Robot Modeling and Control, 2nd Edition

CHAPTER 12FEEDBACK LINEARIZATION

In this chapter we present some basic, but fundamental, ideas from geometric nonlinear control theory. We first give some background from differential geometry to set the notation and define basic quantities, such as manifold, vector field, Lie bracket, and so forth that we will need later. The main tool that we will use in this chapter is the Frobenius theorem, which we introduce in Section 12.1.2.

We then discuss the notion of feedback linearization of nonlinear systems. This approach generalizes the concept of inverse dynamics of rigid manipulators discussed in Chapter 9. The idea of feedback linearization is to construct a nonlinear control law as an inner-loop control, which, in the ideal case, exactly linearizes the nonlinear system after a suitable state space change of coordinates. The designer can then design the outer-loop control in the new coordinates to satisfy the traditional control design specifications such as tracking and disturbance rejection.

In the case of rigid manipulators the inverse dynamics control of Chapter 9 and the feedback linearizing control are the same. The main difference between inverse dynamics control and feedback linearization, as we shall see, is to find the “right” set of coordinates with respect to which the dynamics can be rendered linear by feedback. In the case of inverse dynamics, no change of coordinates is necessary.

As we shall see, the full power of the feedback linearization technique for manipulator ...