A time-dependent symplectic network for non-convex path planning problems with linear and nonlinear dynamics

We propose a novel neural network architecture (TSympOCNet) to address high--dimensional optimal control problems with linear and nonlinear dynamics. An important application of this method is to solve the path planning problem of multi-agent vehicles in real time. The new method extends our previous SympOCNet framework by introducing a time-dependent symplectic network into the architecture. In addition, we propose a more general latent representation, which greatly improves model expressivity based on the universal approximation theorem. We demonstrate the efficacy of TSympOCNet in path planning problems with obstacle and collision avoidance, including systems with Newtonian dynamics and non-convex environments, up to dimension 512. Our method shows significant promise in handling efficiently both complex dynamics and constraints.