— We study 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 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. Examples illustrating our method are given.
Guanfeng Liu, Jeffrey C. Trinkle, N. Shvalb