Motion Control of a Spatial Elastic Manipulator in the Presence of Measurement Noises

This paper presents a method for the end effector motion control of a spatial three-link robot having elastic second and third links including measurement noises. In the derivation of equations of motion, not to face with complex equations of motion, each link is modeled as though the links are not connected and the restrictions on the links due to connecting them by joints are written as constraint equations. After that the Lagrange multipliers are eliminated and the constraint equations at the acceleration level are substituted into the equations of motion to reduce the number of equations. To handle the non-minimum phase property, the equations of motion of the elastic manipulator are divided as the equations corresponding to a pseudostatic equilibrium and the equations of the deviations from them. Definition of the pseudostatic equilibrium used in this study can be given as a hypothetical state in which the end effector velocity and the end effector acceleration possess their reference values while the elastic deflections are instantly constant. The advantages of this control method are that the elastic deflections and the control inputs required for the pseudostatic equilibrium are obtained by an algebraic method and the feedback stabilization control inputs for the deviation equations are determined without linearizing the dynamic equations. The required measurements are obtained from the strain gauges on the links, the encoders placed on the joints and the position sensors attached to the end effector. For each sensor, a low pass filter is used. Simulations are made with low and high values of crossover frequencies to show the positive and negative effects of filtering on the responses of the system.