# GuSTO: Guaranteed Sequential Trajectory Optimization via Sequential Convex Programming

## TL;DR

GuSTO is a trajectory optimization framework with theoretical guarantees that outperforms existing methods in success rate, quality, and speed for control-affine systems with drift.

## Contribution

GuSTO extends SCP-based trajectory optimization with rigorous convergence guarantees and an accelerated implementation for control-affine systems.

## Key findings

- GuSTO outperforms state-of-the-art methods in success rates.
- GuSTO achieves higher solution quality.
- GuSTO reduces computation times.

## Abstract

Sequential Convex Programming (SCP) has recently seen a surge of interest as a tool for trajectory optimization. However, most available methods lack rigorous performance guarantees and they are often tailored to specific optimal control setups. In this paper, we present GuSTO (Guaranteed Sequential Trajectory Optimization), an algorithmic framework to solve trajectory optimization problems for control-affine systems with drift. GuSTO generalizes earlier SCP-based methods for trajectory optimization (by addressing, for example, goal-set constraints and problems with either fixed or free final time) and enjoys theoretical convergence guarantees in terms of convergence to, at least, a stationary point. The theoretical analysis is further leveraged to devise an accelerated implementation of GuSTO, which originally infuses ideas from indirect optimal control into an SCP context. Numerical experiments on a variety of trajectory optimization setups show that GuSTO generally outperforms current state-of-the-art approaches in terms of success rates, solution quality, and computation times.