A Simple Approach to Kinematic Inversion of Redundant Mechanisms

This work addresses the problem of kinematic inversion of complex redundant mechanisms. The inverse problem for redundant mechanisms is known to be ill-posed Using the multibody formalism and the capability to automatically write the equations of motion of mechanisms provided by general multibody software, a simple algorithm is proposed for the solution of the inverse kinematics problem for redundant robotic systems. The algorithm, in its basic form, is equivalent to the classical Moore-Penrose pseudo-inverse applied to the Jacobian matrix of the constraints. The inverse solution is found in a least squares sense: among the infinite admissible solutions, the one with minimum norm is chosen. Little extra effort allows the computation of optimized inverse kinematics. In this case, the solution is found in a weighted least squares sense. Weights can be automatically chosen by an optimization algorithm in order to minimize a given cost function, or assigned by the user based on engineering judgment. Among the advantages of the proposed approach, it is worth mentioning its simplicity and the possibility to be used within generic multibody software with very limited effort.