Using Puiseux series to control non-redundant robots at singularities

Abstract

It is shown that the joint solution for a nonredundant robot following a piecewise analytic path can be expressed at kinematic singularities using a fractional power series (or Puiseux series). This is of use because the derivatives of such joint solutions often become infinite at singularities, making it difficult to track the path without incurring very large joint velocities and accelerations. Puiseux series provide a way to smoothly reparameterize the joint solution at singularities, which can be applied to path timing and perhaps other aspects of robot control.