Robust Visual Control Based on the Epipolar Geometry

Abstract

In this chapter, we present a new control scheme that exploits the epipolar geometry but, unlike previous approaches based on two views, it is extended to three views, gaining robustness in perception. Additionally, robustness is also improved by using a control law based on sliding mode theory in order to solve the problem of pose regulation. The core of the chapter is a novel control law that achieves total correction of the robot pose with no auxiliary images and no 3D scene information, without need of commuting to any visual information other than the epipolar geometry and applicable with any central camera. Additionally, the use of sliding mode control avoids the need of a precise camera calibration in the case of conventional cameras and the control law deals with singularities induced by the epipolar geometry. The effectiveness of the approach is tested via simulations, with kinematic and dynamic models of the robot, and real-world experiments.