Probabilistic motion planning for parallel mechanisms

Despite the increasing interest in parallel mechanisms during the last years, few researchers have addressed the motion planning problem for such systems. The few existing techniques lie in a representation of the workspace of the mechanism (or its boundary). However, obtaining this representation is generally too difficult, only partial solutions exist for particular cases. In this paper we propose a general approach based on probabilistic motion planning techniques. This approach does not need any modeling of the robot's workspace. It combines random sampling techniques with simple but general geometric algorithms that guide the sampling toward feasible configurations satisfying the closure constraints of the parallel mechanism. The efficiency and the generality of the method are demonstrated onto several complex mechanisms mode up with serial or parallel associations of Stewart platforms, or created with several redundant robots manipulating an object.