Cooperative Control of Distributed Autonomous Vehicles in Adversarial Environments

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Cooperative Control of Distributed
AutonomousVehicles in Adversarial Environments
2.5 Year MURI Research Review November 18, 2003
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Team vs Team Siege

• Combat decisions
• Communication decisions
• Real-time computations
• Multivehicle (re)grouping
• Trajectory execution
• As well as
• Above Resource allocation
• Below Servoloops
• Parallel Human intervention

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Lots of Issues Approaches
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Core MURI Research

• Our approach
• Extract distill essential elements with well
  formulated subproblems.
• Develop core theory understand
  limitations/trade-offs.
• Develop supporting computational algorithms.
• Illustrate motivate new directions in test-bed
  examples.
• Recognize traceable and transportable
  implications.

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Dimensions of Cooperative Control

• Distributed control computation
• The defining feature of cooperative control
  problems.
• Adversarial Interactions
• Uncertain Evolution
• Complexity Management

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Evolution of Dimensions

• Year 2
• Distributed control computation
• (Virtual) Hierarchy
• Adversary Uncertainty
• Finite-state representations

• Proposal Year 1
• Scalability, modeling reduction
• High level planning
• Low level execution
• Communications

• Year 2.5
• Distributed control computation
• Adversarial Interactions
• Uncertain Evolution
• Complexity Management

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Todays Agenda
Discuss on-going work across universities in
context of dimension.

• Explore multiple facets of research challenge.
• Recognize multiple dimensionality.

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Cross Dimensional Threads

• Explore multiple facets of research challenge.
• Recognize multiple dimensionality.
• Enemy Models
• Coordinating Actions
• Constructive Algorithms
• Roboflag Drill

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Enemy Model 1/5MILP Methods for Multi-Vehicle
Systems

• RoboFlag Drill problem with semi-intelligent
  targets
• Encode vehicle dynamics, obstacle avoidance,
  target intelligence, and group objective as a
  mixed integer linear program (MILP). Solving the
  MILP gives the optimal group strategy.

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Enemy Model 2/5Linear-Programming-Based
Multi-vehicle Path Planning with Adversaries

• Objective
• Minimize the number of adversaries that enter a
  protected area.
• Explore the utility of Linear Programming for
  trajectory planning.
• Represent Enemy as probabilistic diffusion
• Potential Advantages
• Reduce complexity with LPs
• (versus mixed integer LPs)
• Allow 2-sided optimization
• (versus scripted adversaries)

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Enemy Model 3/5Probability Map of the
Environment with Moving Opponents

• Map Building

PDF of Each Opponent

• Path Planning
• Find a sequence of cells connecting the origin
  and the destination using Dijkstra algorithm
• Plan a path considering the centers of the
  sequence of cells as waypoints

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Enemy Model 4/5Linear Quadratic Gaussian (LQG)
Differential Games with Different Information
Patterns
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Enemy Model 5/5Distributed Convergence to Nash
Equilibria

• Can individual agents reach strategic equilibrium
  without declaration of their intentions?
• Utility Strategic robustnessAdaptation vs
  fragile planning

Conventional Methods Agents chase other agent
behaviors Alternative Distributed feedback
stabilization
Game Theory Literature It cant be done
(40yrs) Standard Counterexample
Anti-coordination Game P1 wants to deviate from
P2 P2 wants to deviate from P3 P3 wants to
deviate from P1 Each player only has 2 movesall
cant be satisfied
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Coordinating Actions 1/6Consensus in Networks
with Mobile Agents and Switching Topology
Formation switching using balanced graphs
Attitude Alignment for Large Collections of
Vehicles

• Approach
• Design cooperative control protocols for networks
  of mobile agents and analyze their convergence,
  performance, and robustness properties.

