A solution to the adaptive visual servoing problem

We address, and solve, a basic adaptive visual servoing problem whose solution was hampered by the nonlinear dependence of the system dynamics on the unknown parameters. Namely, we present a globally convergent vision-based position controller for a planar two-links manipulator in the so-called fixed-camera configuration, where the camera orientation and scale factor are considered unknown. The controller design technique of immersion and invariance is used to derive a smooth adaptive scheme that ensures global asymptotic regulation without overparametrization, projections or persistency of excitation assumptions. In the case of tracking, we establish error bounds that depend on the speed of the reference trajectory, and can be reduced (eventually to zero) with improved prior knowledge on the camera scale factor. The efficacy of the approach is shown through simulations.