Combining Homotopy Methods and Numerical Optimal Control to Solve Motion Planning Problems
Combining Homotopy Methods and Numerical Optimal Control to Solve Motion Planning Problems
复制标题
结合同伦方法和数值最优控制解决运动规划问题
DOI：
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发表时间：
2017
期刊：
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通讯作者：
Daniel Axehill
中科院分区：
文献类型：
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作者：
Kristoffer Bergman;Daniel Axehill
本文提出了一种使用数值最优控制技术计算非凸环境中运动规划问题的局部解的系统方法。它将最先进的数值最优控制工具的使用范围扩展到了这些工具以前无法应用的问题类别。如今，这些问题通常使用基于随机或图形搜索的运动规划器来解决。一般原则是定义一个同伦，将原始问题转化为或最好松弛为易于解决的问题。在这项工作中，研究表明，通过将顺序二次规划（SQP）方法与同伦方法相结合，逐渐将问题从松弛问题转变为原始问题，可以计算出运动规划问题的实际相关的局部最优解。该方法在具有挑战性的 2D 和 3D 环境中的运动规划问题中得到了证明，其中所提出的方法显着优于最先进的数值最优控制方法和通常用作基准的最先进的基于采样的开源优化规划器。
This paper presents a systematic approach for computing local solutions to motion planning problems in nonconvex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal control tools to problem classes where these tools have previously not been applicable. Today these problems are typically solved using motion planners based on randomized or graph search. The general principle is to define a homotopy that transforms, or preferably relaxes, the original problem to an easily solved problem. In this work, it is shown that by combining a Sequential Quadratic Programming (SQP) method with a homotopy approach that gradually transforms the problem from a relaxed one to the original one, practically relevant locally optimal solutions to the motion planning problem can be computed. The approach is demonstrated in motion planning problems in challenging 2D and 3D environments, where the presented method significantly outperforms both a state-of-the-art numerical optimal control method and a state-of-the-art open-source optimizing sampling-based planner commonly used as benchmark.