• Accomplishments
• Theory for agreement protocols in networks of
  mobile agents with switching communications
  topology
• Analysis of speed of reaching consensus in a
  group of vehicles/agents based on second
  eigenvalue of graph Laplacian

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Coordinating Actions 2/6Mode Estimation of
Switching Linear Systems
Objective 1 - Want to design
Given
Objective 2 - Given rq, the rate of qk, find
suitable D and f such that
that parallels the classical Kalman filtering
performance analysis, where
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Coordinating Actions 3/6Observation of CCL-like
Programs

• Problem Determine state of communications
  protocol used by a group of robots given their
  physical movements.
• Assumptions Protocol and motion control are
  described in CCL like language.
• Results
• Definitions of observability, etc. for CCL
  programs
• Construction and analysis of an observer that
  converges when the system is "weakly" observable
• Construction of an efficient observer for
  Roboflag drill in particular.

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Coordinating Actions 4/6Adaptive Languages in
Uncertain Environments

• Elements
• Symbol grounding
• Language learning
• Language evolution

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Coordinating Actions 5/6Adaptive Models in
Interactive Markov Chains

• Start with two dynamically coupled systems with
  centralized objective.
• Each subsystem makes simplified model of other.
• Each subsystem designs local optimal controller
  based on modified cost.
• After simulation/experience, subsystems revise
  models.
• Will it converge? What is performance?
• Anticipate FP proof

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Coordinating Actions 6/6 Communications under
Bandwidth Limitations
Strategy and path planning
Has access to information about the vehicles and
adversarial environment.
Central Command
Generates references and control signals.
Wireless digital link
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Constructive Algorithms 1/3Flocking with
Obstacle Avoidance

• Stability of flocks is formalized.
• A flock contains a, b, and g agents with specific
  tasks
• a maintains a distance d from an a agent.
• b repels an a agent and exists if a exists.
• g behaves like an a agent but is fixed.
• Split/Rejoin and Squeezing maneuvers w/ local
  information.
• Consensus under switching topology addressed for
  directed graphs.

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Constructive Algorithms 2/3Decomposition Methods

• Decomposition
• We use trajectory generation and obstacle
  avoidance primitives to pose cooperative planning
  problems such as the target assignment problem
  (ex. RoboFlag Drill).
• Problems are effectively reduced to combinatorial
  optimization problems

Greedy
Branch Bound

• Branch Bound algorithm
• Form a search tree and explore using upper and
  lower bounds to prune branches.
• Upper bound is computed using greedy cost to go
  algorithm thus you can stop at any point in your
  search and use the best feasible solution found
  from the greedy algorithm.

• Complexity
• We show the target assignment problem is NP-hard.

• Multi-level MPC algorithm
• For semi-intelligent targets.
• Run each level of the hierarchy in an MPC
  framework at rate governed by the complexity of
  the level. RTG gt ROA gt RBB

Jub Jopt
Steps
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Constructive Algorithms 3/3CCL Computation and
Control Language
"soup" of guarded commands
P(k1,k2) initializers guard1rule1
guard2rule2 ... S(k1,k2)P(k1,k2)C(k11)
sharing y,u
composition union
non-shared variables remain local to component
programs
CCL Protocol forDecentralized Target Allocation

• CCL Interpreter
• Formal programming language for control and
  computation. Interfaces with libraries in other
  languages.

• Automated Verification
• CCL encoded in the Isabelle theorem prover basic
  specs verified semi-automatically. Investigating
  various model checking tools.

• Formal Results
• Formal semantics in transition systems and
  temporal logic. RoboFlag drill formalized and
  basic algorithms verified.

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Roboflag Drill

• MILP Planning.
• Hierarchical decomposition.
• Model reduction.
• LP planning.
• Adaptive representations.
• CCL protocols.
• CCL observers.

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Dimensions as Specific Core Challenges
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Proposal Expected Insights

• How to address scalability through modeling
  decomposition.
• How to address computational complexity in
  hierarchical designs.
• How to develop reliable multi-layered cooperative
  strategies.
• How to counter adversarial actions with
  constrained communications.
• How to integrate local optimizations for
  collective performance.
• How to synchronize cooperating elements through
  modeling and ID.
• How to exploit neurological models to design
  cooperating elements.
• How to achieve reliable communications in
  hierarchical structures.
• How to derive adaptive languages for autonomous
  operations.

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Todays Agenda
Discuss on-going work across universities in
context of dimension.

• Explore multiple facets of research challenge.
• Recognize multiple dimensionality.