Source-linked AI summary
RingNav: Task-Shaped Circular Memory for Visual Heading
Naitri Rajyaguru, Aryan Tajne, Stephen Jardim, Cornelia Fermuller, Yiannis Aloimonos
TL;DR
Small robots have limited computation and memory, while visual navigation systems can maintain more state than a task requires. RingNav fixes heading memory to S1 and learns only turns between images; its turn error improves over a similarly sized learned-memory model, with exact zero turns for identical frames and exact cancellation under sequence reversal.
Problem
Visual navigation systems can recover and maintain more state than a task requires, despite small robots’ limited computation and memory.
Source: §I · p. 1Method
Results
0.810° to 0.636°: restricting persistent state to S1 reduces turn MAE relative to PairGRU.
Source: C. State and Update Ablation · p. 5Takeaways & Limitations
RingNav transfers from synthetic training to real Crazyflie flight without fine-tuning and continues returning estimates under tested motion-blur, low-light, and low-contrast degradations.
Source: §V · p. 8The fixed geometric update cannot correct an inaccurate or unobservable visual increment; improving visual turn estimation remains future work.
Source: §V · p. 8
Abstract
from arXiv · showhide
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 \textbf{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.
I. INTRODUCTION
Visual navigation can recover more state than small-robot tasks require, while computation and memory are limited. RingNav applies task-shaped memory to heading by storing it on S1, learning only visual turns, and fixing the circular update.
I. INTRODUCTION
- Visual navigation is difficult on small robots with limited computation and memory, although tasks may require only a small part of the state recovered by VO or SLAM.VO estimates camera motion; SLAM additionally maintains an environment representation for localization –.Source: §I · p. 1
- Task-specific representations and smaller estimators reduce navigation costs, but the information that must persist also varies with the behavior.The range described runs from no persistent state for reactive control to full pose for metric navigation, consistent with task-driven estimation –.Source: §I · p. 1
- Task-shaped memory fixes the state and update rule when the task specifies them, leaving learning to estimate how that state changes from observations.Different tasks can therefore require different persistent-memory structures, as illustrated by Table I.Source: §I · p. 1, Table I · p. 1
A. Key Contributions
- The paper experimentally studies task-shaped memory for heading on S1 and evaluates degraded or missing visual input, real Crazyflie transfer, and edge runtime.The evaluation also compares rotation-only and full visual-motion estimators.Source: §I · p. 1, A. Key Contributions • · p. 2
- 10.6k parameters: RingNav estimates the visual turn between consecutive images and directly rotates a persistent heading state on S1.The estimator is constrained to predict zero turn for identical images and opposite turns when image order is reversed.Source: §I · p. 1, A. Key Contributions • · pp. 1–2
II. RELATED WORK
Prior visual-navigation work spans rotation-only and full visual-motion estimation, compact navigation for small robots, and structured representations of orientation. RingNav uses a known circular heading state and fixed rotation update, learning the turn from an ordered image pair.
II. RELATED WORK
- Rotation-only visual estimators recover camera rotation without translation or an explicit 3D map, while full visual odometry estimates both rotation and translation –,,.Feature-based rotation can require feature extraction, matching, and geometric estimation.Source: §II · p. 2
- RingNav imposes exact sign reversal on visual-turn estimates when the order of an image pair is reversed, then uses the turn to update persistent heading on S1.Prior relative-pose work has enforced inverse consistency under image-order reversal.Source: §II · p. 2
- Compact learned navigation, event-based visual odometry, route memories, visual homing, and teach-and-repeat reduce computation or the information that must be estimated –.Task-driven estimation seeks representations sufficient for a behavior rather than recovery of the full physical state,.Source: §II · p. 2
III. METHOD
- RingNav fixes the persistent heading state to the circle and its update to rotation, leaving the visual turn between images to be learned.Heading is periodic because a full rotation returns the robot to the same direction; the method describes the state as S1.Source: §II · p. 2, §III · p. 2
A. Visual Increment Network
- The visual-increment network takes an ordered image pair, using 320×320 RGB images concatenated channel-wise before a convolutional encoder and gated scalar head.The encoder uses four stride-2 convolutions with 8, 12, 16, and 24 output channels, followed by global average pooling and a two-layer MLP.Source: A. Visual Increment Network · p. 2
B. Antisymmetric Projection
RingNav forms a visual turn by evaluating each image pair in both temporal orders and taking the antisymmetric component. That increment rotates a persistent heading state on S1, with exact reversal and identical-frame properties.
