Learning-Based Stable Optimal Guidance for Spacecraft Close-Proximity Operations

TL;DR

This paper introduces a machine learning framework that combines control Lyapunov functions with supervised learning to achieve certifiably stable, optimal spacecraft rendezvous guidance, extending to nonlinear systems with safety guarantees.

Contribution

It develops a neural Lyapunov function and guidance policy that ensure stability and optimality, addressing the lack of formal guarantees in traditional black-box ML methods.

Findings

The method guarantees stability and near-optimal guidance in simulations.

The neural Lyapunov function is positive definite and certifies stability.

The approach is extensible to nonlinear control-affine systems.

Abstract

Machine learning techniques have demonstrated their effectiveness in achieving autonomy and optimality for nonlinear and high-dimensional dynamical systems. However, traditional black-box machine learning methods often lack formal stability guarantees, which are critical for safety-sensitive aerospace applications. This paper proposes a comprehensive framework that combines control Lyapunov functions with supervised learning to provide certifiably stable, time- and fuel-optimal guidance for rendezvous maneuvers governed by Clohessy-Wiltshire dynamics. The framework is easily extensible to nonlinear control-affine systems. A novel neural candidate Lyapunov function is developed to ensure positive definiteness. Subsequently, a control policy is defined, in which the thrust direction vector minimizes the Lyapunov function's time derivative, and the thrust throttle is determined using minimal required throttle. This approach ensures that all loss terms related to the control Lyapunov function are either naturally satisfied or replaced by the derived control policy. To jointly supervise the Lyapunov function and the control policy, a simple loss function is introduced, leveraging optimal state-control pairs obtained by a polynomial maps based method. Consequently, the trained neural network not only certifies the Lyapunov function but also generates a near-optimal guidance policy, even for the bang-bang fuel-optimal problem. Extensive numerical simulations are presented to validate the proposed method.