  18. Game-theoretic concepts(Feron and DeMot) • Problem: • Navigation of a number of vehicles to a target • Target located at a position that is known with respect to the vehicles or in a known region with a certain known probability distribution • Vehicles have visual information about a local part of the environment • Adversarial, unknown environment • Issues: • Many cooperating vehicles vs. single vehicle missions • Continuously updating available information • Approach: • Game theory

  19. Illustrative Example ? Agent Agents Two-agent game One agent gets to target fast Pure strategy Single-agent game Get to target fast Requires mixed strategy Obstacle Adversary Target

  20. Initial Observations • Multiple vehicles yield pure strategies whereas for single vehicles a mixed strategy is optimal • Continuously information updates? • Applicability of certainty equivalence principles • (eg Basar & Bernhardt, Birkhauser, 1991) • More general setting: nature chooses the position of an arbitrary amount of obstacles in the unexplored areas - Need for well-defined models

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