B. Antisymmetric Projection
- The shared image-pair mapping is evaluated in both temporal orders, and its antisymmetric component gives the visual increment.The figure shows the half-difference acting on the persistent state through a circular rotation.Source: B. Antisymmetric Projection · p. 2, Figure 2 · p. 3
- Reversing an image pair exactly reverses the predicted increment, identical images produce zero, and reversed sequences cancel in exact arithmetic.The ordered image-pair network is evaluated in both temporal orders with shared parameters, but requires a separate evaluation for each ordering.Source: B. Antisymmetric Projection · pp. 2–3
- The persistent heading state lies on S1 and advances through a fixed rotation by the predicted visual increment.The rotation preserves the manifold in exact arithmetic; projection only corrects finite-precision changes in vector norm, and the update has no learned parameters.Source: C. Latent Manifold Dynamics on S1 · p. 3
- The updated heading is recovered from the latent state, so successive visual increments propagate heading through the fixed circular update.Source: C. Latent Manifold Dynamics on S1 · p. 3
D. Training Objective
RingNav trains the visual increment with local and multi-horizon path-integration losses, alongside regularization of ordered predictions. Its persistent state evolves by a fixed update and receives no direct loss.
D. Training Objective
- Training uses 24-frame windows with stride sampled uniformly from {1, 2}; validation and evaluation use stride 1.Within a window, consecutive samples are indexed as It and It+1.Source: D. Training Objective · p. 3
- The local visual-increment loss supervises predicted turns, while path-integration loss supervises accumulated turn over horizons H = {2, 4, 8}.The accumulated-turn target is the wrapped ground-truth heading change over k transitions.Source: D. Training Objective · p. 3
- Ordered predictions receive additional supervision, and their symmetric component is penalized.Antisymmetry of the projected increment follows by construction; the auxiliary losses regularize the ordered predictions before projection.Source: D. Training Objective · pp. 3–4
- The persistent state receives no direct loss because its evolution is fixed by Eq. (12).Source: D. Training Objective · p. 4
- At inference, each new image is paired with the preceding image to estimate an increment, advance the state, and recover heading.The method is causal and requires no future frames, map, keyframes, or learned latent-state transition.Source: D. Training Objective · p. 4
IV. EXPERIMENTS
The experiments are organized around five questions about heading accuracy, design choices, degraded inputs, real-world transfer, and hardware requirements.
IV. EXPERIMENTS
- Q1 asks how accurately RingNav estimates heading across CompTest, HDH-Bench, and real data.Source: §IV · p. 4
- Q2 examines the effects of the S1 heading state, fixed rotation update, and antisymmetric visual turn.Source: §IV · p. 4
- Q3 asks how RingNav behaves when visual input is degraded or missing.Source: §IV · p. 4
- Q4 asks whether RingNav transfers to the real world without fine-tuning.Source: §IV · p. 4
- Q5 asks what computation and memory RingNav requires on resource-constrained hardware.Source: §IV · p. 4
A. Experimental Setup
The evaluation uses synthetic benchmarks and Crazyflie flights, with no real-world data used for training or model selection. Turn and accumulated-turn metrics are scored using dataset-specific heading conventions and defined baseline coverage rules.
