Hand-eye calibration of IMU and camera without external equipments

To relate measurements made by visual and inertial sensors, we must solve the hand-eye calibration (HEC) equation AX=XB, where X denotes an unknown rotation and translation between camera and inertial measurement unit (IMU), and A and B respectively represent the calculated movement transformations related with the camera and IMU. This paper introduces a systematic framework to jointly calibrate IMU and relative transformations X with a linear decomposition algorithm which is composed by Kronecker product and singular value decomposition. Without the requirements of external equipments including Robot Operating System or specific hardware and of the A and B featured the identical rotation angle, it enables the extension to the arbitrary set-up and the noise in rotation. The details of our framework are given, together with a validity of A and B movements followed by results of real experiments, showing that the enough precision and more robustness can be achieved.