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

Abstract

In this work, an output-feedback adaptive SP-SD-type control scheme for the global position stabilization of robot manipulators with bounded inputs is proposed. Compared with the output-feedback adaptive approaches previously developed in a boundedinput context, the proposed velocity-free feedback controller guarantees the adaptive regulation objective globally (i.e. for any initial condition), avoiding discontinuities throughout the scheme, preventing the inputs from reaching their natural saturation bounds and imposing no saturation-avoidance restrictions on the choice of the P and D control gains. Moreover, through its extended structure, the adaptation algorithm may be configured to evolve either in parallel (independently) or interconnected to the velocity estimation (motion dissipation) auxiliary dynamics, giving an additional degree of design flexibility. Furthermore, the proposed scheme is not restricted to the use of a specific saturation function to achieve the required boundedness, but may involve any one within a set of smooth and non-smooth (Lipschitz-continuous) bounded passive functions that include the hyperbolic tangent and the conventional saturation as particular cases. Experimental results on a 3-degree-of-freedom manipulator corroborate the efficiency of the proposed scheme.

Closed-loop identification and tracking control of Lagrangian systems under input constraints

“…In order to keep the control scheme bounded, the work developed in [4] defines and makes use of a general class of saturation functions, however we make use of the hyperbolic tangent since it is a individual case of such mentioned definition. Given that the hyperbolic tangent is a globally Lipschitz, strictly increasing sigmoidal function, it can be proved (see [7]) that it satisfies the following properties Lemma 2: For a given positive constant k, the hyperbolic tangent function, satisfies 1. ς tanh(ς) > 0 for all ς = 0; 2. | tanh(ς)| < 1 for all ς ∈ R.…”