A. Experimental Setup
- Evaluation covers 16 TartanAir Visual SLAM Challenge trajectories, 196 HDH-Bench trajectories from four unseen rendered scenes, and 35 Crazyflie sequences.The Crazyflie set comprises 23 clean flights and 12 degraded sequences derived from four turning flights; training uses 104 sequences and validation uses eight additional TartanAir trajectories.Source: A. Experimental Setup · p. 4
- No real-world data is used for training or model selection, and training excludes listed visual-degradation and repeated-frame augmentations.Excluded augmentations include blur, flicker, rolling shutter, lens contamination, low light, low contrast, camera freeze, and repeated frames.Source: A. Experimental Setup · p. 4
- The reported metrics include mean absolute turn error and mean absolute accumulated turn error over four-second sliding windows.Four seconds corresponds to 40, 96, and 125 transitions at the nominal CompTest, HDH-Bench, and Crazyflie sampling rates, respectively.Source: A. Experimental Setup · p. 4
- Repeated-run baselines are summarized by median turn MAE, D4s, and coverage; transitions without estimates score as zero turn, and methods below 80% median coverage are marked ×.TartanVO, DPVO, and ORB-SLAM2 use five runs; DROID-SLAM uses 11 runs on CompTest and five on HDH-Bench and Crazyflie.Source: A. Experimental Setup · p. 4
- Ground-truth heading is world yaw for TartanAir, optical-axis azimuth for HDH-Bench, and airframe azimuth for Crazyflie, with no initial-orientation or trajectory alignment before scoring.Turn conventions for the compared methods vary by camera convention.Source: A. Experimental Setup · p. 4
B. Heading Estimation
RingNav is evaluated against rotation-only and full visual-motion estimators across CompTest, HDH-Bench, and Crazyflie. Results vary by benchmark, while RingNav completes the full HDH-Bench set and performs competitively on Crazyflie.
B. Heading Estimation
- 0.417° turn MAE and 34.5° four-second accumulated turn error: RingNav completes all 196 HDH-Bench trajectories, while Visual Gyro falls below 80% coverage.The scenes include environments absent from training; representative estimates are shown in Fig. 3.Source: Table II · p. 5, B. Heading Estimation · p. 5, Figure 3 · p. 5
- 0.458° turn MAE and 22.2° four-second accumulated turn error: RingNav compares with Visual Gyro’s 0.511° and 26.9° at 83.4% pooled coverage on Crazyflie.RingNav also improves over the zero-turn baseline on all three evaluation sets.Source: Table II · p. 5, B. Heading Estimation · p. 5
- 0.323° turn MAE and 6.8° four-second accumulated turn error for Visual Gyro compare with 0.589° and 17.6° for RingNav on CompTest.The full visual-motion estimators are also more accurate than RingNav on this benchmark.Source: Table II · p. 5, B. Heading Estimation · p. 5
C. State and Update Ablation
The ablation separates the effects of the circular state, fixed rotation update, and antisymmetric visual-turn constraint. The circular state improves heading metrics over a learned state, while the order-reversal constraint yields exact forward–reverse cancellation.
C. State and Update Ablation
- The ablation compares PairGRU, learned-S1, exact-S1, skew-S1, and full RingNav using the same training data and lightweight visual encoder.PairGRU has 10,890 parameters and a 64-byte state; learned-S1 has 9,642 parameters, while the other S1 variants have 10,600 parameters and 8-byte states.Source: C. State and Update Ablation · p. 5
- Restricting state to S1 reduces turn MAE from 0.810° for PairGRU to 0.636° and four-second accumulated turn error from 20.6° to 19.6°; fixed rotation alone changes accuracy little.Exact-S1 reaches 0.641° turn MAE and 19.7° accumulated turn error, so fixing the update does not by itself improve visual-turn estimation.Source: C. State and Update Ablation · p. 5
- Erev = 0 for RingNav and skew-S1, while unconstrained variants accumulate a nonzero residual; RingNav also has the lowest turn MAE and four-second accumulated turn error among five compact models.The exact constraint costs 41.48 MMAC per RingNav update, using two ordered 320 × 320 RGB evaluations.Source: C. State and Update Ablation · p. 6
- With the same world-heading turn sequence, learned updates accumulate tens of degrees of state error over long sequences, while fixed FP32 rotation remains near zero after 105 updates.Panel B isolates the state update from the image network.Source: C. State and Update Ablation · p. 6
D. Degraded and Missing Visual Input
RingNav’s behavior under degraded or missing visual input depends on whether identical frames mean no motion or a camera freeze. Its structural constraints prevent spurious turns on identical frames, but cannot reveal motion during a freeze.
