Kinematic Calibration In Robotic Hand-eye System

With the rapid development of science and technology,robotic vision systems have been more and more widely used in many fields.A robotic vision system composed of visual sensor(s)(camera(s),ultrasound probe,endoscopic camera,etc.)and a robot is called a hand-eye system and usually consists of an eye-in-hand system and an eye-tohand system.There are two typical fixed transformations in the hand-eye system:(1)hand-eye transformation;and(2)the robot-world transformation.Sometimes a hand-eye system contains two fixed transformations that need to be determined simultaneously.The robotic hand-eye system acquires image information through vision sensors and then feeds the image information back to the control system to perform the relevant tasks.The degree of integration between the visual sensor system and the robot system directly determines the degree of task completion.Therefore,when using the hand-eye system to perform a task,the kinematic relationship between the robot system and the vision sensor system must first be determined,i.e.,the hand-eye system calibration.The process of determining the robot-world transformation and the hand-eye transformation through modeling,experiments and parameter identification is called robotworld calibration and hand-eye calibration,respectively.In this paper,the following three key problems are studied around modeling and parameter identification for 6-degree-of-freedom serial robots:(1)modeling for robot-world calibration complied with Lie group conjugate operation;(2)Separating coordinate invariants in the model;(3)parameter identification based on screw theory.To address these four key problems,the main research of this paper is as follows:(1)A mathematical model for robot-world calibration is established.Based on the equivalence of the DH model and the POE model,a model of the robot-world calibration represented by the homogeneous matrices is derived.Subsequently,the kinematic loop based on the hand-eye system gives the interpretation of the physical meaning corresponding to the dual equations.Further,the relationship between the Lie group SE(3)and Ad(SE(3))converts the dual equations represented by the homogeneous matrix to the dual equations represented by the finite displacement screw matrix.The representation of the model is well developed to provide different computational models for further parameter identification.(2)Separation of coordinate invariants in the dual equations based on the rotation tensor and the motion tensor.For the dual equations represented by the homogeneous matrices,the rotation tensor is introduced to reveal the nature of the coordinate transformation of the components of second-order tensor of the rotation equation.Further,the coordinate transformation of the components of the second-order tensor is expressed as the coordinate transformation of the components of the first-order tensor according to the Rodrigues formula of the rotation matrix,and the analytic solution of the rotation is derived.For the dual equation represented by the finite displacement screw matrices,the motion tensor is introduced,and the dual equations are expressed as an equivalent coordinate transformation of the components of the first-order tensor according to the Rodrigues formula for the finite displacement screw matrices.The theoretical model to achieve parameter identification is clarified,and the rotational and translational analytic solutions of the dual equations are derived.(3)The separable and simultaneous methods of identification based on the screw theory are developed based on whether the rotation and translation of the rigid body motion are decoupled or not,and the classification criteria are proposed.Decoupling the rotation and translation of the homogenous matrices,for the nonlinear rotation equation,three identification methods are proposed,representing different choices of whether to parameterize the rotation matrices and the parameterization,respectively.Through various simulations and experimental tests,it is verified that the representation of rotation does not affect the identification results.According to the description of screw motion for rotation and translation,the finite displacement rotation matrix is decoupled into a rotation part and a translation part,and the parameter identification is developed by combining tensor product,quaternion conjugate and dual algebra.The application of dual algebra in robot kinematics is extended,the parameter identification system is improved,the factors affecting the identification results are systematically analyzed,the identification methods proposed in this paper are compared,and the applicability conditions of each method are evaluated.Compared with the existing studies,the factors affecting the identification results are analyzed theoretically and have universal applicability,which provides guidance for engineering applications.