MURI Telecon, Update 7/26/2012

Summary, Part I:

Completed: proving and validating numerically optimality conditions for Distributed Optimal Control (DOC) problem; conservation law analysis; direct method of solution for DOC problems; computational complexity analysis; application to multi-agent path planning.

Submitted paper on developments above to Automatica.

Completed: modeling of maneuvering targets by Markov motion models; derivation of (corresponding) multi-sensor performance function representing the probability of detection of multiple distributed sensors; application to multi-sensor placement.

Submitted paper on developments above to IEEE TC.

In progress: application of methods above to multi-sensor trajectory optimization for tracking and detecting Markov targets based on feedback from a Kalman-Particle filter.

Submitted paper on developments above to MSIT 2012; another journal paper on developments above in preparation.

MURI Telecon, Update 7/26/2012

Summary, Part II:

Completed: comparison of information theoretic functions for multi-sensor systems performing target classification.

Published paper on above developments in SMCB –Part B, Vol. 42, No. 1, Feb 2012.

In progress: comparison of information theoretic functions for multi-sensor systems performing (Markov) target tracking and detection.

Submitted paper on above developments to SSP 2012; another journal paper on developments above in preparation.

Completed: derived new approximate dynamic relations for hybrid systems.

Submitted paper on above developments to JDSM.

In progress: integrating DOC for multiple tasks and distributions with consensus based bundle algorithm (CBBA); apply DOC to non-parametric Bayesian models of sensors/targets.

In progress: develop DOC reachability proofs in the presence of communication constraints, for decentralized DOC.

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DOC Background

Classical Optimal Control: Determines the optimal control law and trajectory for a single agent or dynamical system.

Characterized by well-known optimality conditions and numerical algorithms

Applied to a single agent for trajectory optimization, pursuit-evasion, feedback control (auto-pilots) ..

Does not scale to systems of hundreds of agents

Distributed Systems: A system of multiple autonomous dynamic systems that communicate and interact with each other to achieve a common goal.

Swarms: Hundreds to thousands of systems; homogeneous; minimal communication and sensing capabilities. Decentralized control laws: stable; non-optimal; and, do not meet common goal.

Multi-agent systems: few to hundreds of systems; heterogeneous; advanced sensing and, possibly, communication capabilities. Centralized vs. decentralized control laws: path planning; obstacle avoidance; must meet one or more common goals, subject to agent constraints and dynamics.

Benchmark Problem: Multi-agent Path Planning

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The agent microscopic dynamics are given by the unicycle model with constant velocity, which amounts to the following system of ODEs,

Where:

controlonacceleratilinearu

controlvelocityangularu

velocitylinearvangleheading

coordinateyycoordinatexx

a :

:

::

::

aiiii

iiii

uvu

vyvx

)sin()cos(Agent:

The number of components (m) in the Gaussian mixture is chosen by the used based on the complexity of the initial and goal PDFs.

Example with m = 4

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Initial PDF, p(xi, t0)

: Fixed obstacle

Goal PDF, h(xi, tf) Pr(xi)

Results: Optimal PDF (m = 4)

6

: Fixed obstacle

Pr(xi): Optimal PDF

Agents’ Optimal Trajectories

7: Fixed obstacle

Pr(xi): Optimal PDF

Agent’s control input (Sample)

: Individual agent (unicycle)

Feedback control of agents via DOC.

Example with m = 6

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Initial PDF, p(xi, t0)

: Fixed obstacle

Goal PDF, h(xi, tf) Pr(xi)

Results: Optimal PDF (m = 6)

9: Fixed obstacle

Pr(xi): Optimal PDF

Agents’ Optimal Trajectories

10: Fixed obstacle

Pr(xi): Optimal PDF

Agent’s control input (Sample)

: Individual agent (unicycle)

Feedback control of N = 200 agents via DOC.