Online Time-Informed Kinodynamic Motion Planning of Nonlinear Systems

TL;DR

This paper introduces DIKU, a deep learning-based method leveraging Koopman operator theory to efficiently approximate time-informed sets for nonlinear systems, significantly improving kinodynamic motion planning speed and accuracy.

Contribution

The paper presents a novel deep invertible Koopman operator model and a sampling-based reachability analysis approach for real-time TIS approximation in nonlinear control systems.

Findings

Outperforms existing methods in TIS approximation accuracy.

Achieves near real-time TIS computation.

Enhances time-optimal kinodynamic motion planning performance.

Abstract

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.