Quasi-minimal computation of the dynamic model of a robot manipulator utilizing the newton-euler formalism and the notion of augmented body

Abstract

Real-time dynamic control of robot manipulators requires on-line computation of the dynamic model that expresses the generalized forces to be applied to their joints, as a function of their generalized coordinates, velocities and accelerations. To do this, this paper presents a method of computation of this model that uses a quasiminimal number of elementary arithmetical operations and that can be applied systematically to robot manipulators with a simple kinematic chain structure and revolute and/or prismatic joints. To reach this quasi-minimal number, use if primarily made of the following : * a computation that is intrinsic rather than extrinsic, analytical rather than numerical and iterative rather than developed ; * the Newton-Euler formalism rather than the Lagrangian one and * the notion of augmented body, generalized to this type of structure. An example demonstrates that the computation of the dynamic model of an industrial robot manipulator with six revolute joints (the most complicated case in practice) can be effected with less than 300 arithmetical operations (adds and multiplies).