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MURI Telecon, Update 7/26/2012

MURI Telecon, Update 7/26/2012. Summary, Part I:

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MURI Telecon, Update 7/26/2012

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  1. 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.

  2. 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.

  3. DOC Background • 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. • 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 3

  4. Benchmark Problem: Multi-agent Path Planning The agent microscopic dynamics are given by the unicycle model with constant velocity, which amounts to the following system of ODEs, Agent: Where: The number of components (m) in the Gaussian mixture is chosen by the used based on the complexity of the initial and goal PDFs. 4

  5. Example with m = 4 Goal PDF, h(xi, tf) Initial PDF, p(xi, t0) Pr(xi) : Fixed obstacle 5

  6. Results: Optimal PDF (m = 4) Pr(xi): Optimal PDF : Fixed obstacle 6

  7. Agents’ Optimal Trajectories Feedback control of agents via DOC. Pr(xi): Optimal PDF Agent’s control input (Sample) : Individual agent (unicycle) : Fixed obstacle 7

  8. Example with m = 6 Goal PDF, h(xi, tf) Initial PDF, p(xi, t0) Pr(xi) : Fixed obstacle 8

  9. Results: Optimal PDF (m = 6) Pr(xi): Optimal PDF : Fixed obstacle 9

  10. Agents’ Optimal Trajectories Feedback control of N = 200 agents via DOC. Pr(xi): Optimal PDF Agent’s control input (Sample) : Individual agent (unicycle) : Fixed obstacle 10

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