. Visual servoing, using image-based control or positionbased control, generally gives satisfactory results. However, in some cases, convergence and stability problems may occur. The aim of this paper is to emphasize these problems by considering an eye-in-hand system and a positioning task with respect to a static target which constrains the six camera degrees of freedom. To appear in: The Confluence of Vision and Control, Lecture Notes in Control and Informations Systems, Springer-Verlag, 1998. 1 Introduction The two classical approaches of visual servoing (that is image-based control and position-based control) are different in the nature of the inputs used in their respective control schemes [28,10,14]. Even if the resulting robot behaviors thus also differ, both approaches generally give satisfactory results: the convergence to the desired position is reached, and, thanks to the closed-loop used in the control scheme, the system is stable, and robust with respect to camera calib...

In this paper, we determine the analytical form of the interaction matrix related to any moment that can be computed from segmented images. The derivation method we present is based on Green's theorem. We apply this general result to classical geometrical primitives. We then consider using moments in image-based visual servoing. For that, we select six combinations of moments to control the six degrees of freedom of the system. These features are particularly adequate, if we consider a planar object and the configurations such that the object and camera planes are parallel at the desired position. The experimental results we present show that a correct behavior of the system is obtained if we consider either a simple symmetrical object or a planar object with complex and unknown shape.

: The work presented in this paper fits into the realm of robotics and computer vision. The problem we seek to solve is the accomplishment of robotics tasks by using visual information provided by a particular sensor, mounted on a robot end effector. This sensor consists of two laser stripes fixed rigidly to a camera, projecting light planar on the scene. First, we explain the approaches employed in robot control, using information provided by a vision sensor. More specifically, we explain the visual servoing approach, which corresponds to the one we have developed. Then, we express the modelling of visual information from a scene consisting of spherical objects, by using several representations in the image. This modelling permits us to establish a relation between the variations of visual information and camera velocities. Finally, both in simulation and in our experimental cell, results are presented. They concern the positioning task with respect to a sphere, and show the robustnes...

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We present a probabilistic method for noisy sensor based robotic navigation in dynamic environments. The method generates an optimal trajectory by considering as optimality criteria the probability of not colliding with the obstacles and the probability of accessing an operational position with respect to a moving target object. Estimates of the obstacle's kinematic parameters and measures of confidence in these estimates are used to produce the probability of collision associated with any robot displacement. The probability of collision is derived in two steps: a stochastic model is defined in the kinematic state space of the obstacles, and collision events are given simple geometric characterizations in this state space. The support of the Defense Advanced Research Projects Agency (ARPA Order No. 6989) and the U.S. Army Engineer Topographic Laboratories under Contract DACA76-89-C-0019 is gratefully acknowledged, as is the help of Sandy German in preparing this paper. 1 Introduction...

A framework for vision-guided manipulation is presented. The framework uses a hierarchical structure to efficiently tessellate the visual and control space, based on which the robot learns how to control its hand according to what is seen. Several networks, which store the learned knowledge, are automatically generated through the learning process. This framework makes it possible to deal with complex relationships among the sensors and the hand without relying on the availability of accurate information about the sensory and mechanical systems. Contents 1 Introduction 3 1.1 General Descriptions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.2 Complete Systems : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2 Issues and Motivation 7 2.1 Issues : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 2.1.1 Redundancy : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 2...

Abstract — This paper deals with visual servoing from three points. Using the geometric properties of the spherical projection of points, a new decoupled set of six visual features is proposed. The main originality lies in the use of the distances between spherical projection of points to define three features that are invariant to camera rotations. The three other features present a linear link with respect to camera rotations. In comparison with the classical perspective coordinates of points, the new decoupled set does not present more singularities. In addition, using the new set in its non-singular domain, a classical control law is proven to be ideal for rotational motions. These theoretical results as well as the robustness to errors of the new decoupled control scheme are illustrated through simulation results. I.

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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. I.

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