Trajectory tracking control for robot manipulators with no velocity measurement using semi-globally and globally asymptotically stable velocity observers

During the last decade the class of rigid robot systems has been the subject of intensive research in the field of systems and control theory, particularly owing to the inherent nonlinear nature of rigid robots. For the same reason, these systems have widely been used to exemplify general concepts in nonlinear control theory. As a result of this excessive research activity a large variety of control methods for rigid robot systems have been proposed, such as, proportional-integral-derivative (PID) control (Kelly, 1995), computed torque control (Luh et al., 1980), which achieve the trajectory tracking objective by feedback linearization of the nonlinear robot dynamics, adaptive control (Ortega & Spong, 1989), variable structure control (Slotine & Sastry, 1983), fuzzy control (Chang & Chen, 2000), passivity based control (Ryu et al, 2004; Bouakrif et al., 2010) and iterative learning control (Bouakrif et al., 2007; Tayebi, 2007). Many of these previous controllers require the complete state measurements, that is position and velocity, is available for feedback. Unfortunately, in practice this assumption can only partially be fulfilled for two reasons. First, although robot systems generally are equipped with high precision sensors for position measurements, velocity measurements are often contaminated with a considerable amount of noise. This circumstance may reduce the dynamic performance of the manipulator, since in practice, the values of the controller gain matrices are limited by the noise present in the velocity measurements (Khosla & Kanade, 1988). Second, in robotic applications today velocity sensors are frequently omitted owing to the considerable savings in cost, volume and weight that can be obtained this way. A good solution of this problem is the use of the velocity observers to reconstruct the missing velocity signal starting from the available position measurements. Due to the nonlinear and coupled structure of the robot dynamical model, the problem of designing observers for robots is a very complex one. Recently, exploiting the structural properties of the robot dynamics, a number of conceptually different methods for both regulation and tracking control of robots equipped with only position sensors have been developed (Canudas dewit et al., 1992; Paden & Panja, 1988). (Berghuis & Nijmeijer, 1993) presented a controller2