Nonlinear Control and Chaotic Vibrations of Perturbed Trajectories of Manipulators

We study different types of manipulators’ attractors and propose a motion control method. In our analysis the manipulator’s motion is perturbed and its stability investigated using the nonlinear equations of perturbations and linearized equations for practical control. In order to realize a practical control the common areas of stability for nonlinear and linear models are identified. The maps of stability calculated as functions of model parameters are proposed as a tool for motion control. The spectrum of Lyapunov exponents is introduced as a practical measure of motion quality. The procedure allows choosing a way of reaching system stability in order to avoid undesired attractors. Additionally, the possibility of the occurrence of strange chaotic attractors in manipulators, ways they appear, and codimension 2 bifurcations have been analyzed.