Rapidly Exploring Random Trees with Physics-Informed Neural Networks for Constrained Energy-Optimal Rendezvous Problems

This article introduces physics-informed neural networks (PINNs) to the field of motion planning by utilizing a PINN framework as the steering function in the kinodynamic rapidly-exploring random tree (RRT*) algorithm. The goal of this paper is to show that PINN-based methods can be used successfully for aerospace motion planning applications. We test the RRT* algorithm coupled with PINN steering, what we call PINN-RRT*, by solving spacecraft energy-optimal motion planning problems governed by the Hill–Clohessy–Wiltshire (HCW) equations of motion and nonlinear equations of relative motion (NERM), where a deputy satellite must rendezvous with a chief satellite while avoiding spherical keep-out-zones and complying with an approach corridor. The particular PINN framework we employ approximates the solution of nonlinear two-point boundary value problems (TPBVPs), which must be solved to form connections between waypoints in the RRT* tree, via the Theory of Functional Connections (TFC). TFC enables the PINN to analytically satisfy the boundary conditions (BCs) of the TPBVP. Thus, the admissible solution search space of each nonlinear TPBVP is reduced to just the trajectories that already satisfy the BCs. Using our proposed approach, each energy-optimal TPBVP solution during the run-time of the PINN-RRT* algorithm was computed in centiseconds and with an average error on the order of machine epsilon for both the HCW and NERM dynamics.