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

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.