Reliable and efficient trajectory generation methods are a fundamental need for autonomous dynamical systems of tomorrow. The goal of this article is to provide a comprehensive tutorial of three major convex optimization-based trajectory generation methods: lossless convexification (LCvx), and two sequential convex programming algorithms known as SCvx and GuSTO. In this article, trajectory generation is the computation of a dynamically feasible state and control signal that satisfies a set of constraints while optimizing key mission objectives. The trajectory generation problem is almost always nonconvex, which typically means that it is not readily amenable to efficient and reliable solution onboard an autonomous vehicle. The three algorithms that we discuss use problem reformulation and a systematic algorithmic strategy to nonetheless solve nonconvex trajectory generation tasks through the use of a convex optimizer. The theoretical guarantees and computational speed offered by convex optimization have made the algorithms popular in both research and industry circles. To date, the list of applications includes rocket landing, spacecraft hypersonic reentry, spacecraft rendezvous and docking, aerial motion planning for fixed-wing and quadrotor vehicles, robot motion planning, and more. Among these applications are high-profile rocket flights conducted by organizations like NASA, Masten Space Systems, SpaceX, and Blue Origin. This article aims to give the reader the tools and understanding necessary to work with each algorithm, and to know what each method can and cannot do. A publicly available source code repository supports the provided numerical examples. By the end of the article, the reader should be ready to use the methods, to extend them, and to contribute to their many exciting modern applications.
翻译:可靠且高效的轨迹生成方法是未来自主动态系统的基本需要。 本条的目的是为三种基于轨迹生成方法提供全面的辅导: 无损失的混凝土( Lcvx) 和两套被称为 SCvx 和 GuSTO 的连续曲线编程算法。 在本篇文章中, 轨迹生成是一个动态可行的状态和控制信号的计算, 该信号既满足一系列制约因素,又优化关键任务目标。 轨迹生成问题几乎总是非 convex, 这通常意味着它不易于在自主的飞行器上找到高效且可靠的解决方案。 我们讨论的三种算法, 即使用不亏损的混凝土优化( Lcvx) 和两个连续的 convex 编程编程算算算算算算算算法, 使得在研究和产业界圈内的算法很受欢迎。 迄今的应用清单包括火箭着陆、 航天器超声波再回路支持、 航天器集合和对接合和对接合、 固定翼和四重轨道飞行器的飞行规划、 机器人移动运动规划以及更多的算法, 这些应用都无法让每一条路路路路路、 系统了解。 这些应用方法能、 、 和马路路路路路路路路路路路路路路路路的计算法、 、 、 向各个、 向各个、 向每一分析、 向每一分析、 向可读、 向读、 提供它们提供和更多工具提供它们、 、 、 向每一分析工具系统、 提供高度分析工具系统、 提供高路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路、 。