Trajectory Optimization for Minimum Threat Exposure using Physics-Informed Neural Networks

TL;DR

This paper develops physics-informed neural networks to efficiently solve boundary value problems for trajectory optimization, minimizing threat exposure in vehicle navigation, overcoming limitations of traditional methods.

Contribution

It introduces a PINN-based approach for solving BVPs in optimal control, including a conditioned PINN that generalizes across initial states, enhancing computational efficiency.

Findings

PINNs accurately solve the BVP with low numerical error.

The conditioned PINN eliminates the need for retraining for different initial states.

The method effectively finds trajectories minimizing threat exposure.

Abstract

We apply a physics-informed neural network (PINN) to solve the two-point boundary value problem (BVP) arising from the necessary conditions postulated by Pontryagin's Minimum Principle for optimal control. Such BVPs are known to be numerically difficult to solve by traditional shooting methods due to extremely high sensitivity to initial guesses. In the light of recent successes in applying PINNs for solving high-dimensional differential equations, we develop a PINN to solve the problem of finding trajectories with minimum exposure to a spatiotemporal threat for a vehicle kinematic model. First, we implement PINNs that are trained to solve the BVP for a given pair of initial and final states for a given threat field. Next, we implement a PINN conditioned on the initial state for a given threat field, which eliminates the need for retraining for each initial state. We demonstrate that the PINN outputs satisfy the necessary conditions with low numerical error.