The role of viscous friction damping in adaptive output feedback tracking control of manipulators

Adaptive control of robot manipulators has been an active research topic in the last 15 years. The main motivation of this has been the interest in adding a reliable degree of robustness to the closed–loop system, specially in manufacturing system, where the manipulator frequently achieves pick and place tasks of materials and parts, whereby adaptation of the payload changes helps to guarantee the motion control. See, e.g., [4] for a reference on globally asymptotically stable adaptive algorithms, which guarantee the asymptotic tracking of the joint desired trajectory. However, in most of the adaptive controllers the joint velocity is assumed to be measurable for feedback. In practice, the joint velocity measurement might be contaminated by noise, hence the control system performance may be reduced. The presence of noise in the measurements and the discretization of the controller also limits the values of the controller gains. For these reasons, the problem of designing motion control algorithms that deal with the velocity reconstruction (output feedback) and the parameter adaptation is important. Even in the trajectory design for The problem of adaptive output feedback tracking control of manipulators consists in designing a control algorithm by using only joint position measurements and a parameter estimation update law, so that the error between the time–varying desired position and the position of the system goes asymptotically to zero for a set of initial conditions. This paper addresses this control problem. As pointed out in [3], despite the numerous algorithms of adaptive controllers and of tracking controller–observer schemes, there are relatively few algorithms which combine both adaptive schemes and velocity reconstruction. Our literature review does not cover all previous work on adaptive output feedback tracking control for robots. Only a brief description of the key results proposed latter than 1996 is provided. In [3] an adaptive scheme with boundedness of the estimated parameters and uniform ultimate boundednes for tracking and observation errors was proposed. Inspired in the approach introduced by Loria [8], Zhang et al. [15] proposed a controller that depends in the initial condition of a dynamic extension. A redesign of the approach introduced in [15] is proposed in the work of Zergeroglu et al. [14], but presenting the global convergence of the position and tracking errors. Let us notice that these approaches were extended by Dixon et al. [5] to the problem of adaptive trajectory tracking control of manipulators with flexible joints by using only position measurements of the robot actuators and links. In a similar way, in this work the global convergence of the link position and velocity errors was shown.