Manipulation planning: Addressing the crossed foliation issue

This paper deals with manipulation planning. First, we propose a new tool called the constraint graph to describe the various motion constraints relative to a manipulation planning problem. Then, we describe a problem arising for some manipulation planning problems called the crossed foliation issue. We propose a extension of RRT algorithm that explores the leaves of the foliations generated by motion constraints and that solves the crossed foliation problem. Finally, we show a wide variety of problem that our approach can solve.