Geodesic Path Planning using Exponential Map with Injectivity Radius
Mahsa Soroori Khosroshahi, Kooktae Lee · 2025
Geodesic path planning is crucial in applications such as robotics, computer graphics, and autonomous navigation, focusing on finding the shortest path between two points on a curved surface while accounting for intrinsic geometry. Traditional methods, including energy function minimization, heat flow, and curvature-based techniques, often face local minima and computational inefficiencies, particularly in irregular environments. This paper presents a novel method that integrates the exponential map with the injectivity radius, ensuring globally optimal paths. Our approach avoids local minima, guarantees the shortest path, and provides real-time computational efficiency. Simulations show that our method outperforms existing techniques in optimality, local minima avoidance, and computation time.