IMUnet: Lightweight Stability Estimator

• The paper adapts the original IMUNet 1D CNN to regress a scalar stability score from inertial and velocity data, achieving a test MSE of 0.0074 on unseen terrain.
• The model replaces traditional physics-based metrics with a vision-derived C3 score, allowing robust stability prediction without force sensing or terrain reconstruction.
• The network processes an 8×200 input tensor from high-frequency IMU and interpolated velocity measurements, demonstrating practical benefits for off-road task scheduling and edge deployment.

IMUnet is a name used in multiple research contexts, but in off-road robotics it denotes a lightweight proprioceptive regression network adapted to estimate mobile robot platform stability directly from inertial and velocity measurements. In "Learning to Predict Mobile Robot Stability in Off-Road Environments," IMUnet is fine-tuned to map short windows of IMU and velocity data to a scalar stability score, using a vision-derived supervisory signal during training and requiring no terrain model, force sensing, or online vision at deployment (Rose et al., 17 Jul 2025). The off-road formulation is derived from the original IMUNet architecture for inertial navigation and positioning, a lightweight 1D CNN designed for edge-device inference from raw IMU sequences (2208.00068).

1. Definition and problem setting

In the off-road stability setting, IMUnet addresses real-time estimation of the stability of a wheeled unmanned ground vehicle in unstructured terrain using only onboard proprioceptive data: 6-axis IMU signals and planar velocity. The input is a short temporal window of inertial and velocity measurements, and the output is a scalar stability score for that window. The intended behavior is that the predicted score increases with dynamic disturbance, terrain roughness, and speed, and can therefore be used for downstream decision-making such as whether precision actuation should be executed under current motion conditions (Rose et al., 17 Jul 2025).

This formulation is explicitly motivated by deployment constraints. Classical off-road stability estimation typically depends on terrain geometry, contact locations, support polygons, force or wrench measurements, and accurate center-of-mass estimation. The off-road IMUnet formulation instead seeks a data-driven surrogate that is low-cost, proprioceptive-only, and robust to the measurement difficulties encountered on deformable or rugged terrain. Vision is used only to generate supervisory labels during data collection; inference is proprioceptive-only (Rose et al., 17 Jul 2025).

A recurrent misconception is to treat this IMUnet output as a formal safety margin. The paper does not do that. Its target is an operationally defined scalar proxy for instability, not a certified rollover metric or an implementation of Static Stability Margin, Zero Moment Point, FASM, MHS, or SM. That distinction is central to the method’s scope (Rose et al., 17 Jul 2025).

2. Operational stability and the C3 supervisory signal

Rather than directly modeling multibody dynamics, the off-road system defines stability through a scalar supervision target called the C3 score. A rigidly mounted Intel RealSense D455 observes a large static ArUco marker placed ahead of the vehicle. If the robot remains kinematically stable, the marker center in the image changes smoothly; if the platform bounces, pitches, rolls, or undergoes abrupt terrain-induced perturbations, the marker center exhibits larger frame-to-frame displacements. C3 therefore measures image-space perturbation of a static visual reference as a proxy for physical instability (Rose et al., 17 Jul 2025).

The frame-level primitive is the circles-crossed (CC) score. For each consecutive frame pair, the previous marker center is used to generate 20 concentric circles with radii increasing from 2 to 40 pixels. The displacement from the previous center to the current center is then converted into a discrete radial motion count by measuring how many circle boundaries are crossed. This count is further normalized by the robot’s current distance to the ArUco marker relative to the maximum travel distance of that run, compensating for the fact that identical pixel motions correspond to different physical motions at different camera-marker distances. The C3 score for a window is the accumulation of these normalized CC values over the frame sequence, and the resulting C3 values are rescaled to $[0,1]$ by dividing by the maximum observed C3 across all terrains (Rose et al., 17 Jul 2025).

The significance of C3 is empirical as well as definitional. Ground-truth statistics in the study show that mean C3 increases with terrain roughness in the ordering pavement $\ll$ grass $\ll$ dirt $\ll$ dirt with rocks, and also increases with speed for each terrain, from $0.5$ to $1.0$ to $1.5\,\mathrm{m/s}$. This suggests that the supervision target is aligned with intuitive physical instability while remaining measurable without force sensing or explicit terrain reconstruction (Rose et al., 17 Jul 2025).

