Motion equation derivation and tip-over evaluations for K mobile manipulators with the consideration of motors mass by the use of Gibbs-Appell formulation

in this paper, the dynamic model of mobile manipulator contains N-rigid links developed for multiple ones with the consideration of the joint motor's mass and end effector load. The single mobile manipulator restrictions and the needs to do the jobs and object manipulation cooperatively and respectively cause to suggest the multiple mobile manipulators. But, the requested precision and the predefined path feature leads to model improvements and system's tip-over evaluations by ZMP and MHS approaches. The extra mathematical operations necessitate for computing the motion equations of K mobile manipulators. Therefore, the recursive Gibbs-Appell formulation has been used to derive the motion equations. In comparison to Lagrange equations, the eliminations of Lagrange multiplier for non-holonomic constraints don't need in this formulation. As well as, the computational complexity decrease comparatively. The tip-over checking approaches define and used for stable robot manipulations. But, the explained approaches just provide the stable margins without sensing about the physical events happen during the motion instability. The angle of reversal calculates for the suggested system to represent the domain that turnover occurs when this angle seen during the motion. The Simulations results perform for a five-link mobile manipulator in MAT LAB software. Next, by using stability checking approaches, it has been cleared that the reversal limit of rotation should be defined to improve the previous criterion margins.