A recursive algorithm to exploit a multiple-arm space manipulator equations of motion by the Lagrange method in terms of quasi-coordinates

According to high degrees of freedom of multiple-arm space manipulators, it is cumbersome to exploit equations of motion of such systems. In this paper, an algorithm is provided by using Lagrange equations in terms of quasi-coordinates to construct equations of motion of a space robot with multiple arms which each arm has an arbitrary number of links. Lack of constructing kinematic energy, lack of calculating partial derivatives and being a recursive algorithm resulted in diminished volume of calculations. To exploit equations of motion, first equations of motion have been expressed by Lagrange formulation in terms of quasi-coordinates. Then the calculation of partial derivative terms has been done by using recursive kinematic equations. At the end a dual arm robot, which each arm has two links with three degrees of freedom spherical joints, has been modeled by the recursive algorithm presented in this paper and simulated by MATLAB. Then, the results of simulation have been compared by line graphs conducted by ADAMS. Authenticity of the aforementioned algorithm has been proved by correspondence of attained figures.