1. Introduction

The aim of system control is to move a system from a given initial state to a given final state or reference trajectory. If it is defined by a deviation between a measured or estimated output variable and a reference setpoint or trajectory, it is called closed-loop control. It can also be designed to reject disturbances, model errors and external environmental actions on the system. The complexity of control increases depending on whether the system is single-input/ single-output or multi-input/multi-output, or whether it is represented by a system of linear or non-linear differential equations, with stable or unstable equilibrium points. Humanoid robots present a number of control challenges. They are polyarticulated mechanical systems that can have more than thirty degrees of freedom ddl. They are mobile in their environment. Contacts with the environment can be of different kinds: unilateral...