Some geometric and topological data-driven methods in robot motion path planning (Q6641602)

As the title suggests, this is an overview of geometric and topological methods in robot motion path planning. It appears to be an accessible survey that might be of interest to people interested in entering the field. The article focuses more on general ideas and provides plenty of references for further reading. After an introduction to the general concept of motion planning, Section 2 consists of a short survey on topological complexity, artificial potential vector fields, and some concepts from topological data analysis, in particular persistent homology. In Section 3, preliminaries on discrete Morse theory are introduced, a short survey on the comparison with smooth Morse theory is presented, and advantages of data-driven applications of discrete Morse theory are discussed. Section 4 is the main part of the chapter: an overview of three general methods in motion planning, namely skeletonization, density-based modeling, and parallelized and distributed planning. As part of these overviews, it is also mentioned to what extent discrete Morse theory has been applied to the respective methods. The chapter concludes with Section 5, which presents and discusses a collection of typical problems in motion planning.\N\NFor the entire collection see [Zbl 1547.55002].