Redundantly Actuated 3RRR Parallel Planar Manipulator - Numerical Analyses of its Dynamics Sensitivity on Modifications of its Platforms Inertia Parameters

Abstract

Below, numerical analyses, as well as dynamics of a complex mechanism, are presented. Two objectives are focused: inverse dynamic model is needed (dedicated to be use in the model predictive controller); an identification method is searched (some trajectory parameters are controlled, when specific trajectory is tracked under an open-loop model-based control), as selected parameters must be identified for the model. A redundantly actuated mechatronic system is considered (in the present case some planar, parallel manipulator). When the redundancies are present, traditional torque estimation techniques can not be used directly (a non-square matrix is present in the equations). Thus, the right Moore-Penrose pseudo-inverse is used to estimate them. To model the mechanism - multibody dynamics is used. Its dynamics equations are nonlinear in respect to the joints position (displacements are significant during the mechanism motion). An open-loop model-based control algorithm is postulated for the system (the subcomponents from the closed-loop controller will not be considered in the present paper). As the real parameters of the controlled object can differ from the ones proposed in the controller, obtained trajectories differ from the requested (open-loop controller is used only). Correlations between the inertia error and the trajectory errors are tested. Sensible trajectory parameters are searched to estimate inertia of the controlled object. At present, analyses are restricted to numerical experiments, only.