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

RoboFlag An experimental platform for multi- vehicle cooperative control in uncertain and adversarial environments

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

Leverage RoboCup Technology

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

RoboFlag Simulation Environment

Hardware Environment

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

The RoboFlag Drill: Matt Earl Defenders Attackers Constraints Defender objective: pick u(t) to minimize number of attackers within defense zone at time T. Attacker objective: pick v(t) to maximize number of attackers within defense zone at time T.

Problem: Consider the RoboFlag Drill with the following assumptions irrational attackers (drones) full and perfect information collisions are ok simple 2nd order defender dynamics Model as a discrete time mixed logical dynamical (MLD) system (Bemporad & Morari 1999) linear dynamics logical rules inequality constraints

Defenders constraints (must not enter defense zone) dynamics intercept regionintercept region (dotted region in figure above)

Attackers auxiliary binary variables dynamics

Optimal control policy we convert the system into MLD form using HYSDEL (Torrisi, Bemporad, and Mignone 2000) this can be written as a mixed integer linear program (MILP)

Results MILP problem: 4040 integer variables, 400 continuous variables,13580 constraints CPLEX solves in 244 seconds on Linux PIII 866MHz

Results

Evaluation of this approach for cooperative control Good Bad easy to model complex systems easy to formulate complex tasks via a cost function to minimize and constraints to be satisfied handles very general constraints codes available for solving mixed integer programs gives optimal strategy computationally intensive constraints only enforced at discrete times. does not exploit structure

A new approach to reduce computation Exploit structure of the problem by considering the discrete and continuous parts separately.

Form an intercept tree - Prune intercept tree - Find feasible paths within tree Exploit motion primitives

Path Planning under Uncertainty: Myungsoo Jun MAIN IDEAS: Construction of probability map from available data Measurement data A priori statistics of environments Convert the probability map to a directed graph Path planning by solving shortest path problem in digraph Capture uncertainty in information with a probabilistic approach

Probability Map Building Measurement update by measured data Time update by a priori statistics of environment Map building sensor characteristics environment statistics From this can obtain probability distribution that at least one opponent is at a certain location

Conversion to Digraph DigraphProbability Map

Examples Dynamic ReplanningCase with Multiple Vehicles

Simulation

Contribution and Future Work Consideration of time and velocity in path planning for multiple vehicles Consideration penalty for frequent acceleration and deceleration Improving map building computation for real-time application Building a probability map in uncertain dynamic environments Path planning of multiple vehicles in uncertain dynamic environments based on probability maps Integrating map building and path planning Contribution: Future Work:

Obstacle Avoidance in Dynamic Environments: Pritam Ganguly 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. Frazzoli, Dahleh, and Feron

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: with probability one, it returns a feasible path if there exists one. Instead of using a tree data structure, use a grid data structure which takes a large storage space but has faster access time.

Future Work Implement 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. Develop a protocol enabling the decentralization of the above computation, and prove that the protocol achieves the desired objective.

Atif Chaudhry u Survey published research on multiple vehicle control u Investigating relationship between RoboFlag framework and desired military capabilities of autonomous vehicles