Visual servoing without Jacobian using modified simplex optimization

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. 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 to include constraints in the image as well as in joint-space. Online image Jacobian estimation runs at the same time. We successfully validate this method with simulations under the graphic library OpenGL.