Designing image trajectories in the presence of uncertain data for robust visual servoing path-planning

Path-planning allows one to steer a camera to a desired location while taking into account the presence of constraints such as visibility, workspace, and joint limits. Unfortunately, the planned path can be significantly different from the real path due to the presence of uncertainty on the available data, with the consequence that some constraints may be not fulfilled by the real path even if they are satisfied by the planned path. In this paper we address the problem of performing robust path-planning, i.e. computing a path that satisfies the required constraints not only for the nominal model as in traditional path-planning but rather for a family of admissible models. Specifically, we consider an uncertain model where the point correspondences between the initial and desired views and the camera intrinsic parameters are affected by unknown random uncertainties with known bounds. The difficulty we have to face is that traditional path-planning schemes applied to different models lead to different paths rather than to a common and robust path. To solve this problem we propose a technique based on polynomial optimization where the required constraints are imposed on a number of trajectories corresponding to admissible camera poses and parameterized by a common design variable. The planned image trajectory is then followed by using an IBVS controller. Simulations carried out with all typical uncertainties that characterize a real experiment illustrate the proposed strategy and provide promising results.