Kinematic Control of Serial Manipulators Using Clifford Algebra

We exploit the potentials of Clifford algebra to present a singularity free, compact, and computationally efficient scheme for kinematic control of serial manipulators. We introduce and implement the new special proportional-derivative control scheme. The introduced control scheme facilitates a fast motion control for the manipulators and enables them to react to the changes in their set points quickly. Such conditions are common in the context of dynamic working environments and collaborative manipulation scenarios. We describe the kinematics of the manipulators with unit dual quaternions using screw theory. The Lie-group properties of quaternions and dual quaternions are presented and discussed. By means of Lyapunov theory, it will be shown that the controller is globally exponentially stable. Copyright (C) 2020 The Authors.