Mobile Robotics, 2nd Edition

2Feedback Linearization

Due to their multiple rotation capabilities, robots are considered to be strongly nonlinear systems. In this chapter, we will look at designing nonlinear controllers in order to constrain the state vector of the robot to follow a fixed forward path or to remain within a determined area of its workspace. In contrast to the linear approach, which offers a general methodology, to be but is limited to the neighborhood of a point of the state space [KAI 80, JAU 15], nonlinear approaches only apply to limited classes of systems. Nevertheless they allow the effective operating range of the system to be extended. Indeed, there is no general method of globally stabilizing nonlinear systems [KHA 02]. However, there is a multitude of methods that apply to particular cases [SLO 91, FAN 01]. The aim of this chapter is to present one of the more representative theoretical methods (whereas in the following chapter, we will be looking at more pragmatic approaches). This method is called feedback linearization and it requires knowledge of an accurate and reliable state machine for our robot. The robots considered here are mechanical systems whose modeling can be found in [JAU 05]. We will assume in this chapter that the state vector is entirely known. In practice, it has to be approximated from sensor measurements. We will see in Chapter 7 how such an approximation is performed.

2.1. Controlling an integrator chain

As we will show further on in this chapter, feedback ...