This work presents an optimal sampling-based method to solve the real-time motion planning problem in static and dynamic environments, exploiting the Rapid-exploring Random Trees (RRT) algorithm and the Model Predictive Path Integral (MPPI) algorithm. The RRT algorithm provides a nominal mean value of the random control distribution in the MPPI algorithm, resulting in satisfactory control performance in static and dynamic environments without a need for fine parameter tuning. We also discuss the importance of choosing the right mean of the MPPI algorithm, which balances exploration and optimality gap, given a fixed sample size. In particular, a sufficiently large mean is required to explore the state space enough, and a sufficiently small mean is required to guarantee that the samples reconstruct the optimal controls. The proposed methodology automates the procedure of choosing the right mean by incorporating the RRT algorithm. The simulations demonstrate that the proposed algorithm can solve the motion planning problem in real-time for static or dynamic environments.

翻译：本文提出了一种基于最优采样的方法，利用快速探索随机树(RRT)算法和模型预测路径积分(MPPI)算法，解决静态与动态环境下的实时运动规划问题。RRT算法为MPPI算法中的随机控制分布提供标称均值，使其在静态与动态环境中无需精细参数调优即可获得满意的控制性能。我们还讨论了在给定样本量条件下，选择MPPI算法适当均值的重要性——该均值需平衡探索性与最优性差距。具体而言，需要足够大的均值以充分探索状态空间，同时需要足够小的均值以保证样本能重构最优控制。所提方法通过引入RRT算法，自动实现了适当均值的选取流程。仿真结果表明，该算法能够实时求解静态或动态环境下的运动规划问题。