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The main purpose of this paper is to derive the inverse dynamic equation of motion of n-rigid robotic manipulator that mounted on a mobile platform, systematically. To avoid the Lagrange multipliers associated with the nonholonomic constraints the approach of Gibbs-Appell formulation in recursive form is adopted. For modeling the system completely and precisely the 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 also included. In order to reduce the computational complexity, all the mathematical operations are done by only 3×3 and 3×1 matrices. Also, all dynamic characteristics of a link are expressed in the same link local coordinate system. Finally, a computational simulation for a manipulator with five revolute joints that mounted on a mobile platform is presented to show the ability of this algorithm in generating the equation of motion of mobile robotic manipulators with high degree of freedom.

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In this article, a novel intelligent online tip-over avoidance algorithm is presented considering the interactions between the mobile base and manipulator arm. To this end, the newly suggested dynamic stability margin measure named Moment-Height-Stability (MHS) is adopted. Additionally, a function representing the increment of postural stability margin metric is defined based on MHS. The system dynamic equilibrium is then enhanced using a fuzzy logic approach. The response of the suggested method of this paper is compared with that of a previously Force-Angle based proposed one considering a planar mobile manipulator. First the dynamics of the robot is derived using Newton-Euler method via MAPLE 16 and it is verified through the model provided in SimMechanics toolbox of Simulink. The efficiency of the suggested method is illustrated in comparison to the previous one on a destabilizing robot path. Besides, the performance of proposed method of the present study is investigated in the presence of external disturbances. The obtained simulation results reveal the effectiveness of the performance of the suggested technique for stability improvement of wheeled mobile manipulators once encountering unexpected disturbing situations.