16.1 Introduction

It is well known that, disregarding implementation aspects, the sliding mode approach constitutes the most simple and effective control method to deal with the control of complex mechanical systems, in particular robotic systems. Indeed any joint velocity profile can be tracked by a completely decoupled discontinuous control law, exploiting some good properties of the inertia matrix, the complexity of which is relatively independent from the complexity of the model, rapidly increasing with the number of degrees of freedom.

This control approach has not been considered suitable for real implementation due to the so-called chattering phenomenon. This phenomenon, which is tied to the discontinuous nature of the control strategy, is dangerous, not because the control signals chatter, but because they chatter at a frequency that is not sufficiently high due to non-idealities (finite bandwidth of the actuators, time delays, etc.). In this sense, often the use of a continuous approximation of the discontinuous control signals [1], worsens this phenomenon.

Another way to avoid chattering is based on the use of an observer [2] controlled so as to generate a sliding mode on a manifold in the observer state space which tends to coincide with the ideal sliding manifold. The discontinuous high-frequency control is filtered by the high-gain unmodelled dynamics giving rise to a continuous control which turns out to be close to the so-called equivalent control [2].

Another way to avoid chattering without using observers consists of enforcing a second-order...