The calculation of robot dynamics using articulated-body inertias

This paper describes a new method for calculating the acceleration of a robot in response to given actuator forces. The method is applicable to open-loop kinematic chains containing revolute and prismatic joints. The algorithm is based on recursive formulas involving quantities called articulated-body inertias, which represent the inertia properties of collections of rigid bodies connected together by joints allowing constrained relative motion between the bodies. A new, matrix-based notation is introduced to represent articulated-body inertias and other spatial quantities. This notation is used to develop the algorithm, and results in a compact representation of the equations. The new algorithm has a computational requirement that varies linearly with the number of joints, and its efficiency is compared with other published algorithms.