On the Intersection of Computational Geometry Algorithms with Mobile Robot Path Planning

In the mathematical discipline of computational geometry (CG), practical algorithms for resolving geometric input and output issues are designed, analyzed, and put into practice. It is sometimes used to refer to pattern recognition and to define the solid modeling methods for manipulating curves and surfaces. CG is a rich field encompassing theories to solve complex optimization problems, such as path planning for mobile robot systems and extension to distributed multi-robot systems. This brief review discusses the fundamentals of CG and its application in solving well-known automated path-planning problems in single- and multi-robot systems. We also discuss three winning algorithms from the CG-SHOP (Computational Geometry: Solving Hard Optimization Problems) 2021 competition to evidence the practicality of CG in multi-robotic systems. We also mention some open problems at the intersection of CG and robotics. This review provides insights into the potential use of CG in robotics and future research directions at their intersection.