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Image space trajectory generation for image-based visual servoing under large pose error

In spite of its strengths in many aspects, the image-based visual servoing scheme has fatal defects when a desired pose is far from the initial one; out of camera field of view, breaking the stability. One solution to these problems is to generate a desired trajectory in the image space such that the pose errors remain always small. We present a method for image-space trajectory generation that can be utilized in image-based visual servoing when initial errors are large. First, initial and desired points of a gripper are reconstructed up to an unknown projective transformation with an uncalibrated stereo rig. Second, intermediate configurations, with which a smooth and straight motion can be produced, are constructed in the projective space using a conjugate transformation and projective invariants. Finally, an image-space trajectory is obtained by re-projecting the coordinates of those points onto the initial image plane. A computer simulation and experiments are conducted to show the feasibility of the proposed scheme.