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Optimal Control of Nonlinear Systems with Temporal Logic Specifications

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Robotics Research

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 114))

Abstract

We present a mathematical programming-based method for optimal control of nonlinear systems subject to temporal logic task specifications. We specify tasks using a fragment of linear temporal logic (LTL) that allows both finite- and infinite-horizon properties to be specified, including tasks such as surveillance, periodic motion, repeated assembly, and environmental monitoring. Our method directly encodes an LTL formula as mixed-integer linear constraints on the system variables, avoiding the computationally expensive process of creating a finite abstraction. Our approach is efficient; for common tasks our formulation uses significantly fewer binary variables than related approaches and gives the tightest possible convex relaxation. We apply our method on piecewise affine systems and certain classes of differentially flat systems. In numerical experiments, we solve temporal logic motion planning tasks for high-dimensional (10\(+\) continuous state) systems.

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Acknowledgments

The authors thank Matanya Horowitz, Scott Livingston, and Ufuk Topcu for helpful feedback. This work was supported by a NDSEG Fellowship and the Boeing Corporation.

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Authors and Affiliations

  1. California Institute of Technology, Pasadena, CA, USA

    Eric M. Wolff & Richard M. Murray

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  1. Eric M. Wolff
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  2. Richard M. Murray
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Correspondence to Eric M. Wolff .

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Editors and Affiliations

  1. Creative Informatics, The University of Tokyo, Tokyo, Japan

    Masayuki Inaba

  2. School of Electrical Engineering and Com, Queensland Univ of Technology, Brisbane, Queensland, Australia

    Peter Corke

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Wolff, E.M., Murray, R.M. (2016). Optimal Control of Nonlinear Systems with Temporal Logic Specifications. In: Inaba, M., Corke, P. (eds) Robotics Research. Springer Tracts in Advanced Robotics, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-319-28872-7_2

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  • DOI: https://doi.org/10.1007/978-3-319-28872-7_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28870-3

  • Online ISBN: 978-3-319-28872-7

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