| Volume 21 Issue 05/06 - Publication Date: 1 May 2002 |
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| Nonholonomy on Purpose |
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| On Motion Planning for Robotic
Manipulation with Permanent Rolling Contacts |
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| 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 |
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| 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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