Computing Constrained Laplacian Navigation Function Paths in Configuration Space

This paper demonstrates path-planning for complex geometric models using harmonic function solutions to Laplace’s equation in the configuration space of the robot. The principal elements of the system are an approximate representation of the configuration space obstacles, finite element meshing of the free space, and Laplacian solutions to a path between start and end configurations in the free configuration space. Paths found by this system are smooth and free of local minima. Additionally, the full field solution can be used in novel ways to enforce constraints on the computed robot path, such as needed for car-like robots and in the presence of moving obstacles. The system is tested on several scenarios, such as a moving, rotating robot and a translating robot with moving obstacles, that demonstrate the generality of the approach.