Cartesian Impedance Control: The Rigid Body Case

Abstract

In this chapter the classical theory of impedance control for rigid body robots is described. The presentation in Section 3.1 is based on the seminal work of Hogan about the concept of impedance control [Hog85a, Hog85b, Hog85c] and on the Operational Space Formulation by Khatib [Kha87]. In Section 3.2 the case of a desired impedance is analyzed, in which the inertial behavior must not be shaped explicitly. This brings about the problem of designing the damping matrix in an appropriate way. Furthermore, some additional aspects concerning singularity avoidance, the choice of coordinates, and the stiffness design are discussed.

This chapter refers to the rigid body part of the robot model without considering joint elasticities. The presented topics serve as a prerequisite for the design of Cartesian impedance controllers for the flexible joint robot model from Section 2.2.3 and can readily be combined with the controllers from Chapter 5, 6, and 7.