Spacecraft Rendezvous Guidance via Factorization-Free Sequential Convex Programming using a First-Order Method

TL;DR

This paper presents a factorization-free, sequential convex programming approach for spacecraft rendezvous trajectory optimization, utilizing a first-order method for fast and robust solutions with demonstrated effectiveness in simulation.

Contribution

It introduces a novel factorization-free algorithm using inverse-free discretization and a first-order conic solver for nonconvex trajectory optimization problems.

Findings

Robust convergence of the method across different initial conditions

Effective handling of constraints including keepout zones

Fast convergence demonstrated in Monte Carlo simulations

Abstract

We implement a fully factorization-free algorithm for nonconvex, free-final-time trajectory optimization. This algorithm is based on sequential convex programming and utilizes an inverse-free, exact discretization procedure to ensure dynamic feasibility of the converged trajectory and PIPG, a fast, first-order conic optimization algorithm as the subproblem solver. Although PIPG requires the tuning of a hyperparameter to achieve fastest convergence, we show that PIPG can be tuned to a nominal trajectory optimization problem and it is robust to variations in initial condition. We demonstrate this with a monte carlo simulation of the free-final-time rendezvous problem, using Clohessy-Wiltshire dynamics, an impulsive thrust model, and various state and control constraints including a spherical keepout zone.