A hand–eye calibration algorithm based on screw motions

Optimal robot-world and hand-eye calibration with rotation and translation coupling

A classic hand-eye system involves hand-eye calibration and robot-world and hand-eye calibration. Insofar as hand-eye calibration can solve only hand-eye transformation, this study aims to determine the robot-world and hand-eye transformations simultaneously based on the robot-world and hand-eye equation. According to whether the rotation part and the translation part of the equation are decoupled, the methods can be divided into separable solutions and simultaneous solutions. The separable solutions solve the rotation part before solving the translation part, so the estimated errors of the rotation will be transferred to the translation. In this study, a method was proposed for calculation with rotation and translation coupling; a closed-form solution based on Kronecker product and an iterative solution based on the Gauss–Newton algorithm were involved. The feasibility was further tested using simulated data and real data, and the superiority was verified by comparison with the results obtained by the available method. Finally, we improved a method that can solve the singularity problem caused by the parameterization of the rotation matrix, which can be widely used in the robot-world and hand-eye calibration. The results show that the prediction errors of rotation and translation based on the proposed method be reduced to $0.26^\circ$ and $1.67$ mm, respectively.

Hand-eye calibration method with a three-dimensional-vision sensor considering the rotation parameters of the robot pose

Hand-eye calibration is a fundamental step for a robot equipped with vision systems. However, this problem usually interacts with robot calibration because robot geometric parameters are not very precise. In this article, a new calibration method considering the rotation parameters of the robot pose is proposed. First, a constraint least square model is established assuming that each spherical center measurement of standard ball is equal in the robot base frame, which provides an initial solution. To further improve the solution accuracy, a nonlinear calibration model in the sensor frame is established. Since it can reduce one error accumulation process, a more accurate reference point can be used for optimization. Then, the rotation parameters of the robot pose whose slight errors cause large disturbance to the solution are selected by analyzing the coefficient matrices of the error items. Finally, the hand-eye transformation parameters are refined together with the rotation parameters in the nonlinear optimization solution. Some comparative simulations are performed between the modified least square method, constrained least square method, and the proposed method. The experiments are conducted on a 5-axis hybrid robot named TriMule to demonstrate the superior accuracy of the proposed method.

A computationally efficient method for hand-eye calibration

Purpose

Surgical robots with cooperative control and semiautonomous features have shown increasing clinical potential, particularly for repetitive tasks under imaging and vision guidance. Effective performance of an autonomous task requires accurate hand–eye calibration so that the transformation between the robot coordinate frame and the camera coordinates is well defined. In practice, due to changes in surgical instruments, online hand–eye calibration must be performed regularly. In order to ensure seamless execution of the surgical procedure without affecting the normal surgical workflow, it is important to derive fast and efficient hand–eye calibration methods.

Methods

We present a computationally efficient iterative method for hand–eye calibration. In this method, dual quaternion is introduced to represent the rigid transformation, and a two-step iterative method is proposed to recover the real and dual parts of the dual quaternion simultaneously, and thus the estimation of rotation and translation of the transformation.

Results

The proposed method was applied to determine the rigid transformation between the stereo laparoscope and the robot manipulator. Promising experimental and simulation results have shown significant convergence speed improvement to 3 iterations from larger than 30 with regard to standard optimization method, which illustrates the effectiveness and efficiency of the proposed method.

Registration of a hybrid robot using the Degradation-Kronecker method and a purely nonlinear method

Although the registration of a robot is crucial in order to identify its pose with respect to a tracking system, there is no reported solution to address this issue for a hybrid robot. Different from classical registration, the registration of a hybrid robot requires the need to solve an equation with three unknowns where two of these unknowns are coupled together. This property makes it difficult to obtain a closed-form solution. This paper is a first attempt to solve the registration of a hybrid robot. The Degradation-Kronecker (D-K) method is proposed as an optimal closed-form solution for the registration of a hybrid robot in this paper. Since closed-form methods generally suffer from limited accuracy, a purely nonlinear (PN) method is proposed to complement the D-K method. With simulation and experiment results, it has been found that both methods are robust. The PN method is more accurate but slower as compared to the D-K method. The fast computation property of the D-K method makes it appropriate to be applied in real-time circumstances, while the PN method is suitable to be applied where good accuracy is preferred.