Convex Trajectory Planning [About This Issue

Abstract

This <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">IEEE Control Systems</i> issue includes one feature and one application for control. The feature “Convex Optimization for Trajectory Generation,” by Danylo Malyuta, Taylor P. Reynolds, Michael Szmuk, Thomas Lew, Riccardo Bonalli, Marco Pavone, and Behçet Açikmes¸e, provides a tutorial on the optimization methods that have proven themselves in both theory and practice to be fast and reliable at producing dynamically feasible trajectories for nonlinear systems subject to nonconvex constraints. The authors and their colleagues are original developers of the methods discussed: lossless convexification and two sequential convex programming algorithms called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SCvx</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GuSTO</i> . At their core, all three methods leverage a reliable, low-level convex optimizer that solves nonconvex control problems through problem reformulation, linearization, or both. Over the past decade, these methods have generated growing interest across academia and industry, including from organizations such as NASA, Masten Space Systems, SpaceX, and Blue Origin. The article provides the reader with an intimate understanding of what it takes to use—or even extend—each of the methods to generate nontrivial trajectories. Open source code written in the Julia language accompanies the article and can serve as a ready-to-use toolbox for the reader’s further work on sequential convex programming.