A Novel Dual Quaternion Based Cost Effcient Recursive Newton-Euler Inverse Dynamics Algorithm

Abstract

In this paper, the well known recursive Newton-Euler inverse dynamics algorithm for serial manipulators is reformulated into the context of the algebra of Dual Quaternions. Here we structure the forward kinematic description with screws and line displacements rather than the well established Denavit-Hartemberg parameters, thus accounting better efficiency, compactness and simpler dynamical models. We also present here the closed solution for the dqRNEA, and to do so we formalize some of the algebra for dual quaternion-vectors and dual quaternion-matrices. With a closed formulation of the dqRNEA we also create a dual quaternion based formulation for the computed torque control, a feedback linearization method for controlling a serial manipulator's torques in the joint space. Finally, a cost analysis of the main Dual Quaternions operations and of the Newton-Euler inverse dynamics algorithm as a whole is made and compared with other results in the literature.

Dynamics of Mobile Manipulators Using Dual Quaternion Algebra

“…Furthermore, our formulation works for any type of joint because it takes into account arbitrary twists. Thus, our strategy is more general than the work of Miranda et al [67], which considered only manipulators with revolute joints.…”