  In view of the classical visual servoing trajectory planning method which
only considers the camera trajectory, this paper proposes one homography matrix
based trajectory planning method for robot uncalibrated visual servoing. Taking
the robot-end-effector frame as one generic case, eigenvalue decomposition is
utilized to calculate the infinite homography matrix of the robot-end-effector
trajectory, and then the image feature-point trajectories corresponding to the
camera rotation is obtained, while the image feature-point trajectories
corresponding to the camera translation is obtained by the homography matrix.
According to the additional image corresponding to the robot-end-effector
rotation, the relationship between the robot-end-effector rotation and the
variation of the image feature-points is obtained, and then the expression of
the image trajectories corresponding to the optimal robot-end-effector
trajectories (the rotation trajectory of the minimum geodesic and the linear
translation trajectory) are obtained. Finally, the optimal image trajectories
of the uncalibrated visual servoing controller is modified to track the image
trajectories. Simulation experiments show that, compared with the classical
IBUVS method, the proposed trajectory planning method can obtain the shortest
path of any frame and complete the robot visual servoing task with large
initial pose deviation.
