Dynamics of robotic manipulators with wrist-mounted force-torque sensor: a singular perturbation approach

The nature of the dynamics of a rigid link n-degree-of-freedom robotic manipulator with an r-axis wrist-mounted force-torque sensor is examined during execution of a compliant motion task. A kinematic model is developed that models the flexure of the force-torque sensor during contact, and 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 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 results associated with the theory of singularity perturbed systems, it is shown analytically that the manipulator system can be controlled without consideration of the high-frequency parasitic dynamics associated with the force-torque sensor