Geometric Optimization Frameworks in Mobile Robot Path Planning

Global and local path planning plays a crucial role in mobile robot navigation systems, ensuring efficient and collision-free movement through complex environments. However, many challenges such as high computational cost, path and curvature discontinuities, local minima entrapment, real-time computational constraints, and the need to account for dynamic obstacles and motion constraints, make it difficult to determine optimal paths. To overcome these problems, various geometric optimization frameworks have been proposed, leveraging a wide range of techniques from Delaunay triangulation to Model Predictive Control and Artificial Potential Field. This paper aims to provide a comprehensive survey of the optimization frameworks developed for path planning in mobile robots. Particularly, we first provide a fundamental background of the path planning problem and the prominent geometric optimization techniques. We then discuss diverse geometric optimization frameworks proposed to address challenges in different application areas, including global pathfinding, local path planning, and applications that combine both. Finally, we highlight important challenges, open issues, and future research directions of geometric optimization approaches for future path planning systems.