Motion equation of nonholonomic wheeled mobile robotic manipulator with revolute-prismatic joints using recursive Gibbs-Appell formulation

The main intent of this paper is to represent a symbolic algorithm, capable of deriving the equations of motion of N-rigid link manipulators with revolute prismatic (R-P) joints, which mounted on a mobile platform. The presence of prismatic joints besides the revolute ones, as well as the nonholonomic characteristics of the mobile platform makes the derivation of governing equations difficult. So, to derive the kinematic and dynamic equations of motion of such a complex system, and also to avoid computing the Lagrange multipliers associated with the nonholonomic constraints, the application of recursive Gibbs Appell (G-A) formulation is applied. For modeling the system completely and precisely, the dynamic interactions between the manipulator and the mobile platform, the coupling effects due to the simultaneous rotating and sliding motion of the rigid arms, as well as both nonholonomic constraints associated with the no-slipping and the no-skidding conditions are included. Moreover, to improve the computational efficiency of the proposed systematic algorithm, all mathematical operations are done by only 3 x 3 and 3 x 1 matrices. Finally, a numerical simulation for a mobile manipulator with three R-P joints is performed, by using a developed computer program, to show the ability of this algorithm in deriving and solving the equations of motion of such systems. (C) 2014 Elsevier Inc. All rights reserved.