Dynamics of Mobile Manipulators using Dual Quaternion Algebra
This work addresses the modeling of complex robotic systems like mobile manipulators, offering incremental improvements in generality for researchers in robotics and control theory.
The paper tackles the problem of deriving dynamical equations for mobile manipulators by presenting two approaches using dual quaternion algebra: a recursive Newton-Euler formulation and one based on Gauss's Principle of Least Constraint, which are shown to be more general than existing methods and as accurate as classic algorithms in simulations.
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.