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The Computer Journal 1993 36(5):515-524; doi:10.1093/comjnl/36.5.515
© 1993 by British Computer Society
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Path Tracking in Motion Planning

M. J. González-López * and T. Recio *

Dpto. Matematicas, Universidad de Cantabria, Santander 39071, Spain

The inverse kinematics problem asks to determine the configurations of a robot manipulator that places the tip of the robot in a given position and orientation. The generalization of this problem, called path tracking or path following, is to determine if there exists a path of a manipulator in which the tip follows a given path. We study two different versions of this generalized problem: the tracking of the image of a path and the tracking of a path, giving to both of them an algorithmic answer. The main tool to obtain this solution is to construct a Cylindrical Algebraic Decomposition (CAD) of the set of admissible placements of the manipulator, such that is follows the projection onto the variables of the tip and is compatible with a triangulation of the image of the given path. Testing some properties in an oriented graph built from the adjacency graph of this CAD, provides the solution to the mentioned problems.*

Received January 1993. revised May 1993.

* Dpto. Matemáticas, Universidad de Cantabria, Santander 39071, Spain


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