The paper contrasts this with traditional stability metrics. Static Stability Margin requires precise contact locations, an accurate center-of-mass projection, and reliable ground-plane estimation; Zero Moment Point requires full contact wrench information or equivalent force estimation as well as mass, inertia, and center-of-mass parameters. On real off-road wheeled platforms with uncertain contact, deformable terrain, and suspension dynamics, these requirements are difficult to satisfy in a low-cost field system. IMUnet is proposed specifically as an alternative to that instrumentation-heavy regime (Rose et al., 17 Jul 2025).

3. Architecture, input representation, and relation to the original IMUNet

The off-road model adopts the original IMUNet backbone as a regression architecture and repurposes it from inertial navigation to stability estimation. In the original inertial-odometry formulation, IMUNet is a lightweight 1D CNN using a MobileResNet design with depth-wise and point-wise convolutions, ELU activations, and residual topology, built for IMU-based velocity estimation on edge devices; on a Galaxy S10, the reported TensorFlow Lite model size is $1.4\,\mathrm{MB}$ with $387\,\mu\mathrm{s}$ latency (2208.00068). In the off-road paper, the noise-cancellation block from that backbone is removed and the remaining network is fine-tuned to regress a single scalar stability score rather than navigation state (Rose et al., 17 Jul 2025).

The deployed input is an $8 \times 200$ tensor,

$\ll$0

constructed from 200 sequential IMU samples and interpolated planar velocities. The eight channels are $\ll$1. IMU data are acquired from a SwiftNav Duro IMU at $\ll$2, while GPS/RTK position is available at $\ll$3 and used to compute velocity, which is interpolated to IMU timestamps. At $\ll$4, a 200-sample window corresponds to 1 second. Windows corresponding to non-motion states such as boot-up, stationary periods, and alignment maneuvers are removed as outliers (Rose et al., 17 Jul 2025).

The regression problem is formulated as

$\ll$5

with mean squared error

$\ll$6

Here $\ll$7 is the normalized C3 score. The manuscript does not provide full layer-by-layer details for the modified off-road network, although its figure indicates a compact sequence model with a scalar regression head and the text emphasizes efficiency and edge deployment suitability (Rose et al., 17 Jul 2025).

The original IMUNet lineage matters because it clarifies what is inherited and what is changed. The original network was introduced for learned inertial navigation from raw IMU windows in a RoNIN-style pipeline, outputting velocity in the global frame and reconstructing position by integration. The off-road stability variant retains the compact inertial-regression character of that backbone but changes the target, the input dimensionality, and the operational semantics of the output (2208.00068).

4. Data collection, training protocol, and empirical performance

Experiments for the off-road stability model were conducted on an AgileX Scout 2.0 UGV equipped with an NVIDIA Jetson AGX Orin running ROS2, a SwiftNav Duro GNSS/INS providing RTK-GPS at $\ll$8 and IMU at $\ll$9, and an Intel RealSense D455 at $\ll$0. The vehicle performed waypoint-style forward traversals toward a $\ll$1 ArUco marker while IMU, GPS, and camera streams were logged in ROS bags (Rose et al., 17 Jul 2025).

The dataset spans four terrain types—pavement, grass, dirt, and dirt with rocks—and three commanded speeds: $\ll$2, $\ll$3, and $\ll$4. The total dataset consists of 86 runs and approximately 1000 windowed dataframes after preprocessing. For each window, IMU and interpolated velocity form the $\ll$5 input, temporally aligned camera frames generate the C3 score, and the score is normalized into $\ll$6 to produce the regression target (Rose et al., 17 Jul 2025).

The generalization protocol is deliberately terrain-holdout. Pavement, dirt, and dirt-with-rocks are used for training, while grass is withheld entirely for testing. Because the raw dataset is imbalanced across terrain-speed combinations, the training set is balanced by sampling an equal number of dataframes per velocity level within each terrain type, and stratified sampling is applied by binning ground-truth score values so that training and validation preserve similar C3 distributions. Training uses Adam, learning rate $\ll$7, batch size 32, 100 epochs, dropout rate 0.5, and a 15% validation split on an NVIDIA RTX 3500 Ada GPU with CUDA 12.4 (Rose et al., 17 Jul 2025).

The principal quantitative result is a test MSE of 0.0074 on the unseen grass terrain. The paper notes that most prediction errors are close to zero and that the error distribution is slightly biased toward overestimating instability. Predicted scores track ground truth well on relatively stable segments, but the model underfits more strongly at high-instability segments where normalized C3 is large. The authors describe the resulting terrain transfer as limited but meaningful generalization, and they explicitly note that no ablation studies or alternative baselines are yet reported in this pilot study (Rose et al., 17 Jul 2025).

