Robust and uncalibrated visual servoing without Jacobian using a simplex method

In this paper, we present a robot positioning task with respect to a static target using visual servoing and optimization techniques. The vision system is uncalibrated and the kinematic model of the robot may be totally unknown. The displacements of the robot are generated in real time in order to minimize an objective function. The objective function includes the quadratic error between the current target image and the desired target image. A simplex method is used to minimize the objective function. Our method allows the system to include constraints in the image as well as in joint-space. We successfully validate this method, with simulations under the graphic library QpenGL and with experiments on a 6-DOF industrial manipulator.