Research On Uncalibrated Visual Servoing Based On Second-order Cone Programming

Usually,the visual servoing control strategy needs to consider three kinds of constraints:(1)the constraint of the robot's motion ability,that is,the limitation of the mechanical performance on the maximum speed and range of the robot's motion;(2)the image field of view constraint,that is,according to the needs of the task,the image of the target object is limited to the effective field of view of the camera to avoid interruption of visual feedback;(3)the three-dimensional spatial motion range constraint,that is,according to the needs of the task,the three-dimensional motion of the robot flange is limited to a certain spatial range,thereby avoiding unnecessary motion.In practical applications,if these constraints are ignored,the servo result may be unsatisfactory or even fail.In this paper,the monocular robot hand-eye system is taken as the research object.For the uncalibrated visual servoing control problem with constraints,according to Kalman filter and the second-order cone programming(SOCP)model,an uncalibrated visual servoing solution based on second-order cone programming is proposed.Firstly,based on the knowledge of rigid body kinematics and perspective projection,a complete mathematical model of the visual servoing system is established,including the robot kinematics and velocity kinematics model,the camera's distorted pinhole model,and the hand-eye relationship velocity model.This mathematical model provides theoretical preparation for the following system stability analysis and er ror convergence analysis.Secondly,according to the Kalman filter principle,the Jacobian matrix online estimator is designed.The estimator directly estimates the Jacobian matrix relationship between the joint speed of the robot and the change of the visual signal,that is,the velocity relationship between the hand and the eye,in the case of completely not knowing robot kinematic parameters and hand-eye calibration parameters.The estimator on-line provides a system model for uncalibrated visual servoing control strategy.Finally,according to the second-order cone programming model,an uncalibrated visual servoing control strategy based on second-order cone programming is proposed.The control strategy is to transform the control problem with constraints into a second-order cone programming problem at each iteration.By solving the convex programming problem,the control strategy obtains optimal joint velocity control command that satisfies constraints.The control strategy effectively solves the problem of uncalibrated visual servoing control.Both simulation results and experimental results show that uncalibrated visual servoing based on second-order cone programming is an effective,feasible and practical solution in the case of completely not knowing robot kinematic parameters and hand-eye relationship parameters.It makes full use of two-dimensional image information and three-dimensional pose information,which can effectively control image points and camera poses at the same time,ensuring optimal or suboptimal image point motion trajectory and camera motion trajectory.Even in the extreme cases where the classic visual servoing cannot be completed,it still has good dynamic performance and control precision.