This paper proposes a new sampling-based kinodynamic motion planning algorithm, called FMT*PFF, for nonlinear systems. It exploits the novel idea of dimensionality reduction using partial-final-state-free (PFF) optimal controllers.With the proposed dimensionality reduction heuristic, the search space is restricted within a subspace, thus faster convergence is achieved compared to a regular kinodynamic FMT*. The dimensionality reduction heuristic can be viewed as a sampling strategy and asymptotic optimality is preserved when combined with uniform full-state sampling. Another feature of FMT*PFF is the ability to deal with a steering function with inexact steering, which is vital when using learning-based steering functions. Learning-based methods allow us to solve the steering problem for nonlinear systems efficiently. However, learning-based methods often fail to reach the exact goal state. For nonlinear systems, we train a neural network controller using supervised learning to generate the steering commands. We show that FMT*PFF with a learning-based steering function is efficient and generates dynamically feasible motion plans. We compare our algorithm with previous algorithms and show superior performance in various simulations.

翻译：本文提出了一种新的基于采样的动力学运动规划算法——FMT*PFF，适用于非线性系统。该算法利用了部分最终状态自由度（PFF）最优控制器的降维新思想。通过所提出的降维启发式方法，搜索空间被限制在子空间内，从而相比常规动力学FMT*实现更快的收敛速度。该降维启发式方法可视为一种采样策略，在与均匀全状态采样结合时能保持渐近最优性。FMT*PFF的另一个特点在于能够处理具有非精确转向的转向函数，这对于使用基于学习的转向函数至关重要。基于学习的方法使我们能够高效解决非线性系统的转向问题，但这类方法往往难以精确达到目标状态。针对非线性系统，我们采用监督学习训练神经网络控制器以生成转向指令。研究表明，采用基于学习的转向函数的FMT*PFF算法既高效又能生成动力学可行的运动规划。我们将所提算法与先前算法进行对比，并在多种仿真场景中展示了其优越性能。