A new set-point controller with bounded torques for robot manipulators

Output-Feedback Adaptive SP-SD-Type Control with an Extended Continuous Adaptation Algorithm for the Global Regulation of Robot Manipulators with Bounded Inputs

“…In [16] global regulation is aimed for, through a discontinuous scheme that switches among two different control laws, under the consideration of state and output feedback. Both considered control laws keep an SP-SD structure similar to that of [7]; the first one avoids gravity compensation taking high-valued control gains (by means of which the closed-loop trajectories are lead close to the desired position) and the second one considers adaptive gravity compensation terms that are kept bounded by means of discontinuous auxiliary dynamics. Each velocity measurement is replaced by the dirty derivative of the corresponding position in the output-feedback version of the algorithm.…”

“…The exclusive use of a single saturation (at every joint) including all the terms of the controller was further achieved through desired gravity compensation in [13]. Moreover, velocityfree versions of the SP-SD controllers in [7] and [6] (still depending on the exact values of the system parameters) are obtained through the design methodologies developed in [9] and [10]. In [9] global regulation is proven to be achieved when each velocity measurement is replaced by the dirty derivative [14] of the respective position in the SP-SD controller of [7].…”

“…For instance, extensions of the PDgc controller that cope with the input saturation phenomenon have been developed under various analytical frameworks in [6, 7, 8, 9, 10 and 11]. Indeed, assuming the availability of the exact value of all the system parameters and accurate measurements of all the link positions and velocities, a bounded PDgc-based approach was proposed in [6] and [7]. In these works, the P and D terms (at every joint) are each explicitly bounded through specific saturation functions; a continuously differentiable one, or more precisely the hyperbolic tangent function, is used in [6] and the conventional nonsmooth one in [7].…”

“…Moreover, velocityfree versions of the SP-SD controllers in [7] and [6] (still depending on the exact values of the system parameters) are obtained through the design methodologies developed in [9] and [10]. In [9] global regulation is proven to be achieved when each velocity measurement is replaced by the dirty derivative [14] of the respective position in the SP-SD controller of [7]. A similar replacement in a more general form of the SP-SD controller is proven to achieve global regulation through the design procedure proposed in [10] (where an alternative type of dirty derivative, which involves a saturation function in the auxiliary dynamics that gives rise to the estimated velocity, results from the application of the proposed methodology).…”

“…Indeed, assuming the availability of the exact value of all the system parameters and accurate measurements of all the link positions and velocities, a bounded PDgc-based approach was proposed in [6] and [7]. In these works, the P and D terms (at every joint) are each explicitly bounded through specific saturation functions; a continuously differentiable one, or more precisely the hyperbolic tangent function, is used in [6] and the conventional nonsmooth one in [7]. In view of their structure, these types of algorithms have been denoted SP-SD controllers in [12].…”