A variational approach to path planning for hyper-redundant manipulators

Motion planning for hyper-redundant manipulators in a complicated and cluttered workspace is a challenging problem. Many of the path planning algorithms, based on cell decomposition or potential field, fail due to the high dimensionality and complex nature of the C-space. Probabilistic roadmap methods (PRM) which have been proven to be successful in high dimensional C-spaces suffer from the drawback of generating paths which involve a lot of redundant motion. In this paper, we propose a path optimizing method to improve a given path in terms of path length and the safety against the collisions, using a variational approach. The capability of variational calculus to optimize a path is demonstrated on a variety of examples. The approach succeeds in providing a good quality path even in high dimensional C-spaces.