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The problem of robust tracking control of electromechanical systems has been studied and solved by many different approaches within the robot control community (see e.g. Sage et al., 1999; Kelly et al., 2005 and references therein) in order to ensure accurate motion in typical industrial tasks (painting, navigation, cutting, etc). In the last decade, the homogeneity approach attracted considerable interest from the research and engineering communities (see e.g. Lebastard et al., 2006; Ferrara et al., 2006; Bartolini et al., 2006) because it was demonstrated that homogeneous systems with homogeneity degree 0 < η exhibit robustness and finite-time convergence properties (Bhat & Bernstein, 1997; Hong et al., 2001; Orlov, 2005). Control laws based on the homogeneity approach (Bhat & Bernstein, 1997; Hermes, 1995; Orlov, 2003a; Rosier, 1992) are attractive in robotic applications because they can cope with many mechanical perturbations, including external vibrations, contact forces, and nonlinear internal phenomena such us Coulomb and viscous friction, dead zone and backlash, while it is possible to ensure exact tracking to continuously differentiable desired trajectories. Several homogeneous controllers and studies have been proposed in the literature. For example, Rosier (1992) constructed a homogeneous Lyapunov function associated with homogeneous dynamic systems. Hermes (1995) addressed the homogeneous stabilization control problem for homogeneous systems. Bhat and Bernstein (1997) examined the finite time stability of homogeneous systems. Levant (2005a, 2005b) developed robust output-feedback high-order sliding mode controllers that demonstrate finite-time convergence (see also (Fridman & Levant, 1996; Fridman & Levant, 2002)) where the controller design is based on homogeneity reasoning while the accuracy is improved in the presence of switching delay, and the chattering effect is treated by increasing the relative degree. Orlov et al. (2003a, 2003b) proposed applying homogeneous controller to solve the set-point problem dealing with mechanical imperfections such as Coulomb friction, viscous friction, and backlash. Orlov et al., (2005) extended the finite time stability analysis to nonlinear nonautonomous switched systems.

Homogeneous Approach for Output Feedback Tracking Control of Robot Manipulators