Passivity-Based Control

Stabilization of physical systems by shaping their energy function is a well-established technique whose roots date back to the work of Lagrange and Legendre. Potential energy shaping for fully actuated mechanical systems was first introduced in Takegaki and Arimoto (Trans ASME J Dyn Syst Meas Control 12:119--125, 1981) more than 30 years ago. In Ortega and Spong (Automatica 25(6):877--888, 1989) it was proved that passivity was the key property underlying the stabilization mechanism of these designs, and the, now widely popular, term of passivity-based control was coined. In this chapter we summarize the basic principles and some of the main developments of this controller design technique