Robust asymptotically stable visual servoing of planar robots

In this paper we address the visual servoing of planar robot manipulators under fixed-camera configuration. The control goal is to place the robot end-effector over a desired static target by using a vision system equipped with a fixed camera to 'see' the robot end-effector and target. We analyze an image-based controller, whose implementation requires the robot Jacobian, the gravitational torque vector, and the camera orientation. Further, the robot manipulator is not treated as an ideal positioning device but modeled by the Lagrangian dynamics. We formally prove that the overall closed-loop system composed by the full nonlinear robot dynamics and the controller is Lyapunov stable. Also, we demonstrate that the controller is capable to yield an asymptotically stable system which is robust against radial lens distortions and uncertainty in the camera orientation. Simulations on a two degrees of freedom arm are presented to illustrate the controller performance.