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Abstract-In this paper, we present two globally convergent vision-based position controllers for a planar two-links manipulator in the so-called fixed-camera configuration, where the camera orientation and scale factor are considered unknown. This is a basic adaptive visual servoing problem whose solution was hampered by the nonlinear dependence of the system dynamics on the unknown parameters. The controller design techniques of immersion and invariance and nonlinear proportional integral (PI), recently proposed in the literature, are used to derive the smooth adaptive schemes that ensure global asymptotic regulation without overparameterization, projections, or persistency of excitation assumptions. In the case of tracking, we establish error bounds that are reduced, eventually to zero, as the speed of the reference trajectory decreases, and with improved prior knowledge on the camera scale factor, for the immersion and invariance controller, or increasing a tuning gain for the nonlinear PI. The efficacy of the approaches is shown through simulations.

The control of uncertain nonlinear systems by output feedback is addressed. A model-reference tracking sliding mode controller is designed for uncertain plants with arbitrary relative degree. Nonlinearities of a given class are incorporated as state dependent and possibly unmatched disturbances of a linear plant. Such class encompasses nonlinear systems which are triangular in the unmeasured states. In contrast with previous works, exact tracking is achieved by means of a switching strategy based on a locally exact differentiator, and a monitoring function is used to cope with the lack of knowledge of the control direction. Global or semi-global stability properties of the closed-loop system are proved.