A robust control of robot manipulators for physical interaction: stability analysis for the interaction with unknown environments

A robust control designed for multiple degrees-of-freedom (DOF) robot manipulators performing complex tasks requiring frequent physical interaction with unknown and/or uncertain environments is analyzed to provide complete stability conditions and explain its robustness to environmental changes and disturbances. Nonlinear bang–bang impact control was introduced about two decades ago. High-velocity impact experiments using a one DOF robot and a stiff aluminum wall showed superior performance than other controllers. Moreover, it does not use robot dynamics and environmental dynamics for its design. Furthermore, intriguingly, it utilized the nonlinear joint friction, which was commonly regarded as a factor deteriorating the control performance, to subside impact energy sensibly. To date, the stability was, however, not completely proved. Thus, NBBIC was not widely adopted. In this study, thus, complete and sufficient stability conditions of NBBIC for multi-DOF robots are derived based on energy comparisons and \(L_{\infty }^{n}\) space analysis. It was found that the NBBIC stability condition does not require information on the environmental dynamics and disturbances. Stability was affected by the intentional time delay, which was needed to efficiently and effectively estimate the environment and robot dynamics and the accuracy of robot inertia estimate. As was expected, larger friction was better for subsiding the impact force that is expected when impacting an environment at high velocity.