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

Brief update on MIT status 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)

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

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

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 hierarchical system such that it offers safety and performance guarantees by construction –Analysis and verification: robustness analysis problem Consistent hierarchical system

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.

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(  h x,u)) Hover Forward flight Steady left turn Steady right turn

Example of planning in a free environment actual position actual velocity commanded position "maneuver switch"

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?

Programmers generate breadth of functions from commonsense models in light of mission goals. Model-based Autonomy 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.

Model-based Programming of Cooperating Explorers

Programmers and operators must reason through system-wide interactions to : select deadlinesselect deadlines select timing constraintsselect timing constraints allocate resourcesallocate resources Managing Interactions for Cooperation select among redundant proceduresselect among redundant procedures Evaluate outcomesEvaluate outcomes Plan contingenciesPlan contingencies

Model-based Cooperative Programming 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 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

Enroute Mission Scenario HOME RENDEZVOUS RESCUE AREA Diverge RESCUE LOCATION MEETING POINT Station: ABC Station: XYZ ONETWO

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

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

Temporal planning is combined with randomized path planning to find a collision free corridor 45 x init Path 1 x goal X obs

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

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

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