Conferring Robustness to Path-Planning for Image-Based Control

Path-planning has been proposed in visual servoing for reaching the desired location while fulfilling various constraints. Unfortunately, the real trajectory can be significantly different from the reference trajectory due to the presence of uncertainties on the model used, with the consequence that some constraints may not be fulfilled hence leading to a failure of the visual servoing task. This paper proposes a new strategy for addressing this problem, where the idea consists of conferring robustness to the path-planning scheme by considering families of admissible models. In order to obtain these families, uncertainty in the form of random variables is introduced on the available image points and intrinsic parameters. Two families are considered, one by generating a given number of admissible models corresponding to extreme values of the uncertainty, and one by estimating the extreme values of the components of the admissible models. Each model of these families identifies a reference trajectory, which is parametrized by design variables that are common to all the models. The design variables are hence determined by imposing that all the reference trajectories fulfill the required constraints. Discussions on the convergence and robustness of the proposed strategy are provided, in particular showing that the satisfaction of the visibility and workspace constraints for the second family ensures the satisfaction of these constraints for all models bounded by this family. The proposed strategy is illustrated through simulations and experiments.