Advances in Trajectory Optimization for Space Vehicle Control

Abstract

Space mission design places a premium on cost and operational efficiency. The search for new science and life beyond Earth calls for spacecraft that can deliver scientific payloads to geologically rich yet hazardous landing sites. At the same time, the last four decades of optimization research have put a suite of powerful optimization tools at the fingertips of the controls engineer. As we enter the new decade, optimization theory, algorithms, and software tooling have reached a critical mass to start seeing serious application in space vehicle guidance and control systems. This survey paper provides a detailed overview of recent advances, successes, and promising directions for optimization-based space vehicle control. The considered applications include planetary landing, rendezvous and proximity operations, small body landing, constrained attitude reorientation, endo-atmospheric flight including ascent and reentry, and orbit transfer and injection. The primary focus is on the last ten years of progress, which have seen a veritable rise in the number of applications using three core technologies: lossless convexification, sequential convex programming, and model predictive control. The reader will come away with a well-rounded understanding of the state-of-the-art in each space vehicle control application, and will be well positioned to tackle important current open problems using convex optimization as a core technology.

Successive Convexification for Optimal Control with Signal Temporal Logic Specifications

“…Optimal control (trajectory optimization) of unmanned vehicles has been extensively studied. The reader is referred to [12] for an overview of the field. In particular, convex optimization and convexification based technologies have been developed for more than a decade now [2,3], while newer 6-DoF (Degrees of Freedom) formulations with attitude control have been studied in recent years [10,20,21].…”

“…From package delivery to traffic monitoring, from aerial photograph to fieldwork on modern farms, careful and autonomous trajectory planning is of utmost importance to ensure safety and mission requirements satisfaction. An onboard optimal-control-based guidance system is proved to be highly effective in this regard [12]. A notable line of work on this subject is the Successive Convexification(SCvx) algorithmic framework [14], which provides both theoretical convergence guarantee and practical real-time solving capability.…”

Proportional-Integral Projected Gradient Method for Model Predictive Control

“…The constraint x t P X upper bounds the speed of the quadrotor and limits the directions from which the quadrotor approach the charging station. The latter is also known as the approach cone constraint, which is widely used in spacecraft landing [15]. See Fig.…”

“…A challenge of DRS-based infeasibility detection is computing matrix inverse [10,9,11,3]. Such computation becomes expensive as the size of optimization (1) increases, or when optimization (1) is solved repeatedly with different constraint parameters in real-time [14,15]. While such matrix inverse is not necessary for problems with only linear constraints [16,17], whether it is necessary in general for optimization (1) is, to our best knowledge, still an open question.…”