Post on 20-Jan-2016
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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)
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: 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.