Formulation of dynamics, actuation, and inversion of a three-dimensional two-link rigid body system

In this paper, three issues related to three-dimensional multilink rigid body systems are considered: dynamics, actuation, and inversion. Based on the Newton-Euler equations, a state space formulation of the dynamics is discussed that renders itself to inclusion of actuators, and allows systematic ways of stabilization and construction of inverse systems. The development here is relevant to robotic systems, biological modeling, humanoid studies, and collaborating man-machine systems. The recursive dynamic formulation involves a method for sequential measurement and estimation of joint forces and couples for an open chain system. The sequence can start from top downwards or from the ground upwards. Three-dimensional actuators that produce couples at the joints are included in the dynamics. Inverse methods that allow estimation of these couples from the kinematic trajectories and physical parameters of the system are developed. The formulation and derivations are carried out for a two-link system. Digital computer simulations of a two-rigid body system are presented to demonstrate the feasibility and effectiveness of the methods. © 2005 Wiley Periodicals, Inc.