5. Applications, interpretation, and limitations

The immediate application proposed for the off-road IMUnet variant is gating of tasks that are sensitive to platform disturbance. In mobile manipulation, high predicted instability can be used to delay grasping or precise arm motion; in precision sensing, data capture can be scheduled only when predicted C3 is low. The paper highlights agriculture and space exploration as concrete domains in which uneven terrain directly affects image quality, actuation precision, and instrument safety (Rose et al., 17 Jul 2025).

A broader implication is its role as a supervisory bridge between proprioception and exteroception. Because C3 is measured offline using vision while inference is proprioceptive-only, the learned stability signal can be used to label traversability or dynamic roughness for later perception-based models. The paper therefore positions IMUnet as a possible component in near-to-far self-supervision, costmap augmentation, and stability-aware planning. It is also proposed as a fallback signal when cameras or LiDAR are degraded, enabling cautious driving or conservative planning based solely on IMU and velocity (Rose et al., 17 Jul 2025).

At the same time, the limitations are explicit. The dataset is pilot-scale, approximately 1000 windows, and restricted to a single robot platform, one sensor configuration, and a limited terrain set. High-instability cases remain underrepresented. The output is a heuristic pose-deviation proxy rather than a formal safety margin, so no safety guarantee is claimed. No comparisons are provided against simple IMU heuristics, classical physics-based metrics, or alternative learned baselines; no ablation isolates the contribution of velocity channels relative to raw IMU; and no experimental real-time deployment study is reported, even though the backbone is intended to be efficient (Rose et al., 17 Jul 2025).

These limitations also delimit interpretation. The reported result supports the feasibility of learned proprioceptive stability estimation, but it does not establish equivalence to rollover predictors or support direct replacement of formal safety metrics in safety-critical systems. A plausible implication is that IMUnet is best understood, at this stage, as a deployable disturbance estimator whose main value lies in task scheduling and supervision rather than certified stability analysis.

6. Nomenclature, homonymous models, and later usage

The term IMUnet is not unique across arXiv-scale literature. In practice, it should be interpreted from domain context.

Name	Domain	Role
IMUnet / IMUNet (Rose et al., 17 Jul 2025)	Off-road robotics	Proprioceptive stability regressor
IMUNet (2208.00068)	Inertial odometry	Lightweight 1D CNN for navigation
IMNet (Liu et al., 2019)	MIMO-OFDM detection	DL detector for index modulation
Implicit U-Net / IMUnet (Marimont et al., 2022)	3D medical segmentation	Implicit decoder replacing 3D U-Net decoder
iUNets (Etmann et al., 2020)	Invertible imaging networks	Fully invertible U-Net architecture

The off-road model is directly descended from the inertial-odometry IMUNet backbone, not from the communications model "IMNet" or from medical-imaging architectures whose names are sometimes abbreviated similarly. The original IMUNet paper defines a mobile-efficient inertial regression network and releases code, datasets, and Android deployment artifacts; that model remains sufficiently influential that later inertial odometry papers still use IMUNet both as a baseline architecture and as the name of a public ARCore-ground-truth dataset (2208.00068, Zhang et al., 22 Jul 2025, Zhang et al., 22 Jul 2025).

This later usage reinforces a second layer of ambiguity. In "ResKACNNet," IMUNet appears both as a depthwise-separable-convolution baseline and as a 9.0-hour ARCore-based inertial-odometry dataset (Zhang et al., 22 Jul 2025). In "FTIN," IMUNet again appears in those two roles, and the paper explicitly contrasts its own frequency-time design with time-domain baselines including IMUNet (Zhang et al., 22 Jul 2025). Separately, medical-image papers use near-homonymous labels for entirely different model families: the Implicit U-Net replaces the 3D U-Net decoder with a coordinate-based implicit localization network (Marimont et al., 2022), and iUNets denote fully invertible U-Net architectures with learnable invertible up- and downsampling (Etmann et al., 2020). A further descriptive usage appears in Mamba-based medical segmentation, where “IMUnet-style” refers generically to U-shaped encoder-decoder models built with Mamba or state-space blocks rather than to a single canonical architecture (Liu et al., 2024).

In encyclopedia terms, the most precise interpretation is therefore contextual. In off-road robotics, IMUnet denotes a learned proprioceptive stability estimator trained against a C3 supervisory signal (Rose et al., 17 Jul 2025). In inertial navigation, IMUNet denotes the original lightweight edge-oriented 1D CNN backbone for IMU-based odometry (2208.00068). Across other fields, similarly spelled names denote unrelated architectures.