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

Abstract

Abstract-This paper is concerned with the use of a sphericalprojection 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.Index Terms-Three points, spherical projection, visual servoing.

Robust image-based visual servoing using invariant visual information

“…This property ensures a direct link between the rotation vector defined from c * R s * c R ⊤ s and the rotational velocities as it has been proven in [19]. In the next paragraph, we define a rotation vector from a set of N points in the image.…”

“…Recently, in [7] and [19], an angle-axis representation of a rotation matrix R computed from two projected points on the sphere has been considered to control rotational motions for visual servoing application. The idea behind the rotation formula given in these works is equivalent to attaching an orthonormal frame basis to each camera pose using two projected points onto the unit sphere.…”

“…This paper belongs to a series of works aiming at the selection of optimal visual features for IBVS [17], [18], [19]. These previous works were concerned with approaches that consider performance measures to choose visual features with good decoupling and linearizing properties.…”

“…However, applying non-linear transformations on data obtained from the sensor space changes the noise distribution. For instance, if the image noise is Gaussian white, the noise on invariant features proposed in [18] and [19] is no more Gaussian white since the applied transformation is nonlinear. In practice, if the noise level is low, the use of invariants allows obtaining adequate robustness.…”

“…If the noise level increases, the use of invariants can lead to less robustness at convergence compared to the classical visual features. In this paper, further to proposing new invariants allowing better linearizing properties and decoupling than those proposed in [18] and [19], we address the problem of robustness to noise.…”