Motion Planning in a Stratified Workspace Manifold of a Quadruped Walking Robot

Stratified manifolds are encountered in the configuration manifolds of many robots. Some typical examples are the walking robots [4, 5]. The configuration manifolds of such robots are in general high dimensional with some distinctive features. The most important characteristic feature of stratified manifolds are that they are filled with discontinuities [5]. These discontinuities give rise to certain sub-manifolds which are essentially the boundaries of the workspace manifold. These boundaries or sub-manifolds are known as strata [5]. The most interesting feature of a stratified manifold is that the system is allowed to stay only on these strata. That means even though the workspace of the robot is NW dimensional, it is allowed to stay only on certain sub-manifolds of its workspace whose dimension in general isNS < NW. However there is still a lot more to these stratified manifolds. Even while residing on a stratum in a stratified manifold, the flow of the system is allowed only along certain directions on the strata, called leaves or foliages of the strata [5]. These foliations basically constitute some subsets of the tangent space of the strata. The following example in context to a quadruped robot will make the concept more clear.