Volume 22 Issue 10/11- Publication Date: 1 October 2003
Optimal Camera Trajectory with Image-Based Control
Y. Mezouar and F. Chaumette IRISA/INRIA Rennes, Campus de Beaulieu, 35042 Rennes cedex, France

Image-based servo is a local control solution. Thanks to the feedback loop closed in the image space, local convergence and stability in the presence of modeling errors and noise perturbations are ensured when the error is small. The principal deficiency of this approach is that the induced (3D) trajectories are not optimal and sometimes, especially when the displacement to realize is large, these trajectories are not physically valid leading to the failure of the servoing process. In this paper we address the problem of finding realistic image-space trajectories that correspond to optimal 3D trajectories. The camera calibration and the model of the observed scene are assumed unknown. First, a smooth closed-form collineation path between given start and end points is obtained. This path is generated in order to correspond to an optimal camera path. The trajectories of the image features are then derived and efficiently tracked using a purely image-based control. A second path planning scheme, based on the potential field method is briefly presented. It allows us to introduce constraints in the desired trajectory to be realized. Such constraints are, for instance, to ensure that the object of interest remains in the camera field of view and to avoid the robot joints limits. Experimental results obtained on a six-degrees-of-freedom eye-in-hand robotic system are presented and confirm the validity of the proposed approach.

Multimedia Key
= Video = Data = Code = Image
Example One: Positioning task described in Section 6.2 (correctly calibrated system) seen by the controlled camera. The red and blue crosses represent respectively the current desired position of the features. The green crosses represent the current desired position of the features (that is their planned trajectories). (4.4MB)
Example Two: Same example with badly calibrated camera. (5.1MB)
Example Three: Positioning task described in Section 7.2 seen by the controlled camera. (8.1MB)
Example Four: Initial image with plannrd trajectories (Section 8.2). (70kb)
Example Five: Desired image (Section 8.2). (29kb)
Example Six: Initial Robot Configuration (Section 8.2). (44kb)
Example Seven: Final robot configuration (Section 8.2). (43kb)
Example Eight: Motion during the positioning task (Section 8.2) seen by a camera observing the robot. (2.3MB)
Example Nine: Same example seen by the controoled camera (Section 8.2). The blue and green crosses represent respectively the current and desired features. The red crosses represent the current desired position of the features (i.e., their planned trajectories). (2.3MB)
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