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A Visibility-Based Pursuit-Evasion Game with a Circular Obstacle

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Abstract

In this paper, we address a visibility-based target tracking game for the scenario when the environment contains a circular obstacle. The game is originally formulated in four dimensions, but due to the symmetry of the environment, the dimension of the state space can be reduced to three. The control policies of the players on possible barrier surfaces are computed on the basis of semipermeability of the barriers. A standard surface, that can be a barrier, is constructed using Isaacs’ techniques. It is shown that the surface lies outside the game space. This opens up the possibility that the evader might be able to win the underlying game of kind for all initial positions in the game space or that the set of such win positions does not coincide with the game space and is determined by some barrier surfaces, construction of which may represent an independent difficult problem. We present the construction of the optimal control policies, and trajectories for the players near the usable part on the terminal manifold by analyzing a related game of degree.

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Acknowledgments

The work of S. Bhattacharya was supported in part by ISU research initiation grants. The work of T. Başar was supported in part by the US Air Force Office of Scientific Research (AFOSR) MURI Grant FA9550-10-1-0573. The work of N. Hovakimyan was supported in part by AFOSR.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Iowa State University, Ames, IA, 50011, USA

    Sourabh Bhattacharya

  2. Department of Electrical and Computer Engineering, University of Illinois at Urbana Champaign, Urbana, IL, 61801, USA

    Tamer Başar

  3. Department of Mechanical Engineering, University of Illinois at Urbana Champaign, Urbana, IL, 61801, USA

    Naira Hovakimyan

Authors
  1. Sourabh Bhattacharya
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  2. Tamer Başar
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  3. Naira Hovakimyan
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Corresponding author

Correspondence to Sourabh Bhattacharya.

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Communicated by Kyriakos G. Vamvoudakis.

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Bhattacharya, S., Başar, T. & Hovakimyan, N. A Visibility-Based Pursuit-Evasion Game with a Circular Obstacle. J Optim Theory Appl 171, 1071–1082 (2016). https://doi.org/10.1007/s10957-016-0996-9

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  • DOI: https://doi.org/10.1007/s10957-016-0996-9

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