配置空间是算法机器人学领域使用较为广泛的一种基本概念。机器人学、计算机辅助设计与相关领域的诸多应用都可归类为配置空间方面的计算问题。本文将对近期与配置空间相关的两项重大挑战的解决方案成果进行探讨：①如何高效计算高维配置空间的近似表达；②如何在高维配置空间内高效执行几何学接近度与运动规划查询。基于机器学习与几何学近似技术，笔者在此提出几种新型配置空间构建算法。上述算法对多个配置样本进行碰撞查询。得出的碰撞查询结果将用来计算配置空间的近似表达，可快速聚合至准确的配置空间；同时还提出了基于并行图形处理器（GPU）的算法，以便加速配置空间优化与搜索计算的性能情况。笔者特别设计出了基于GPU的并行k最近邻算法与并行碰撞检测算法，并使用这些算法来加快运动规划。

The configuration space is a fundamental concept that is widely used in algorithmic robotics. Many applications in robotics, computer-aided design, and related areas can be reduced to computational problems in terms of configuration spaces. In this paper, we survey some of our recent work on solving two important challenges related to configuration spaces: ① how to efficiently compute an approximate representation of high-dimensional configuration spaces; and ② how to efficiently perform geometric proximity and motion planning queries in high-dimensional configuration spaces. We present new configuration space construction algorithms based on machine learning and geometric approximation techniques. These algorithms perform collision queries on many configuration samples. The collision query results are used to compute an approximate representation for the configuration space, which quickly converges to the exact configuration space. We also present parallel GPU-based algorithms to accelerate the performance of optimization and search computations in configuration spaces. In particular, we design efficient GPU-based parallel k-nearest neighbor and parallel collision detection algorithms and use these algorithms to accelerate motion planning.