Distributed and Consistent Multi-Robot Visual-Inertial-Ranging Odometry on Lie Groups

Reliable localization is a fundamental requirement for multi-robot systems operating in GPS-denied environments. Visual-inertial odometry (VIO) provides lightweight and accurate motion estimation but suffers from cumulative drift in the absence of global references. Ultra-wideband (UWB) ranging offers complementary global observations, yet most existing UWB-aided VIO methods are designed for single-robot scenarios and rely on pre-calibrated anchors, which limits their robustness in practice. This paper proposes a distributed collaborative visual-inertial-ranging odometry (DC-VIRO) framework that tightly fuses VIO and UWB measurements across multiple robots. Anchor positions are explicitly included in the system state to address calibration uncertainty, while shared anchor observations are exploited through inter-robot communication to provide additional geometric constraints. By leveraging a right-invariant error formulation on Lie groups, the proposed approach preserves the observability properties of standard VIO, ensuring estimator consistency. Simulation results with multiple robots demonstrate that DC-VIRO significantly improves localization accuracy and robustness, while simultaneously enabling anchor self-calibration in distributed settings.