New solutions to the 2D adaptive visual servoing problem with relaxed excitation requirements

In this paper, we present three new globally convergent vision‐based position controllers for a planar manipulator in a 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. Proposing a suitable reparameterization of the systems mathematical model, and exploiting some structural properties of it, we propose three different solutions to the problem. The first one is the certainty equivalent version of the known parameter controller and requires some excitation conditions to ensure global asymptotic convergence. A second version of the controller, which is now slightly more complicated and, possibly, needs to inject some high gain but requires significantly weaker excitation conditions, is given. Finally, we propose a slight modification to the second scheme to achieve the trajectory tracking in finite time. The efficacy of the three adaptive controllers is shown through realistic simulations.