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.

Non-prehensile multi-object rearrangement is a robotic task of planning feasible paths and transferring multiple objects to their predefined target poses without grasping. It needs to consider how each object reaches the target and the order of object movement, which significantly deepens the complexity of the problem. To address these challenges, we propose a hierarchical policy to divide and conquer for non-prehensile multi-object rearrangement. In the high-level policy, guided by a designed policy network, the Monte Carlo Tree Search efficiently searches for the optimal rearrangement sequence among multiple objects, which benefits from imitation and reinforcement. In the low-level policy, the robot plans the paths according to the order of path primitives and manipulates the objects to approach the goal poses one by one. We verify through experiments that the proposed method can achieve a higher success rate, fewer steps, and shorter path length compared with the state-of-the-art.