Geometric Motion Planning

Geometric motion planning focuses on finding optimal, collision-free paths for robots and other systems, considering their physical constraints and the environment's geometry. Current research emphasizes efficient algorithms, such as sampling-based methods and those leveraging convex optimization or diffusion models, to address the computational challenges posed by high-dimensional systems and complex environments. These advancements are crucial for improving the autonomy and efficiency of robots in various applications, including multi-robot coordination, payload transport, and locomotion optimization for complex systems. The development of robust and scalable methods for planning in non-Euclidean spaces is also a significant area of ongoing investigation.