Dynamics of Mobile Manipulators using Dual Quaternion Algebra

Email: bruno.adorno@manchester.ac.uk 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. Keywords: Mobile Manipulator Dynamics, Dual Quaternion Algebra, Newton-Euler Model, Gauss's Principle of Least Constraint, Euler-Lagrange Equations, Gibbs-Appell Equations, Kane's Equations. 1 INTRODUCTION In the last thirty years, there have been an expressive amount of papers dealing with different representations for robot modeling. Notorious examples can be found in the works of Feather-stone [1-3], McCarthy [4-6], Selig [7,8], and Bayro-Corrochano [9], among many others. One of the reasons for such investigations is that the complexity of a robotic system goes far beyond the complexity of the mechanism itself. A typical robotic system involves motion/force/impedance control, path planning, task planning, and many more higher-level layers. Therefore, representations that are very useful for robot modeling, such as homogeneous transformation matrices, not necessarily are easy to use when performing pose control or impedance control, for example [10].