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Abstract

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.

Keywords

dextrous manipulation nonholonomic mechanical systems motion planning flat systems Liouvillian systems

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