Motion path planning is an intrinsically geometric problem which is central for design of robot systems. Since the early years of AI, robotics together with computer vision have been the areas of computer science that drove its development. Many questions that arise, such as existence, optimality, and diversity of motion paths in the configuration space that describes feasible robot configurations, are of topological nature. The recent advances in topological data analysis and related metric geometry, topology and combinatorics have provided new tools to address these engineering tasks. We will survey some questions, issues, recent work and promising directions in data-driven geometric and topological methods with some emphasis on the use of discrete Morse theory.

翻译：运动路径规划是一个本质上的几何问题，在机器人系统设计中占据核心地位。自人工智能早期起，机器人与计算机视觉便成为推动计算机科学发展的两大领域。许多由此产生的问题——例如描述可行机器人位形的位形空间中运动路径的存在性、最优性及多样性——均具有拓扑性质。拓扑数据分析及相关度量几何、拓扑学与组合学的最新进展，为应对这些工程任务提供了新工具。本文将综述数据驱动的几何与拓扑方法中的若干问题、挑战、近期研究及有前景的方向，并着重探讨离散莫尔斯理论的应用。