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 using a simplex method and a Newton-like method. Our method allows for the inclusion of constraints in the image as well as in jointspace. On-line image Jacobian estimation runs at the same time, and is used to accelerate convergence near the target. We successfully validate this method with simulations under the graphic library OpenGL, and practical experiment with industrial manipulators.