Interval-Arithmetic-Based Robust Control of Fully Actuated Mechanical Systems

We propose a control approach for fully actuated mechanical systems using interval arithmetic, which guarantees global uniform ultimate boundedness of the tracking error and robust performance despite model uncertainties and input disturbances. Existing robust control methods often require computationally expensive or empirical estimations of bounds of state-dependent, nonlinear perturbations, arising from model mismatches. Our robust feedback control approach is different and removes these difficulties by using interval arithmetic to determine online the worst case perturbation acting on the error dynamics. We present two interval-arithmetic-based robust controllers by robustifying inverse-dynamics and passivity-based nominal control schemes. The effectiveness of our approach is demonstrated on a real robot manipulator with uncertain dynamics.