NeuRIO: A Streaming Neural Estimator for Zero-Shot Sim-to-Real Multi-Robot Relative Inertial Odometry

Neural inertial odometry has demonstrated strong potential for motion estimation in challenging environments, yet inertial-only preintegration remains sensitive to IMU bias and uncertainty. To this end, this paper introduces \textbf{PLATO}:\emph{Preintegration Learning from Accurate Trajectory Observations}, a likelihood-based framework that leverages accurate trajectory observations to jointly learn IMU bias dynamics modeled by a neural ordinary differential equation(NODE) and gyroscope and accelerometer noise covariances. Optimization exploits the sparse structure of the negative log-likelihood, with IMU noise-parameter gradients computed by forward differentiation. A tailored double-adjoint scheme couples a discrete invariant-error adjoint with a continuous-time adjoint for the bias NODE, enabling memory-efficient likelihood optimization over the nested bias-dynamics and IMU-preintegration rollouts. Validation on EuRoC shows improved performance, and underwater robot experiments demonstrate applicability under intermittent lighting failures and visual degradation.

Neural inertial odometry increasingly uses networks as learned measurements inside filtering pipelines. Such measurements should transform consistently under arbitrary IMU mounting conventions: their mean must transform as a vector, and their covariance must transform congruently as a second-order tensor. We present GINIO, a geometric SO(3)-equivariant interface for neural inertial odometry under arbitrary rotations of the IMU measurement frame. Given calibrated IMU windows, our framework predicts a motion measurement and uncertainty obeying these tensorial laws. To support efficient sensor-frame learning, we introduce Last-Frame Alignment (LFA), a deterministic preprocessing step that is provably equivalent to world-frame training for SO(3)-equivariant predictors. The connected estimator tracks sensor-local states such as IMU bias, separating nuisance estimation from the geometric law enforced by the learned measurement. We instantiate the same interface in filter-connected NIO, AirIO-style recurrent aerial prediction, EqNIO-style full-SO(3) canonicalization, and ResNet-style temporal backbones. On TLIO, GINIO achieves 2.018 m ID/SO(3) ATE while EqNIO degrades to 76.389 m, using 11.6x fewer FLOPs. On NanoBench, our AirIO-style instantiation improves ATE from 5.579 m to 1.430 m without external attitude input, and our ResNet-style instantiation reaches 0.581 m ATE versus 0.645 m for ResNet1D. On Fetch, GINIO empirically reduces unseen physical-remount ATE from 8.15 m to 0.50 m without retraining, demonstrating robustness beyond the exact coordinate-frame guarantee. For uncertainty, spectral covariance reduces covariance-equivariance error by over three orders of magnitude compared with a diagonal head.

Classical leader-follower formation control suffers from single points of failure and error propagation, and relies on absolute localization sensors that are ill-suited for GPS-denied environments. We present a learned, vision-only estimator that maps each robot's monocular image, together with messages exchanged over a communication graph, directly to its 6-DoF relative pose. Its key ingredient is the implicit virtual leader (IVL): a non-physical reference frame at the team centroid, implicitly learned inside a Transformer-based graph neural network, so that estimation has no privileged node and needs no absolute localization. The estimator additionally reports well-calibrated aleatoric (heteroscedastic GNLL) uncertainty alongside epistemic (MC~Dropout) uncertainty, compared systematically across simulation and real-world test sets. Trained only in simulation, the estimator generalizes to unseen scenes, to larger unseen team sizes, and to an external real-world benchmark. It exhibits no single point of failure: removing any one robot costs at most $1.24\times$ the median removal, and removing $71\%$ of the communication links costs $1.77\times$ in position error without retraining. Trained on real-robot data from a single platform, it transfers without modification to a heterogeneous team, estimating relative pose to $0.22$,m and $1.6^\circ$ on physical robots, where it drives closed-loop formation control.