Volume 21 Issue 05/06 - Publication Date: 1 May 2002
Nonholonomy on Purpose
On Motion Planning for Robotic Manipulation with Permanent Rolling Contacts
Bálint Kiss and Jean Lévine Centre Automatique et Systèmes Ecole des Mines de Paris Fontainebleau, France and Béla Lantos Department of Control Engineering and Information Technology Budapest University of Technology and Economics Budapest, Hungary
We address the motion planning problem (open-loop trajectory design) for manipulating rigid bodies with permanent rolling contacts without slipping. This problem is related in particular to dextrous manipulation with robotic hands, consisting in changing the position and orientation of the manipulated object together with its grasp. We prove the flatness property for planar structures allowing to solve the motion planning problem by simple interpolation, without need to integrate the system differential equations and without quasi-static approximations. Though this property fails to be valid for general three-dimensional hand structures, similar results can be obtained for special structures thanks to the notion of Liouvillian systems. The links between flat or Liouvillian hand-object structures and non-holonomy of the contacts between fingers and object are also discussed. Several examples are studied in detail.
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Example One (0.8 MB)
Example Two (1.6 MB)
Subsection 4.2 (1.6 MB)
Subsection 4.3 (2.1 MB)
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