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Utilizing Stochastic Processes for Computing Distributions of Large-Size Robot Population Optimal Centralized Control

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Distributed Autonomous Robotic Systems

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 83))

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Abstract

Motivated by the success of stochastic process sampling methods in solving complex estimation problems, we explore the possibility to utilize stochastic processes for computing optimal control for a large-size robot population. We assume that the individual robot state is composed of discrete and continuous components, while the population is controlled in a probability space. The optimal control solution is based on an infinite dimensional Pontryagin-like minimum principle, which involves an evaluation of systems of partial differential equations. The paper shows that these equations can be evaluated with computations involving stochastic process samples. This is an important result because generating stochastic process multi-dimensional trajectories is much easier than solving corresponding multi-dimensional partial differential equations. The proposed evaluations are illustrated and verified by an example of the centralized optimal control for a large-size robot population.

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Author information

Authors and Affiliations

  1. Applied Mathematics and Statistics Department, Baskin School of Engineering, UC Santa Cruz, Santa Cruz, 1156 High Street, CA, 95064, USA

    Dejan Milutinović

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  1. Dejan Milutinović
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Correspondence to Dejan Milutinović .

Editor information

Editors and Affiliations

  1. EPFL ENAC IIE DISAL, Station 2, Lausanne, 1015, Switzerland

    Alcherio Martinoli

  2. EPFL STI IMT LSRO, Station 9, Lausanne, 1015, Switzerland

    Francesco Mondada

  3. 430 UCB, Engineering Drive 1111, Boulder, 80309, Colorado, USA

    Nikolaus Correll

  4. EPFL ENAC IIE DISAL, Station 2, Lausanne, 1015, Switzerland

    Grégory Mermoud

  5. , Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, 30332, Georgia, USA

    Magnus Egerstedt

  6. , Mechanical Engineering & Mechanics, Drexel University, Randell 115, Chestnut St. 3141, Philadelphia, 19104, Pennsylvania, USA

    M. Ani Hsieh

  7. , Department of Electrical Engineering and, University of Tennessee, Middle Drive 1520, Knoxville, 37996, Tennessee, USA

    Lynne E. Parker

  8. Maersk Mc-Kinney Moller Institute, University of Southern Denmark, Campusvej 55, Odense, 5230, Denmark

    Kasper Støy

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Milutinović, D. (2013). Utilizing Stochastic Processes for Computing Distributions of Large-Size Robot Population Optimal Centralized Control. In: Martinoli, A., et al. Distributed Autonomous Robotic Systems. Springer Tracts in Advanced Robotics, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32723-0_26

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  • DOI: https://doi.org/10.1007/978-3-642-32723-0_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32722-3

  • Online ISBN: 978-3-642-32723-0

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