Multivehicle Cooperative Control Raffaello DAndrea Mechanical

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Multi-vehicle Cooperative ControlRaffaello
DAndreaMechanical Aerospace Engineering
Cornell University
OUTLINE

• Progress on RoboFlag Test-bed
• MLD approach to Multi-Vehicle Cooperation
• Obstacle Avoidance in Dynamic Environments
• Path Planning with Uncertainty

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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
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What is RoboFlag?
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RoboFlag System
Vision computer
Arbiter
Overhead cameras
Computers for each entity
.
.
.
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.
RF transceiver
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SOFTWARE ARCHITECTURE
LOW LEVEL CONTROL INTERFACE
WIRELESSINTERFACE
LOCAL
MACHINE VISIONBASEDGLOBAL ANDLOCAL SENSING
VEHICLEHIGH LEVELCONTROL
VEHICLEHIGH LEVELCONTROL
VEHICLELOW LEVELCONTROL
VEHICLELOW LEVELCONTROL
COMMUNICATIONS NETWORKSIMULATOR
GLOBAL
ARBITER
CENTRALCONTROL
HUMANINTERFACE
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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
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SIMPLE COMMUNICATIONS NETWORK MODEL
Bi,j data units
Bi,j data units
buffer Li,j
Bi,j data units
buffer Li,j -1
buffer 0
Ui
Uj
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People

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

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The RoboFlag Drill
Start out simple and work up (Earl and DAndrea
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

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The RoboFlag Drill Modeling
Model drill as a mixed logical dynamical system
subject to constraints (MLD system) (Bemporad and
Morari 99)
Defender dynamics
Constraints
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The RoboFlag Drill Modeling
Attacker dynamics
Constraints
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The RoboFlag Drill MLD form
Converting logic expressions into inequalities
using HYSDEL (Torrisi et al. 00) we can write
system in MLD form
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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
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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

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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

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People

• Matthew Earl (Graduate Student)

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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.

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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.
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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.

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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.

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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.

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People

• Pritam Ganguly (Graduate Student)

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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

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Probability Map Building

• Measurement update by measured data

sensor characteristics

• Time update by a priori statistics of environment

environment statistics

• Map building

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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
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Digraph
Probability Map
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Simulation
Dynamic Replanning
Case with Multiple Vehicles
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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

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People

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