modeling and planning with robust hybrid automata
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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) - PowerPoint PPT PresentationTRANSCRIPT
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
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(hx,u))
HoverForward flight
Steady left turn
Steady right turn
Example of planning in a free environment
0 5 10 15 20 25 30 35 40-300
-200
-100
0
100
200
300
400
actual positionactual velocitycommanded 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 ofCooperating Explorers
Programmers and operators must reason through system-wide interactions to :
• select deadlinesselect deadlines• select timing select timing
constraintsconstraints• allocate resourcesallocate resources
Managing Interactions for Cooperation
• select among select among redundant redundant proceduresprocedures
• 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-theoreticTemporal 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
HOMEHOME
RENDEZVOUSRENDEZVOUS RESCUERESCUE AREAAREA
Diverge
RESCUE LOCATIONRESCUE LOCATION
MEETING POINTMEETING POINT
Station: ABC
Station: XYZ
ONETWO
Enroute Activity:
RendezvousRendezvous Rescue AreaRescue Area
Corridor 2
Corridor 1
Corridor 3
Enroute
3
1
4 5
8
9 10
13
2
6 7 11 12
425
440
30
1
0
0
0
0 0
0
0
0
0
[450,540]
price = 425
price = 425
price = 440
price = 0
price = 0
price = 0
price = 30 price = 0
price = 1 price = 0
price = 0
price = 0
0price = 425
Path P = 1 3 4 5 8
9 10
11 12
13 2
Extend Path
Enroute Activity:
• Least cost threads of execution generated by extended auction algorithm
Start Node : 1End Node: 2
Temporal planning is combined with randomized path planning to find a collision free corridor
4 5
xinit
Path 1
xgoal
Xobs
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
TargetAdversary
Agents
Two-agent gameOne agent gets to target fastPure strategy
Agent
Single-agent gameGet to target fastRequires 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