Computer-aided modeling and control of multibody systems for robotics application

A closed-form formalism for modeling an analysis of constrained multibody systems subject to control and its application to robot dynamics are presented. The algorithm is derived from the virtual work principle and is cast in a recursive and matrix-vector form. The effects of a moving reference frame are included allowing simulation of a multibody system such as a robot on a moving base. The formalism can be applied to holonomic and simple nonholonomic systems. A symbolic program that can formulate, simplify, and linearize the equations of motion has been developed. The procedure symbolically eliminates the constraint forces and redundant coordinates, and generates the equations in a closed form. The formalism is then used to simulate a biped robot walking on a vibrating platform. Optimal control is used to compute the joint torques. The study shows that the closed-form formalism holds promise in the simulation of robotic systems