Singularities of serial robots: Identification and distance computation using geometric algebra

Abstract

The singularities of serial robotic manipulators are those configurations in which the robot loses the ability to move in at least one direction. Hence, their identification is fundamental to enhance the performance of current control and motion planning strategies. While classical approaches entail the computation of the determinant of either a 6?xn or nxn matrix for an n degrees of freedom serial robot, this work addresses a novel singularity identification method based on the six-dimensional and three-dimensional geometric algebras. It consists of identifying which configurations cause the exterior product of the twists defined by the joint axes of the robot to vanish. In addition, since rotors represent rotations in geometric algebra, once these singularities have been identified, a distance function can be defined in the configuration space C such that its restriction to the set of singular configurations S allows us to compute the distance of any configuration to a given singularity.