Generalized n-Dimensional Rigid Registration: Theory and Applications

The generalized rigid registration problem in high-dimensional Euclidean spaces is studied. The loss function is minimized with an equivalent error formulation by the Cayley formula. The closed-form linear least-square solution to such a problem is derived which generates the registration covariances, i.e., uncertainty information of rotation and translation, providing quite accurate probabilistic descriptions. Simulation results indicate the correctness of the proposed method and also present its efficiency on computation-time consumption, compared with previous algorithms using singular value decomposition (SVD) and linear matrix inequality (LMI). The proposed scheme is then applied to an interpolation problem on the special Euclidean group SE(n) with covariance-preserving functionality. Finally, experiments on covariance-aided Lidar mapping show practical superiority in robotic navigation.

A Novel Point Set Registration-Based Hand-Eye Calibration Method for Robot-Assisted Surgery

Pedicle screw insertion with robot assistance dramatically improves surgical accuracy and safety when compared with manual implantation. In developing such a system, hand-eye calibration is an essential component that aims to determine the transformation between a position tracking and robot-arm systems. In this paper, we propose an effective hand-eye calibration method, namely registration-based hand-eye calibration (RHC), which estimates the calibration transformation via point set registration without the need to solve the AX=XB equation. Our hand-eye calibration method consists of tool-tip pivot calibrations in two-coordinate systems, in addition to paired-point matching, where the point pairs are generated via the steady movement of the robot arm in space. After calibration, our system allows for robot-assisted, image-guided pedicle screw insertion. Comprehensive experiments are conducted to verify the efficacy of the proposed hand-eye calibration method. A mean distance deviation of 0.70 mm and a mean angular deviation of 0.68° are achieved by our system when the proposed hand-eye calibration method is used. Further experiments on drilling trajectories are conducted on plastic vertebrae as well as pig vertebrae. A mean distance deviation of 1.01 mm and a mean angular deviation of 1.11° are observed when the drilled trajectories are compared with the planned trajectories on the pig vertebrae.

Significance of Camera Pixel Error in the Calibration Process of a Robotic Vision System

Although robotic vision systems offer a promising technology solution for rapid and reconfigurable in-process 3D inspection of complex and large parts in contemporary manufacturing, measurement accuracy poses a challenge for its wide deployment. One of the key issues in adopting a robotic vision system is to understand the extent of its measurement errors which are directly correlated with the calibration process. In this paper, a possible source of practical and inherent measurement uncertainties involved in the calibration process of a robotic vision system are discussed. The system considered in this work consists of an image sensor mounted on an industrial robot manipulator with six degrees of freedom. Based on a series of experimental tests and computer simulations, the paper gives a comprehensive performance comparison of different calibration approaches and shows the impact of measurement uncertainties on the calibration process. It has been found from the error sensitivity analysis that minor uncertainties in the calibration process can significantly affect the accuracy of the robotic vision system. Further investigations suggest that inducing errors in image calibration patterns can have an adverse effect on the hand–eye calibration process compared to the angular errors in the robot joints.

A multiple closed-loops robotic calibration for accurate surgical puncture

BACKGROUND

Robotic puncture system increasingly demands stringent standard in target location accuracy. The positional and orientational transformation relationships among all components of the system are supposed to be calibrated and identified preoperatively.

AIMS

The target location performance is directly determined by the calibration result. Therefore, a multiple closed-loops calibration approach is proposed to achieve high-level calibration accuracy in robotic puncture system. MATERIALS & METHODS: This method takes as input the three-dimensional position information of the retro-reflective markers mounted on the surgical tool, which is detected by the optical tracking system in real time during robotic movement. There is less complicated mathematical derivation and calculation in the presented algorithm by applying the closed-loop principle.

RESULTS

Experimental results validate that it can achieve accurate robotic target location with less input data and computation-cost, satisfying the clinical puncture requirements.

DISCUSSION

The spatial calibration between robotic arm and optical tracking system efficiently realised by the presented approach present an alternative which can be safely applied to the robotic puncture system for accurate insertion.

CONCLUSION

Overall, a multiple closed-loops calibration approach is proposed in this work, which may increase surgical efficiency.

