A Sampling-Based Algorithm with the Metropolis Acceptance Criterion for Robot Motion Planning

Motion planning is one of the important research topics of robotics. As an improvement of Rapidly exploring Random Tree (RRT), the RRT* motion planning algorithm is widely used because of its asymptotic optimality. However, the running time of RRT* increases rapidly with the number of potential path vertices, resulting in slow convergence or even an inability to converge, which seriously reduces the performance and practical value of RRT*. To solve this issue, this paper proposes a two-phase motion planning algorithm named Metropolis RRT* (M-RRT*) based on the Metropolis acceptance criterion. First, to efficiently obtain the initial path and start the optimal path search phase earlier, an asymptotic vertex acceptance criterion is defined in the initial path estimation phase of M-RRT*. Second, to improve the convergence rate of the algorithm, a nonlinear dynamic vertex acceptance criterion is defined in the optimal path search phase, which preferentially accepts vertices that may improve the current path. The effectiveness of M-RRT* is verified by comparing it with existing algorithms through the simulation results in three test environments.