Motion planning for a class of planar closed-chain manipulators

The paper reports studies on the motion planning 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 the planning problem can be solved exactly. The worst-case complexity of the algorithm is O(k³ N³), where N is the maximum number of links in a leg. Examples illustrating the method are given.