The Modeling of Redundantly Actuated Mechanical Systems

Abstract

Abstract Dynamics modeling is essential in the design and control of mechanical systems, the focus of the paper being redundantly actuated systems, which bring about special challenges. The authors resort to the natural orthogonal complement (NOC), based on an adaptation of screw theory, to derive the dynamics model. Benefiting from the elimination of the constraint wrenches, the NOC offers a simple, systematic alternative to the modeling of redundantly actuated mechanical systems. The optimum actuator-torque distribution is determined via Euclidean-norm minimization; then, by relying on the QR-decomposition, an efficient and robust method is produced to compute explicitly the right Moore–Penrose generalized inverse of the coefficient matrix. The methodology is illustrated via a case study involving a redundantly actuated parallel-kinematics machine with three degrees of freedom and four actuators.