Kinematic modelling of tasks under constraints. Application to fine motion and calibration

This article deals with problems of motion control and calibration including kinematic constraints. First, we present a method aimed at automatically providing a kinematic numerical model to represent a task being achieved on a mechanical structure composed of rigid bodies. The framework proposed is based on a systematic graph describing this mechanical system, that guides the computation of the basic kinematic relationships. An insight into the constrained motion control problems is gained through the analysis of the linear dependencies of the model. We apply this method to compute trajectories of a polyhedral object in contact with others objects. Our formalism here makes use of faces, edges and vertices of the objects, which provides an easy description of tasks, and a rapid computation of good trajectories, even for three dimensional tasks. These results supports the flexibility and the domain of application of our method. Some applications are presented at the end of the article to illustrate our approach.