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.

Stereo Camera Head-Eye Calibration Based on Minimum Variance Approach Using Surface Normal Vectors

This paper presents a stereo camera-based head-eye calibration method that aims to find the globally optimal transformation between a robot’s head and its eye. This method is highly intuitive and simple, so it can be used in a vision system for humanoid robots without any complex procedures. To achieve this, we introduce an extended minimum variance approach for head-eye calibration using surface normal vectors instead of 3D point sets. The presented method considers both positional and orientational error variances between visual measurements and kinematic data in head-eye calibration. Experiments using both synthetic and real data show the accuracy and efficiency of the proposed method.

Adjoint Transformation Algorithm for Hand-Eye Calibration with Applications in Robotic Assisted Surgery

Hand–eye calibration aims at determining the unknown rigid transformation between the coordinate systems of a robot arm and a camera. Existing hand–eye algorithms using closed-form solutions followed by iterative non-linear refinement provide accurate calibration results within a broad range of robotic applications. However, in the context of surgical robotics hand–eye calibration is still a challenging problem due to the required accuracy within the millimetre range, coupled with a large displacement between endoscopic cameras and the robot end-effector. This paper presents a new method for hand–eye calibration based on the adjoint transformation of twist motions that solves the problem iteratively through alternating estimations of rotation and translation. We show that this approach converges to a solution with a higher accuracy than closed form initializations within a broad range of synthetic and real experiments. We also propose a stereo hand–eye formulation that can be used in the context of both our proposed method and previous state-of-the-art closed form solutions. Experiments with real data are conducted with a stereo laparoscope, the KUKA robot arm manipulator, and the da Vinci surgical robot, showing that both our new alternating solution and the explicit representation of stereo camera hand–eye relations contribute to a higher calibration accuracy.

A flexible method combining camera calibration and hand–eye calibration

We consider the conventional techniques of vision robot system calibration where camera parameters and robot hand–eye parameters are computed separately, i.e., first performing camera calibration and then carrying out hand–eye calibration based on the calibrated parameters of cameras. In this paper we propose a joint algorithm that combines the camera calibration and the hand–eye calibration together. The proposed algorithm gives the solutions of the cameras' parameters and the hand–eye parameters simultaneously by using nonlinear optimization. Both simulations and real experiments show the superiority of our algorithm. We also apply our algorithm in the real application of the robot-assisted surgical system, and very good results have been obtained.

A hand–eye calibration algorithm based on screw motions

When computer vision technique is used in robotics, robotic hand–eye calibration is a very important research task. Many algorithms have been proposed for hand–eye calibration. Based on these algorithms, we introduce a new hand–eye calibration algorithm in this paper, which employs the screw motion theory to establish a hand–eye matrix equation by using quaternion and gets a simultaneous result for rotation and translation by solving linear equations. The algorithm proposed in this paper has high accuracy and stable computational efficiency and can be understood easily. Both simulations and real experiments show the superiority of our algorithm over the comparative algorithms.

Adaptive motion selection for online hand–eye calibration

While a robot moves, online hand–eye calibration to determine the relative pose between the robot gripper/end-effector and the sensors mounted on it is very important in a vision-guided robot system. During online hand–eye calibration, it is impossible to perform motion planning to avoid degenerate motions and small rotations, which may lead to unreliable calibration results. This paper proposes an adaptive motion selection algorithm for online hand–eye calibration, featured by dynamic threshold determination for motion selection and getting reliable hand–eye calibration results. Simulation and real experiments demonstrate the effectiveness of our method.

A note on using only position equations for robotic hand/eye calibration

In two previous papers, we proposed an iterative algorithm for robotic hand/eye calibration. We stated that the iterative algorithm has two distinct advantages over traditional linear approaches: it is less sensitive to noise and it can calibrate the hand/eye matrix by using only relative sensor position measurements. In this correspondence, we point out that although the iterative algorithm does not require direct measurement of the sensor relative rotation, it still needs the user to provide the same amount of sensor orientation information. We also explain why the accuracy performance of the iterative algorithm was not improved by the inclusion of rotation equations.