Kinematic Modeling and Control of Robot Manipulators via Unit Quaternions: Application to a Spherical Wrist

Unit quaternions have become a useful tool for describing rotations in space. This paper shows the application of unit quaternions (also called Euler parameters) to solve the problem of modeling and control of robot manipulators. First, a quaternion-based algorithm that allows to obtain the direct kinematic model of serial manipulators from the Denavit-Hartenberg parameters is introduced. This method is an alternative to the traditional one using homogeneous matrices. Then, a novel kinematic controller that uses Euler parameters as a set of nonminimal state variables is studied, including its Lyapunov stability analysis. Finally, to show the feasibility of the proposed scheme, the kinematic model of a typical spherical wrist is obtained and some simulations are carried out, showing the fulfillment of the control aim