RingNav: Task-Shaped Circular Memory for Visual Heading

Naitri Rajyaguru; Aryan Tajne; Stephen Jardim; Cornelia Fermuller; Yiannis Aloimonos

cs.ROOct 13, 2026

RingNav: Task-Shaped Circular Memory for Visual Heading

Authors: Naitri Rajyaguru, Aryan Tajne, Stephen Jardim, Cornelia Fermuller, Yiannis Aloimonos

Organizations: University of Maryland, College Park

Abstract

Tiny robots have limited computation and memory, yet visual navigation systems often maintain more state than a task requires. We ask whether persistent memory can instead be shaped by the task. We present RingNav, a $10.6$ k--parameter visual heading estimator that constrains its memory to the circular manifold $S^1$ . RingNav learns only the turn between consecutive images, while heading is composed directly on the circle. On the TartanAir Visual SLAM Challenge, RingNav reduces mean absolute turn error by $27\%$ and accumulated heading error over $4$ sec by $15\%$ relative to a similarly sized learned-memory model. The structured update also gives exactly zero turn for identical frames and exact cancellation under sequence reversal. Without fine-tuning, RingNav transfers to real-world drone experiments and continues estimating heading under severe visual degradation. RingNav runs at $27.3$ Hz on Raspberry Pi Zero 2W and can be deployed on an ultra-low power GAP8 processor at $33.4$ Hz.

Figures & tables

Fig. 1: Task-shaped memory for visual heading. RingNav estimates the visual turn between consecutive images and maintains heading as a persistent circular state. On a real Crazyflie flight, its heading estimate follows motion-capture ground truth around the trajectory. The estimator uses 10.6k trainable parameters.

Task dependence	State	DoF	State update
Heading	$S^{1}$	1	circular rotation
Heading + progress	$S^{1}\times\mathbb{R}$	2	rotation + addition
Heading + cyclic progress	$T^{2}=S^{1}\times S^{1}$	2	two circular rotations
3D bearing	$S^{2}$	2	$SO(3)$ action
Planar pose	$SE(2)$	3	rigid-body composition
3D pose	$SE(3)$	6	rigid-body composition

TABLE I: Task-selected persistent state. Different behaviors require different information to persist over time.

Fig. 2: RingNav pipeline. A shared image-pair network processes consecutive observations in both temporal orders. Their half-difference gives the visual increment $\widehat{\Delta\psi}_{t}$ , which acts on the latent manifold $S^{1}$ through $R(\widehat{\Delta\psi}_{t})$ , advancing the persistent state from $s_{t}$ to $s_{t+1}$ and yielding the updated heading $\hat{\psi}_{t+1}$ .

Reference
Method	CompTest	HDH-Bench	Crazyflie
Zero turn	0.861 / 22.3	1.741 / 158.7	0.774 / 65.2
Full Visual Motion
TartanVO	0.206 / 4.8	0.267 / 22.9	0.347 / 12.1
DPVO	0.177 / 4.2	0.106 / 5.3	0.336 / 4.3
DROID-SLAM	0.198 / 4.6	0.148 / 7.0	0.343 / 4.4

TABLE II: Heading estimation across domains. Turn MAE / four-second accumulated turn error

D_{4\mathrm{s}}

, in degrees.

\times

denotes coverage below

80\%

; the best result within each method group is bolded.

Fig. 3: Heading estimates on HDH-Bench. Ground truth, RingNav, and Visual Gyro on representative trajectories.

A. End-to-End Heading Estimation
Variant	State	Update	Turn MAE	$D_{4\mathrm{s}}$	$E_{\rm rev}$ ( ∘ )
PairGRU	learned	learned	0.810	20.6	53.4
learned- $S^{1}$	$S^{1}$	learned	0.636	19.6	3,205
exact- $S^{1}$	$S^{1}$	fixed	0.641	19.7	6,190
skew- $S^{1}$	$S^{1}$	fixed	0.607	17.9	0
RingNav	$S^{1}$	fixed	0.589	17.6	0

TABLE III: Ablation of the latent state, update, and visual increment. (A) End-to-end heading estimation and forward–reverse error. (B) State error after repeated updates with the same turn sequence.

Fig. 4: Heading under degraded and missing visual input. Example inputs and heading estimates under image degradation, camera freeze, and near-dark observations.

Method	Clean	Blur	Flicker	Roll. shutter	Lens dirt
Full Visual Motion
TartanVO	0.105/7.9	0.104/8.0	0.105/7.9	0.107/7.9	0.529/16.4
DPVO	0.021/0.12	0.022/0.13	0.021/0.12	0.022/0.17	$\times$
DROID-SLAM	0.069/1.00	0.076/1.0	0.023/0.18	0.049/0.99	0.625/16.0
Rotation / Heading Only
Visual Gyro	0.141/5.8	$\times$	0.151/6.0	0.142/5.9	0.535/15.8

TABLE IV: Heading under degraded and missing visual input. (A) Turn MAE / four-second accumulated turn error under image degradation. (B) Predicted turn magnitude, accumulated turn error over the test interval, and local residual RMSE over the following 20 transitions.

	RingNav		Visual Gyro
Platform	RAM (MiB)	Hz	RAM (MiB)	Hz
Pi 5	73.8	199	104.5	3.50
Pi 4	68.4	63.3	102.1	1.21
Pi Zero 2W	68.2	27.3	130.2	0.349
GAP8 (AI-deck)	0.49	33.4	7.83	0.1

TABLE V: Edge deployment across hardware platforms. Heading-update rate and peak runtime memory on different embedded boards.

Fig. 5: Heading on real Crazyflie flights. Ground truth, RingNav, and Visual Gyro on representative degraded sequences.

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Visual navigation policies have grown to hundreds of millions of parameters trained on billions of frames, with geometry, mapping, and control learned implicitly. We propose a decomposed point-goal navigation system in which operations with known closed-form structure, such as projective geometry, occupancy, and coordinate transforms, are computed analytically and serve as interfaces between three small learned modules: an egress predictor that grounds the episode goal as a local subgoal in the current view, a navigation predictor that estimates a goal-conditioned posterior over where trajectories travel, and an endpoint-pinned residual diffusion generator that samples trajectory shapes from this posterior. Only 0.58M out of 23M parameters are trained, on 44k frames, in under one GPU-hour. Across 6060 point-goal episodes in 60 environments, the system attains competitive success rates with the lowest collision rate among evaluated methods. We further show that under this decomposition, the frozen image encoder can be replaced by a 0.54M MobileNetV2 at a -2.0 SR cost, bringing the full system under 1.2M parameters. It also transfers to no-goal exploration by retraining only the 123k-parameter egress head, and its failure modes under sensor corruption are transparent and analytically correctable. We deploy and evaluate the system zero-shot on a low-cost UGV, running navigation and localization on a Jetson Orin Nano in real-time.

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