Dynamic modeling of nonholonomic wheeled mobile manipulators with elastic joints using recursive Gibbs–Appell formulation

This paper focuses on the study of dynamic modeling of nonholonomic wheeled mobile robotic manipulators, which consist of a serial manipulator with elastic joints and an autonomous wheeled mobile platform. To avoid computing the Lagrange multipliers associated with the nonholonomic constraints, the approach of Gibbs-Appell (G-A) formulation in recursive form is adopted. For modeling the system completely and precisely, dynamic interactions between the manipulator and the mobile platform, as well as both nonholonomic constraints associated with the no-slipping and the no-skidding conditions, are included. Based on developed formulation, an algorithm is proposed that recursively and systematically derives the equation of motion. In this algorithm, in order to improve the computational complexity, all mathematical operations are done by only 3×33×3 and 3×13×1 matrices. Also, all dynamic expressions of a link are expressed in the same link local coordinate system. Finally, two computational simulations for mobile manipulators with rigid and elastic joints are presented to indicate the capability of this algorithm in generating the equation of motion of mobile robotic manipulators with high degree of freedom.