Two solutions to the adaptive visual servoing problem

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.