Modification of a PD+ controller for the orbital stabilization of the motions of an all-wheel drive mechanical system

The problem of the orbital stabilization of the forced periodic motions of a non-linear all-wheel drive mechanical system is considered within the framework of a model that is widely used in problems of the planning of the motions and feedback design for industrial robotic manipulators. The basic result is the explicit indication of one of the possible redundant sets of coordinates tranverse to the nominal motion and the derivation of the linearization of their behaviour in an explicit form. The latter enabled us to validate the original approach in the controller design problem and to analyse the behaviour of the closed system in the neighbourhood of the nominal motion. The analytical results are illustrated by solving the problem of stabilizing the motion of the working tool of an industrial ABB IRB140 robotic manipulator that is suboptimal with respect to its high-speed response taking account of the known constraints imposed on the limiting values of the angular velocities of the individual robot components.