H∞ Control for Walking Robots Robust to the Bounded Uncertainties in the State and the Model

In recent years, we have seen a constant increase in the capabilities of walking robots, leading to early cases of their practical use, and a much broader application is expected in the near future. However, creating a robust control design (in the presence of disturbances and model uncertainties) for walking robots still remains a challenge. One challenging source of uncertainty is the combination of the contact constraints and the lack of full state information, which can potentially lead to an offset (a steady-state error) in the robot’s position, interfering with tasks requiring high accuracy and deteriorating the overall performance of the robot. This is further exacerbated by the presence of multiplicative model uncertainties, common to mobile robots. In this work, we introduce an H∞ control formulation designed to attenuate this type of disturbance. The proposed method can handle norm-bounded multiplicative uncertainties in the state, control, and disturbance matrices using a full-state static feedback control. The resulting control design procedure is a single semidefinite program which provides a large computational advantage over the alternative dynamic feedback controller methods. We demonstrate the effectiveness of the method in comparison with the alternative formulations in simulation. We demonstrate that the method can be effectively tuned using a regularization term in the cost function. We show that the upper bounds on the H∞ gain of the closed-loop system can be effectively tightened post control design.