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A Stochastic Optimal Enhancement of Feedback Control for Unicycle Formations

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Distributed Autonomous Robotic Systems

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 104))

Abstract

We consider an optimal feedback control approach for multiple nonholonomic vehicles to achieve a distance-based formation with their neighbors using only local observations. Beginning with a non-optimal feedback formation control, each agent determines an additive correction term to its non-optimal control based on an elliptic Hamilton-Jacobi-Bellman equation so that its actions are optimal and robust to uncertainty. In order to avoid offline spatial discretization of the stationary, high-dimensional cost-to-go function, we exploit the stochasticity of the distributed nature of the problem to develop an equivalent estimation problem in a continuous state space using a path integral representation. Consequently, each agent independently computes its optimal feedback control using a discrete-time Unscented Kalman smoother. Our approach is illustrated by a numerical example in which five agents achieve a pentagon with aligned and equal velocities.

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Authors and Affiliations

  1. University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA, 95064, USA

    Ross P. Anderson & Dejan Milutinović

Authors
  1. Ross P. Anderson
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  2. Dejan Milutinović
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Correspondence to Ross P. Anderson .

Editor information

Editors and Affiliations

  1. Mechanical Engineering and Mechanics, Drexel University, Philadelphia, USA

    M. Ani Hsieh

  2. Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland, USA

    Gregory Chirikjian

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Anderson, R.P., Milutinović, D. (2014). A Stochastic Optimal Enhancement of Feedback Control for Unicycle Formations. In: Ani Hsieh, M., Chirikjian, G. (eds) Distributed Autonomous Robotic Systems. Springer Tracts in Advanced Robotics, vol 104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55146-8_19

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  • DOI: https://doi.org/10.1007/978-3-642-55146-8_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55145-1

  • Online ISBN: 978-3-642-55146-8

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