9 Passivity-Based Control

Abstract

Dynamics of a robot naturally satisfy passivity whether its tool endpoint is free to move or constrained on a surface of an object or environment. This property is inherent to the fact that. robot dynamics can be derived from a variational forni based on the concept of EL(Eu1er- Lagrange) formalism. In this paper it is shown that a class of robust and effective controllers can be designed by referring to the variational form. These controllers have a simple structure and can be designed without using the exact knowledge of kinematic and dynamic parameters and thereby are robust against parameter uncertainties. It is also shown that a class of H-infinity controllers for suppression of the effect of external disturbances can be designed naturally without solving Hamilton-Jacobi’s differential equations. Even in the case of a system of dual fingers with flexible and soft finger-tips grasping a rigid or deformable object, the dynamics satisfy passivity, from which feedback control schemes can be devised for realizing dynamic stable grasp ing and dexterous manipulation.