Multi-vehicle Cooperative Control Raffaello D’Andrea Mechanical & Aerospace Engineering Cornell University u Progress on RoboFlag Test-bed u MLD approach to Multi-Vehicle Cooperation u Obstacle Avoidance in Dynamic Environments u Path Planning with Uncertainty OUTLINE

ACTUATE SENSE LOW LEVEL CONTROL HIGH LEVEL CONTROL COMMS VEHICLE SENSE COMMS PROCESSING GLOBAL SENSING COMMS HIGH LEVEL DECISION MAKING CENTRAL CONTROL COMMUNICATIONS NETWORK COMMS SYSTEMS OF INTEREST HUMAN INTERFACE COMMS

What is RoboFlag?

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

SOFTWARE ARCHITECTURE VEHICLE HIGH LEVEL CONTROL LOW LEVEL CONTROL INTERFACE COMMUNICATIONS NETWORK SIMULATOR WIRELESS INTERFACE CENTRAL CONTROL MACHINE VISION BASED GLOBAL AND LOCAL SENSING VEHICLE HIGH LEVEL CONTROL ARBITER VEHICLE LOW LEVEL CONTROL LOCAL GLOBAL HUMAN INTERFACE

HARDWARE ARCHITECTURE MACHINE VISION COMPUTER INTERFACE AND ARBITRATION COMPUTER WIRELESS HARDWARE CENTRAL CONTROL AND COMMUNICATIONS NETWORK COMPUTER VEHICLE(S) HIGH LEVEL CONTROL COMPUTER VEHICLE VEHICLE(S) HIGH LEVEL CONTROL COMPUTER HUMAN INTERFACE COMPUTER WIRELESS HARDWARE LOCAL HARDWARE PORT HUMAN INTERFACE COMPUTER

SIMPLE COMMUNICATIONS NETWORK MODEL: B i,j data units buffer L i,j B i,j data units buffer L i,j -1buffer 0 UiUi UjUj

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

The RoboFlag Drill 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 Start out simple and work up (Earl and D’Andrea ‘02)

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

The RoboFlag Drill: Modeling Attacker dynamics Constraints

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

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

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 constraints CPLEX solves in 244 seconds on Linux PIII 866MHz

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

People u Matthew Earl (Graduate Student)

Obstacle Avoidance in Dynamic Environments Objective: Computationally fast algorithms for path planning in multi-agent adversarial environments with delayed information. APPROACH Game Theoretic: Avoiding a rational adversary in a delayed environment can be modeled as a non-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.

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.

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.

Randomized Algorithm Feasible Path found, update costs Initialize tree with starting position Randomly generate primary node and also a start point node and also a start point from the already generated tree Is Path(start,primary) feasible yes Generate random secondary points and add them to the tree Is Path(secondary, destination) feasible yes No No 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.

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 achieves the desired objective.

People u Pritam Ganguly (Graduate Student)

Path Planning under Uncertainty 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 Uncertainty in information leads naturally to probabilistic approach Motivation:

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

Conversion to Digraph DigraphProbability Map

Simulation Dynamic ReplanningCase with Multiple Vehicles

Contribution and Future Work 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 Building a probability map in uncertain dynamic environments Path planning of multiple vehicles in uncertain dynamic environments based on probability map Contribution: Future Works:

People u Myungsoo Jun (Post-Doc) u Atif Chaudry (Graduate Student)