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Multi-Vehicle Cooperative Control for RoboFlag Test-bed

This paper discusses the progress made on the RoboFlag test-bed and presents a MLD approach to multi-vehicle cooperation, obstacle avoidance in dynamic environments, and path planning with uncertainty.

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Multi-Vehicle Cooperative Control for RoboFlag Test-bed

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  1. Multi-vehicle Cooperative ControlRaffaello D’AndreaMechanical & Aerospace Engineering Cornell University • Progress on RoboFlag Test-bed • MLD approach to Multi-Vehicle Cooperation • Obstacle Avoidance in Dynamic Environments • Path Planning with Uncertainty OUTLINE

  2. SYSTEMS OF INTEREST CENTRALCONTROL SENSE GLOBALSENSING PROCESSING HIGH LEVELDECISION MAKING COMMS COMMS COMMUNICATIONS NETWORK COMMS COMMS COMMS COMMS COMMS ACTUATE COMMS HUMANINTERFACE LOW LEVELCONTROL HIGH LEVELCONTROL VEHICLE SENSE

  3. What is RoboFlag?

  4. RoboFlag System Vision computer Arbiter Overhead cameras Computers for each entity . . . . . RF transceiver

  5. SOFTWARE ARCHITECTURE LOW LEVEL CONTROL INTERFACE WIRELESSINTERFACE LOCAL MACHINE VISIONBASEDGLOBAL ANDLOCAL SENSING VEHICLEHIGH LEVELCONTROL VEHICLEHIGH LEVELCONTROL VEHICLELOW LEVELCONTROL VEHICLELOW LEVELCONTROL COMMUNICATIONS NETWORKSIMULATOR GLOBAL ARBITER HUMANINTERFACE CENTRALCONTROL

  6. HARDWARE ARCHITECTURE WIRELESSHARDWARE HARDWARE PORT INTERFACE ANDARBITRATIONCOMPUTER MACHINE VISIONCOMPUTER HARDWARE PORT WIRELESSHARDWARE LOCAL LOCAL VEHICLE(S)HIGH LEVELCONTROL COMPUTER VEHICLE(S)HIGH LEVELCONTROL COMPUTER VEHICLE HUMAN INTERFACECOMPUTER CENTRAL CONTROLANDCOMMUNICATIONS NETWORKCOMPUTER VEHICLE HUMAN INTERFACECOMPUTER

  7. SIMPLE COMMUNICATIONS NETWORK MODEL: Bi,j data units buffer 0 Bi,j data units buffer Li,j -1 Bi,j data units buffer Li,j Ui Uj

  8. People • Michael Babish (Research Support) • Andrey Klochko (Programmer) • JinWoo Lee (Post-Doc) • 30 UG and M.Eng. students

  9. The RoboFlag Drill Start out simple and work up (Earl and D’Andrea ‘02) • Attacking robots are drones directed toward defense zone • Defending robots want to intercept attackers before they enter the defense zone • Constraints: defenders must avoid collisions and must not enter the defense zone; defenders have limited control authority

  10. The RoboFlag Drill: Modeling Model drill as a mixed logical dynamical system subject to constraints (MLD system) (Bemporad and Morari ‘99) Defender dynamics Constraints

  11. The RoboFlag Drill: Modeling Attacker dynamics Constraints

  12. The RoboFlag Drill: MLD form Converting logic expressions into inequalities using HYSDEL (Torrisi et al. ‘00) we can write system in MLD form

  13. The RoboFlag Drill Strategy synthesis using an optimization approach (Bemporad and Morari ‘99) Using this modeling approach the cost can easily model a wide array of objectives We take the cost to be the total score of the drill Objective: Find control input that minimizes the cost subject to the dynamics and constraints

  14. The RoboFlag Drill: Results The optimization problem reduces to a mixed integer linear program (MILP) • 3 defenders, 8 attackers • MILP problem: • 4040 integer variables • 400 continuous variables • 13580 constraints • CPLEX solves in 244 seconds on Linux PIII 866MHz

  15. The RoboFlag Drill FUTURE WORK: • Better modeling to avoid discretization in time • Speed up solution time • Perform optimization repeatedly (MPC) to obtain strategy for dynamically changing and uncertain environments • Add more components from the RoboFlag game (limited sensor footprint, latency and bandwidth limitations, etc.) • Decentralization

  16. People • Matthew Earl (Graduate Student)

  17. Obstacle Avoidance in Dynamic Environments Objective: Computationally fast algorithms for path planning in multi-agent adversarial environments with delayed information. APPROACH • Game Theoretic:Avoiding arational adversary in a delayed • environment can be modeled as anon-cooperative imperfect • information game . Trajectory generation is an outcome of • such an approach. • Randomized Algorithm:This algorithm uses an existing • trajectory generation routine to generate feasible paths in the • presence of obstacles. One way to incorporate the effect of delay • is to associate with each obstacle a reachability regime over the • delayed steps.

  18. Randomized Algorithm Terminology: • Primary Node: An equilibrium configuration belonging to the state-space of the agent. • Secondary Node: An element of the state space of the agent which lies on the path from the initial point to a primary node.

  19. Randomized Algorithm Main Idea: (Frazzoli,Dahleh & Feron ‘00) • The main idea is to search for random intermediate points in the state-space which might generate a feasible path to the destination. A feasible path being the one without any • collisions. • Among all the feasible paths the one with the lowest cost (eg. time) is then chosen. • The underlying assumption in using this algorithm is that one already has a way of generating trajectories in the absence of obstacles.

  20. Initialize tree with starting position Randomly generate primary node and also a start point from the already generated tree Is Path(start,primary) feasible No yes Generate random secondary points and add them to the tree No Is Path(secondary, destination) feasible yes Feasible Path found, update costs Randomized Algorithm Main Idea and Implementation: • This algorithm is probabilistically complete that is it returns a feasible path if there exists one, else it returns failure, in the probabilistic sense. • Contrary to the tree data structure that was used by the author to store the data, we use a grid data structure which takes a large storage space but has faster access time.

  21. Future Work • Implementing the randomized algorithm framework • for multiple agents in a centralized fashion, which would • be a relatively easy extension to the present • algorithm by increasing the state-space dimension. • Developing a protocol enabling the decentralization • of the above computation. PROVE that the protocol achievesthe desired objective.

  22. People • Pritam Ganguly (Graduate Student)

  23. Path Planning under Uncertainty Motivation: • Uncertainty in information leads naturally to probabilistic approach MAIN IDEAS: • Construction of probability map from available data • Measurement data • A priori statistics • Convert the probability map to a directed graph • Path planning by solving shortest path problem in digraph

  24. Probability Map Building • Measurement update by measured data sensor characteristics • Time update by a priori statistics of environment environment statistics • Map building

  25. Conversion to Digraph 0.015 0.02 0.013 0.02 0.015 0.013 0.015 0.01 0.02 0.015 0.01 0.013 0.013 0.013 0.001 0.001 0.013 0.001 ProbabilityMap Digraph

  26. Simulation Dynamic Replanning Case with Multiple Vehicles

  27. Contribution and Future Work Contribution: • Building a probability map in uncertain dynamic environments • Path planning of multiple vehicles in uncertain dynamic environments based on probability map Future Works: • Finding an algorithm to efficiently integrate map building and path planning • Consideration of time and velocity in path planning for multiple vehicles • Consideration penalty for frequent acceleration and deceleration

  28. People • Myungsoo Jun (Post-Doc) • Atif Chaudry (Graduate Student)

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