Distance-Based and Orientation-Based Visual Servoing From Three Points

This paper is concerned with the use of a spherical-projection model for visual servoing from three points. We propose a new set of six features to control a 6-degree-of-freedom (DOF) robotic system with good decoupling properties. The first part of the set consists of three invariants to camera rotations. These invariants are built using the Cartesian distances between the spherical projections of the three points. The second part of the set corresponds to the angle-axis representation of a rotation matrix measured from the image of two points. Regarding the theoretical comparison with the classical perspective coordinates of points, the new set does not present more singularities. In addition, using the new set inside its nonsingular domain, a classical control law is proven to be optimal for pure rotational motions. The theoretical results and the robustness to points range errors of the new control scheme are validated through simulations and experiments on a 6-DOF robot arm.