Compared to classical methods as Cardan, Fick and Euler angles which are based on homogeneous transformation, dual quaternions [1] offer an advantageous representation of a rigid transformation in 3D-space in many aspects. The dual quaternions have less computer memory cost, computer memory locations, since it needs 8 elements while classical methods require 12 elements, to describe a rotation composed with translation of a rigid body in 3D-space. Thus, the homogeneous transformation methods cost more storage and require a high computational time due to the nonlinearity of the end-effector coordinates. Moreover, these methods impose a well-defined rotation order. While, the dual quaternions method enables the reduction of the number of mathematical operations which leads automatically to minimize the computational cost [2]. Moreover, dual quaternions method permits to avoid discontinuities and singularities that arise from the Euler angle representation based on cylindrical polar coordinates to represent the motion of a rigid body in 3D-space [3].

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].