Probabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems

In recent years, the topic of multi-robot systems has become very popular. These systems have been demonstrated in various applications, including exploration, construction, and warehouse operations. In order for the whole system to function properly, sensor calibrations such as determining the camera frame relative to the IMU frame are important. Compared to the traditional hand-eye & robot-world calibration, a relatively new problem called the AXB = Y CZ calibration problem arises in the multi-robot scenario, where A,B,C are rigid body transformations measured from sensors and X,Y, Z are unknown transformations to be calibrated. Several solvers have been proposed previously in different application areas that can solve for X,Y and Z simultaneously. However, all of the solvers assume a priori knowledge of the exact correspondence among the data streams {Ai}, {Bi} and {Ci}. While that assumption may be justified in some scenarios, in the application domain of multi-robot systems, which may use ad hoc and asynchronous communication protocols, knowledge of this correspondence generally cannot be assumed. Moreover, the existing methods in the literature require good initial estimates that are not always easy or possible to obtain. In this paper, we propose two probabilistic approaches that can solve the AXB = Y CZ problem without a priori knowledge of the correspondence of the data. In addition, no initial estimates are required for recovering X , Y and Z. These methods are particularly well suited for multi-robot systems, and also apply to other areas of robotics in which AXB = Y CZ arises.