DYNAMICS OF ROBOTIC MANIPULATORS WITH WRIST-MOUNTED FORCE-TORQUE SENSOR - A SINGULAR PERTURBATION APPROACH

In this short paper, we examine the nature of the dynamics of a rigid link n-degree-of-freedom robotic manipulator with an r-axis wrist-mounted force-torque sensor during execution of a compliant motion task. Using a kinematic model developed that models the flexure of the force-torque sensor during contact, the dynamic equations of the robot are derived using the Lagrange formulation. In order to display the two time scale nature of the resultant dynamic equations of motion, a transformation of coordinates is first made. Through utilization of the fact that the mechanical stiffness of the flexural components of the force-torque sensor is typically quite large, the dynamic equations of motion of the robot manipulator during contact can be rewritten in standard singular perturbation form. Using existing results associated with the theory of singularly perturbed systems, it is then shown analytically that the manipulator system may be controlled without consideration of the high-frequency parasitic dynamics associated with the force-torque sensor. The results of this short paper provide a theoretical justification for the common engineering practice in which these high-frequency dynamics are ignored in control system design.