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The International Journal of Robotics Research
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Motion Planning for a Class of Planar Closed-chain Manipulators

N. Shvalb

Department of ME, Technion-Israel Institute of Technology, Israel, shvalbn{at}techunix.technion.ac.il

M. Shoham

Department of ME, Technion-Israel Institute of Technology, Israel

G. Liu

Department of Computer Science, Stanford University, Stanford, CA, USA, liugf{at}cs.stanford.edu

J.C. Trinkle

Department of Computer Science, Rensselaer Polytechnic Institute, USA, trink{at}cs.rpi.edu

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 N 3), where N is the maximum number of links in a leg. Examples illustrating the method are given.

Key Words: Motion planning • planar mechanisms • topology • parallel mechanism • connected components

The International Journal of Robotics Research, Vol. 26, No. 5, 457-473 (2007)
DOI: 10.1177/0278364907078094
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