Adaptive tracking control for underactuated mechanical systems with relative degree two

Abstract

The adaptive tracking state-feedback control for underactuated mechanical systems with outputs characterized by global relative degree equal to two is addressed. A new control technique called virtual control is proposed. Fictitious control inputs and outputs are introduced to achieve full actuation: the key step is to find the reference signals for the fictitious outputs so that the resulting virtual adaptive controls are zero. The adaptive control of an underactuated three-link walking robot with unknown torso mass is designed according to the proposed control strategy. Simulations show that adaptation is crucial for stable walking.