Dynamic modelling for robotic manipulators with a force-torque sensor during compliant motion

A complete dynamic model for a rigid link, n-degree-of-freedom robotic manipulator with an r-axis force-torque sensor during contact with a compliant work environment is developed. A Kinematic model is presented for an r-axis force-torque sensor which treats the sensor as an axis joint, where all r axes intersect at a common point. With the resultant kinematic model, the closed-form equations of motion of the manipulator sensor system are developed using a Lagrangian approach. The work environment is modeled as a mechanical impedance with inertia, damping, and stiffness terms. Using of kinematic transformations between the relevant generalized coordinate frames, the work environment dynamic model and manipulator-sensor dynamics are combined into a single set of equations in first-order vector-matrix form. Finally, for completeness, actuator dynamics are included in the system dynamic model, again with the resultant system dynamics in vector-matrix form. A numerical example of a two-degree-of-freedom robot with a two-axis serves to illustrate the kinematic modeling of a force-torque sensor