Online Temporal Calibration for Relative Transformation Estimation Systems

Abstract

In multi-robot systems, the combination of Ultra-Wideband (UWB) and Visual-Inertial Odometry (VIO) enables the correction of odometry drift and relative positioning between robots in a unified global coordinate. However, in traditional 4-DoF (3D position and heading) robot-to-robot Relative Frame Transformation (RFT) estimation, the timestamps of VIO and UWB often suffer from trigger and transmission delays, leading to reduced RFT estimation accuracy due to temporal misalignment. To address this, this letter first derives the observability conditions for time offset augmented RFT estimation using the Fisher Information Matrix (FIM) and the properties of its determinant. Next, two online temporal calibration methods are proposed: (i) the Nonlinear Least Squares (NLS) based method and (ii) Semi-Definite Programming (SDP) relaxation based method. Finally, extensive simulations and real-life experiments show that the proposed NLS and SDP methods with temporal calibration outperform traditional relative transformation estimation (RTE) methods in both relative translation and heading. In most cases, the results of the proposed SDP method are slightly better than the NLS method.