Real-Time Sequential Conic Optimization for Multi-Phase Rocket Landing Guidance

TL;DR

This paper presents SeCO, a real-time, multi-phase rocket landing guidance framework that solves nonconvex optimal control problems efficiently without matrix factorizations, enabling fast and reliable trajectory optimization.

Contribution

Introduction of SeCO, a novel sequential conic optimization paradigm combining SCP and first-order conic methods for real-time multi-phase trajectory optimization.

Findings

SeCO is 2.7 times faster than existing convex solvers.

Successfully solves nonlinear, multi-phase rocket landing guidance problems in real-time.

Handles free-transition-time and convex constraints without mixed-integer formulations.

Abstract

We introduce a multi-phase rocket landing guidance framework that can handle nonlinear dynamics and does not mandate any additional mixed-integer or nonconvex constraints to handle discrete temporal events/switching. To achieve this, we first introduce sequential conic optimization (SeCO), a new paradigm for solving nonconvex optimal control problems that is entirely devoid of matrix factorizations and inversions. This framework combines sequential convex programming (SCP) and first-order conic optimization and can solve unified multi-phase trajectory optimization problems in real-time. The novel features of this framework are: (1) time-interval dilation, which enables multi-phase trajectory optimization with free-transition-time; (2) single-crossing compound state-triggered constraints, which are entirely convex if the trigger and constraint conditions are convex; (3) virtual state, which is a new approach to handling artificial infeasibility in SCP methods that preserves the shapes of the constraint sets; and, (4) the use of the proportional-integral projected gradient method (PIPG), a high-performance first-order conic optimization solver, in tandem with the penalized trust region (PTR) SCP algorithm. We demonstrate the efficacy and real-time capability of SeCO by solving a relevant multi-phase rocket landing guidance problem with nonlinear dynamics and convex constraints only, and observe that our solver is 2.7 times faster than a state-of-the-art convex optimization solver.