Stability of the Robot Compliant Motion Control - Part II : Implementation

We have shown how unstructured modeling was used to derive a general stability condition in Part 1. In Part 2, we focus on the particular dynamics (structures modeling) of the robot manipulator and environment. Using rigid body dynamics, the stability condition for the direct drive robots has been achieved in terms of the Jacobian and robot tracking controller. Combining the structured and unstructured modeling, a stability condition for a particular application can be obtained. This approach has been used to analyze compliant motion on the University of Minnesota robot using a feedforward torque controller. We have obtained a stability condition for this application. Through both simulation and experiment, the sufficiency of this condition has been demonstrated. For a sufficient stability condition, recall that if the condition is satisfied, then the stability is guaranteed; however, if the condition is violated, no conclusion can be made.