An extended robot–world and hand–eye calibration method is proposed in this paper to evaluate the transformation relationship between the camera and robot device. This approach could be performed for mobile or medical robotics applications, where precise, expensive, or unsterile calibration objects, or enough movement space, cannot be made available at the work site. Firstly, a mathematical model is established to formulate the robot-gripper-to-camera rigid transformation and robot-base-to-world rigid transformation using the Kronecker product. Subsequently, a sparse bundle adjustment is introduced for the optimization of robot–world and hand–eye calibration, as well as reconstruction results. Finally, a validation experiment including two kinds of real data sets is designed to demonstrate the effectiveness and accuracy of the proposed approach. The translation relative error of rigid transformation is less than 8/10,000 by a Denso robot in a movement range of 1.3 m × 1.3 m × 1.2 m. The distance measurement mean error after three-dimensional reconstruction is 0.13 mm.

Highly accurate and easy-to-operate calibration (to determine the interior and distortion parameters) and orientation (to determine the exterior parameters) methods for cameras in large volume is a very important topic for expanding the application scope of 3D vision and photogrammetry techniques. This paper proposes a method for simultaneously calibrating, orienting and assessing multi-camera 3D measurement systems in large measurement volume scenarios. The primary idea is building 3D point and length arrays by moving a scale bar in the measurement volume and then conducting a self-calibrating bundle adjustment that involves all the image points and lengths of both cameras. Relative exterior parameters between the camera pair are estimated by the five point relative orientation method. The interior, distortion parameters of each camera and the relative exterior parameters are optimized through bundle adjustment of the network geometry that is strengthened through applying the distance constraints. This method provides both internal precision and external accuracy assessment of the calibration performance. Simulations and real data experiments are designed and conducted to validate the effectivity of the method and analyze its performance under different network geometries. The RMSE of length measurement is less than 0.25 mm and the relative precision is higher than 1/25,000 for a two camera system calibrated by the proposed method in a volume of 12 m × 8 m × 4 m. Compared with the state-of-the-art point array self-calibrating bundle adjustment method, the proposed method is easier to operate and can significantly reduce systematic errors caused by wrong scaling.