Fast Trajectory Optimization via Successive Convexification for Spacecraft Rendezvous with Integer Constraints

TL;DR

This paper introduces a rapid, fuel-efficient spacecraft rendezvous trajectory optimization method using successive convexification and state-triggered constraints, enabling real-time solutions with practical constraints.

Contribution

It presents a novel approach that embeds discrete decision constraints into continuous optimization, significantly reducing solution time compared to traditional mixed-integer programming.

Findings

Achieves up to 90% fuel savings over non-optimized designs.

Generates solutions within seconds suitable for off-line trade studies.

Handles complex constraints like thrust pulse width and plume impingement naturally.

Abstract

In this paper we present a fast method based on successive convexification for generating fuel-optimized spacecraft rendezvous trajectories in the presence of mixed-integer constraints. A recently developed paradigm of state-triggered constraints allows to efficiently embed a subset of discrete decision constraints into the continuous optimization framework of successive convexification. As a result, we are able to solve difficult trajectory optimization problems at interactive speeds, as opposed to a mixed-integer programming approach that would require significantly more solution time and computing power. Our method is applied to the real problem of transposition and docking of the Apollo command and service module with the lunar module. We demonstrate that, within seconds, we are able to obtain trajectories that are up to 90 percent more fuel efficient (saving up to 45 kg of fuel) than non-optimization based Apollo-era design targets. Our trajectories take explicit account of minimum thrust pulse width and plume impingement constraints. Both of these constraints are naturally mixed-integer, but we handle them as state-triggered constraints. In its current state, our algorithm will serve as a useful off-line design tool for rapid trajectory trade studies.