Contact stability in model-based force control systems of robot manipulators

The authors address the stability problem in force control of robot manipulators. They analyze the stability of four well-known model-based force control systems: hybrid force control, resolved acceleration based force control, stiffness control, and impedance control. The analysis is based on linearized models and uses the Routh-Hurwitz criteria. The results show that the stability of the four control systems studied depends upon the feedback gains as well as the manipulator configuration. When an arm engaged in a contact task unexpectedly loses contact with the environment, all control systems studied except the hybrid control remain stable. The cause of instability in contact tasks is that the environmental stiffness matrix increases the equivalent position gain in the control system. If the velocity gain is chosen based only on the position gain neglecting a large environmental stiffness, the resulting system will be highly underdamped and possibly unstable