Nonlinear State Estimation for Trajectory Tracking of a Flexible Parallel Manipulator

Abstract

Lightweight robots can be advantageous when considering the lower energy consumption, the possibility to use smaller motors and the lower material cost. Nevertheless, in such lightweight structures non-negligible flexibilities are inherent which can lead to significant oscillations making the control more difficult. Within this research end-effector trajectory tracking of a parallel manipulator with a highly flexible link is considered. As centerpiece, a new approach to estimate the state of the system of differential algebraic equations is discussed to obtain the end-effector position and velocity. For the estimator, the kinematic loop is treated by a projection tangential to the constraint manifold which is based on a QR decomposition. Subsequently, an Unscented Kalman Filter is applied and the dependent coordinates are obtained by satisfying the algebraic constraint equations with the Newton-Raphson method. The utilized signals for the estimator are on the one hand position measurements of the actuators which are realized as direct drives and on the other hand measurements of strain gauges attached to the long and highly flexible link. As application, a basic end-effector output controller based on an equivalent rigid model and the transfer function of the dominant first bending eigenmode is utilized to enhance the tracking results. The concepts are applied to an experimental rig for validation purposes and to show first results for end-effector estimation with feedback control.