Path Planning Through Variational Dynamic Programming

The path planning problem, i.e., the geometrical problem of finding a collision-free path between two given configurations of a robot moving among obstacles, has been studied by many authors in recent years. Several complete algorithms exist for robots with few degrees of freedom (DOF), but they are intractable for more than 4 DOF. In order to tackle problems in higher dimensions, several heuristic approaches have been developed for various subclasses of the general problem. The most efficient heuristics rely on the construction of potential fields, attracting the robot towards its goal configuration. However, there is no obvious way to extend this approach to manipulation task planning problems. This report presents a novel approach to path planning which does not make use of a potential function to guide the search. It is a variational technique, consisting of iteratively improving an initial path possibly colliding with obstacles. At each iteration, the path is improved by performing a dynamic programming search in a submanifold of the configuration space containing the current path. We call this method Variational Dynamic Programming (VDP). The method can solve difficult high-dimensional path planning problems without using any problem-specific heuristics. Experiments are reported for several computer simulated robots in 2D and 3D workspaces, including manipulator arms and mobile robots with up to 16 DOFs. More importantly, an extension of VDP can solve manipulation planning problems of unprecedented complexity. We report an experiment in dual-arm manipulation planning with 12 DOF in a cluttered workspace.