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

Abstract

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.

The axes of random infinitesimal rotations and the propagation of orientation uncertainty

“…Typically, in robotic applications the propagation of orientation uncertainty is defined as the propagation along different joints (encoders) on a kinematic chain, or in the context of dynamic control the propagation of orientation uncertainty is defined when the orientation at time k + 1 depends on noisy orientation measured at time k [1,2]. In contrast, here we are interested in the static configuration where a fixed orientation of a rigid body is repeatedly measured in the same experimental conditions.…”

Robust Quaternion-based Cooperative Manipulation without Force/Torque Information

“…By taking the time derivative of (14) and (15), employing (2) and certain properties of skew-symmetric matrices (Campa et al, 2006), it can be shown that (Siciliano et al, 2010) e…”

“…On the other hand, the representation using unit quaternions, which is employed in this work, constitutes a singularity-free orientation representation, without complicating the control design. Unit quaternions are employed in (Campa et al, 2006;Caccavale et al, 2000Caccavale et al, , 2008Aghili, 2011) for manipulation tasks and in (Erhart and Hirche, 2016) for the analysis of the interaction dynamics in cooperative manipulation.…”

Concurrent control of position/orientation of a redundant manipulator based on virtual spring-damper hypothesis

“…It has been applied to a spherical wrist, a manipulator, an underwater vehicle, etc. for set-point regulation [13], [14], [15]. There are papers on redundant manipulator control using quaternion.…”