Hand-Eye Camera Calibration with an Optical Tracking System

This paper presents a method for hand-eye camera calibration via an optical tracking system (OTS) faciltating robotic applications. The camera pose cannot be directly tracked via the OTS. Because of this, a transformation matrix between a marker-plate pose, tracked via the OTS, and the camera pose needs to be estimated. To this end, we evaluate two different approaches for hand-eye calibration. In the first approach, the camera is in a fixed position and a 2D calibration plate is displaced. In the second approach, the camera is also fixed, but now a 3D calibration object is moved. The first step of our method consists of collecting N views of the marker-plate pose and the calibration plates, acquired via OTS. This is achieved by keeping the camera fixed and moving the calibration plate, while taking a picture of the calibration plate using the camera. A dataset is constructed that contains marker-plate poses and the relative camera poses. Afterwards, the transformation matrix is then computed, following a least-squares minimization. Accuracy in hand-eye calibration is computed in terms of re-projection error, calculated based on camera homography transformations. For both approaches, we measure the changes in accuracy as a function of the number of poses used for each calibration, while we define the minimum number of poses required to obtain a good camera calibration. Results of the experiments show similar performances for the two evaluated methods, achieving a median value of the re-projection error at N = 25 poses of 0.76 mm for the 2D calibration plate and 0.70 mm for the 3D calibration object. Also, we have found that minimally 15 poses are required to achieve a good camera calibration.