Path Tracking in Motion Planning

Abstract

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.*