Dynamics of Mobile Manipulators using Dual Quaternion Algebra

TL;DR

This paper introduces two general methods for deriving the dynamics of mobile manipulators using dual quaternion algebra, enhancing flexibility and connection to classical formulations, with comparable accuracy to existing algorithms.

Contribution

It presents two novel approaches based on dual quaternion algebra for mobile manipulator dynamics, including a recursive Newton-Euler method and a GPLC-based method with arbitrary constraints.

Findings

Both methods are more general than existing ones.

Simulation shows comparable accuracy to classic algorithms.

GPLC approach handles arbitrary constraints.

Abstract

This paper presents two approaches to obtain the dynamical equations of mobile manipulators using dual quaternion algebra. The first one is based on a general recursive Newton-Euler formulation and uses twists and wrenches, which are propagated through high-level algebraic operations and works for any type of joints and arbitrary parameterizations. The second approach is based on Gauss's Principle of Least Constraint (GPLC) and includes arbitrary equality constraints. In addition to showing the connections of GPLC with Gibbs-Appell and Kane's equations, we use it to model a nonholonomic mobile manipulator. Our current formulations are more general than their counterparts in the state of the art, although GPLC is more computationally expensive, and simulation results show that they are as accurate as the classic recursive Newton-Euler algorithm.