Sampling-based kinodynamic motion planners (SKMPs) are powerful in finding collision-free trajectories for high-dimensional systems under differential constraints. Time-informed set (TIS) can provide the heuristic search domain to accelerate their convergence to the time-optimal solution. However, existing TIS approximation methods suffer from the curse of dimensionality, computational burden, and limited system applicable scope, e.g., linear and polynomial nonlinear systems. To overcome these problems, we propose a method by leveraging deep learning technology, Koopman operator theory, and random set theory. Specifically, we propose a Deep Invertible Koopman operator with control U model named DIKU to predict states forward and backward over a long horizon by modifying the auxiliary network with an invertible neural network. A sampling-based approach, ASKU, performing reachability analysis for the DIKU is developed to approximate the TIS of nonlinear control systems online. Furthermore, we design an online time-informed SKMP using a direct sampling technique to draw uniform random samples in the TIS. Simulation experiment results demonstrate that our method outperforms other existing works, approximating TIS in near real-time and achieving superior planning performance in several time-optimal kinodynamic motion planning problems.

翻译：基于采样的动力学运动规划器（SKMPs）在寻找满足微分约束的高维系统无碰撞轨迹方面具有强大能力。时间感知集（TIS）能够提供启发式搜索域，以加速其收敛至时间最优解。然而，现有的TIS近似方法受限于维度灾难、计算负担以及有限的系统适用范围，例如仅适用于线性和多项式非线性系统。为克服这些问题，我们提出一种结合深度学习技术、Koopman算子理论与随机集理论的方法。具体而言，我们提出一种名为DIKU的带控制U的深度可逆Koopman算子模型，通过使用可逆神经网络改进辅助网络，实现长时域内的状态前向与后向预测。我们开发了一种基于采样的方法ASKU，对DIKU进行可达性分析，以在线近似非线性控制系统的TIS。此外，我们设计了一种在线时间感知SKMP，采用直接采样技术在TIS中抽取均匀随机样本。仿真实验结果表明，我们的方法优于现有其他工作，能够近实时地近似TIS，并在多个时间最优动力学运动规划问题中实现了优越的规划性能。