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.

警察和强盗问题是追赶和逃避问题的经典例子，是机器人技术领域关键研究的一部分。这项研究应专门针对强盗的逃避策略。该研究提出了一种后向视野优化方法来获得这种强盗策略，并解决了具有障碍物的复杂环境中的警察和强盗问题。在这种方法中，强盗实时估计警察的控制变量，以解决在获得完整的追击策略以解决逃避策略方面的困难。这种方法还保证了后退地平线优化问题的实时解决方案。正交搭配用于离散警察和强盗动态模型，然后解决由此产生的非线性规划问题，以获得最优控制。为了提高解的准确性，我们提出了一种迭代的hp自适应网格细化策略，通过调整有限元的数量和Lagrange多项式的阶数来满足最优条件。这种网格细化策略还迭代地使用有限元和并置点，并应用有限元合并策略来提高求解效率。所提出的方法还提供了解决具有障碍物的复杂环境中其他追赶和逃避问题的框架。