Motion planning for a class of planar closed-chain manipulators

We study the motion problem for planar star-shaped manipulators. These manipulators are formed by joining k "legs" to a common point (like the thorax of an insect) and then fixing the "feet" to the ground. The result is a planar parallel manipulator with k - 1 independent closed loops. A topological analysis is used to understand the global structure of the configuration space so that planning problem can be solved exactly. The worst-case complexity of our algorithm is O(k³ N³), where N is the maximum number of links in a leg. A simple example illustrating our method is given