IHUVS: Infinite Homography-Based Uncalibrated Methodology for Robotic Visual Servoing

The construction of task functions in robotic manipulation is of paramount importance for uncalibrated visual servoing. The existing methods generally use image information as control variables and estimate the image Jacobian matrix online, thus possessing issues relating to convergence, and image Jacobian matrix singularities. Therefore, this article proposes a novel methodology dubbed infinite homography-based uncalibrated visual servoing (IHUVS), in which the visual control of the robot end-effector pose is decomposed into its rotational and translational components. The corresponding rotational controller designs the visual servoing task function using the relationship between the infinite homography matrix and rotation matrix, and employs the Kronecker product to derive linear equations for rotational control, as well as to conduct the associated task error analysis. Meanwhile, the translational controller utilizes Kalman filtering for online estimation of the Jacobian matrix that is required by the proportional control scheme. The robot end-effector motion in the Cartesian space is generated via the IHUVS method, without knowing the camera's intrinsic parameters and the robot hand–eye relationship. A simulation analysis is carried out to assess the algorithm's numerical performance, while robotic visual servoing experiments are also conducted to verify the accuracy and efficacy of the proposed IHUVS method.