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Receding Horizon Optimization Method for Solving the Cops and Robbers Problems in a Complex Environment with Obstacles

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Abstract

Cops and Robbers problems are classical examples of pursuit and evasion problems which are parts of key researches in the field of robotics. This study shall specifically focus on the evasion strategies of robbers. This study presents the receding horizon optimization method to obtain such strategies of robbers and solves the Cops and Robbers problems in a complex environment with obstacles. In this method, the robbers estimate the control variables of the cops in real time to address the difficulties in obtaining the complete pursuit strategies of the latter for solving the evasion strategies. This method also guarantees the real-time solutions of receding horizon optimization problems. Orthogonal collocation is utilized to discretize the Cops and Robbers dynamic model, and then the resulting nonlinear programming problem is solved to obtain the optimal control. To improve the accuracy of the solution, we propose an iterative hp-adaptive mesh refinement strategy to satisfy the optimality conditions by adjusting the number of finite elements and the order of Lagrange polynomials. This mesh refinement strategy also iteratively uses finite elements and collocation points as well as applies the finite element merging strategy to improve the solution efficiency. The proposed method also provides a framework for solving other pursuit and evasion problems in a complex environment with obstacles.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under grant number 61773341, the State Key Laboratory Project of China under grant number ICT1804, the Joint Innovation Fund of the China Academy of Launch Vehicle Technology and Universities under grant number CALT201603, and the Equipment Pre-Research Project of China under grant number 30506030302.

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Authors and Affiliations

  1. College of Control Science and Engineering, Zhejiang University, Hangzhou, 310027, China

    Qiang Zhu, Kexin Wang & Zhijiang Shao

  2. Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Lorenz T. Biegler

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  1. Qiang Zhu
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  2. Kexin Wang
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  3. Zhijiang Shao
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  4. Lorenz T. Biegler
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Correspondence to Zhijiang Shao.

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Zhu, Q., Wang, K., Shao, Z. et al. Receding Horizon Optimization Method for Solving the Cops and Robbers Problems in a Complex Environment with Obstacles. J Intell Robot Syst 100, 83–112 (2020). https://doi.org/10.1007/s10846-020-01188-y

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