Derivation of dynamic equations and parametric analysis for dual arm mobile manipulators using recursive Gibbs-Appell formulation

Mobile manipulators with only single robotic arm have been successfully exploited in many tasks. The performance of these kinds of robotic system improves by assembling another robotic arm. In particular, the dual-arm mobile robotic manipulators have been applied in almost all the works that the human being can perform by two hands. Increasing the number of the links besides the dynamic interactions between the manipulator and the mobile platform as well as both nonholonomic constraints of the mobile base makes the manual derivation of motion equations almost impossible. So, this paper proposes a new solution to the problem of dynamic modeling of wheeled mobile manipulators with dual arms in an automatic and systematic approach. To avoid computing the "Lagrange multipliers" associated with the nonholonomic constraints, the equations of motion are derived according to the recursive Gibbs-Appell formulation. Also all the mathematical operations are performed by 3×3 and 3×1 matrices. Finally, this method is applied to a mobile manipulator with two robotic arms to demonstrate the ability of the proposed method in deriving the equations of motion and parametric analysis for such complex systems.