Determination of calibration parameters is essential for the fusion performance of an inertial measurement unit (IMU) and odometer integrated navigation system. Traditional calibration methods are commonly based on the filter frame, which limits the improvement of the calibration accuracy. This paper proposes a graph-optimisation-based self-calibration method for the IMU/odometer using preintegration theory. Different from existing preintegrations, the complete IMU/odometer preintegration model is derived, which takes into consideration the effects of the scale factor of the odometer, and misalignments in the attitude and position between the IMU and odometer. Then the calibration is implemented by the graph-optimisation method. The KITTI dataset and field experimental tests are carried out to evaluate the effectiveness of the proposed method. The results illustrate that the proposed method outperforms the filter-based calibration method. Meanwhile, the performance of the proposed IMU/odometer preintegration model is optimal compared with the traditional preintegration models.

A class of three-legged modular reconfigurable parallel robots is designed and constructed for precision assembly and light machining tasks by using standard active and passive joint modules in conjunction with custom designed links and mobile platforms. Since kinematic errors, especially the assembly errors, are likely to be introduced, kinematic calibration becomes particularly important to enhance the positioning accuracy of a modular reconfigurable robot. Based on the local frame representation of the Product-Of-Exponentials (Local POE) formula, a self-calibration method is proposed for these three-legged modular reconfigurable parallel robots. In this method, both revolute and prismatic joint axes can be uniformly expressed in twist coordinates by their respective local (body) frames. Since these local frames can be arbitrarily defined on their corresponding links, we are able to calibrate them, and yet retain the nominal local description of their respective joints, i.e., the nominal twist coordinates and nominal joint displacements, to reflect the actual kinematics of the robot. The kinematic calibration thus becomes a procedure of fine-tuning the locations and orientations of the local frames. Using mathematical tools from differential geometry and group theory, an explicit linear calibration model is formulated based on the leg-end distance errors. An iterative least-square algorithm is employed to identify the error parameters. A simulation example of calibrating a three-legged (RRRS) modular parallel robot shows that the robot kinematics can be fully calibrated within two to three iterations.