D. Degraded and Missing Visual Input
- Under blur and rolling shutter, RingNav stays close to its clean result; flicker and lens contamination increase error, and lens contamination yields the lowest local turn error but not the lowest four-second accumulated error among estimating methods.The tested degradations include 0.5-frame blur, rolling shutter, flicker, and lens contamination covering 34.6% of the image.Source: D. Degraded and Missing Visual Input · p. 6
- During camera freeze, byte-identical frames make RingNav predict exactly zero turn, accumulating 40.76° of error while the platform rotates; local turn estimation resumes when image change returns, but the heading offset remains.The freeze test uses 24 byte-identical frames.Source: D. Degraded and Missing Visual Input · p. 6
- Across four stationary sequences, PairGRU, learned-S1, and exact-S1 accumulate 2.04°, 2.28°, and 2.69° of false turn, while skew-S1 and RingNav remain at zero.Identical observations cannot introduce a visual turn, but they also cannot reveal motion during a camera freeze; RingNav has no validity signal to distinguish these cases.Source: D. Degraded and Missing Visual Input · pp. 6–7
- With near-dark input, RingNav produces nonzero turns and accumulates 16.46° of error, while DPVO is substantially more accurate.The near-dark test uses a 7.64-stop exposure reduction; weak visual structure remains, unlike the byte-identical freeze input.Source: D. Degraded and Missing Visual Input · pp. 6–7
E. Real-Flight Transfer
On real Crazyflie flights, the frozen RingNav checkpoint transfers without real-image training or model selection. It returns estimates across the tested degradations, while Visual Gyro is more accurate on clean flights and loses coverage under degradation.
E. Real-Flight Transfer
- The zero-shot evaluation uses a frozen RingNav checkpoint on 23 recorded flights and 12 degraded sequences, with no real imagery for training or model selection; inference is offline.The 18,974 transitions come from 640 × 480 FPV video synchronized with motion-capture heading.Source: E. Real-Flight Transfer · p. 7
- On 12 degraded sequences, RingNav reaches 0.602° turn MAE and 41.9° four-second accumulated turn error, while Visual Gyro’s zero-turn scoring gives 0.853° and 70.3°.Visual Gyro coverage is 53.8%, below the reporting threshold; the zero-turn baseline reaches 1.034° turn MAE and 100.0° accumulated error.Source: E. Real-Flight Transfer · p. 7
- On 23 clean flights, Visual Gyro reaches 0.325° turn MAE and 3.3° four-second accumulated turn error, compared with RingNav’s 0.379° and 11.6°.Under motion blur, low light, and reduced contrast, Visual Gyro coverage falls to 79%, 4%, and 78%, respectively, while RingNav returns an estimate for every image pair.Source: E. Real-Flight Transfer · p. 7
F. Edge Deployment
RingNav targets constrained edge hardware with a compact heading state and fast updates. The conclusion emphasizes its structured update, zero-shot transfer, and visual-turn accuracy as its main limitation.
F. Edge Deployment
- In measured Raspberry Pi implementations, RingNav provides a 52–78× higher heading-update rate than Visual Gyro.Table V reports heading-update rate and peak runtime memory across embedded boards; reported rates exclude camera capture.Source: F. Edge Deployment · p. 7, Table V · p. 7
- On GAP8, RingNav reaches 33.4 Hz with the complete runtime in 0.49 MiB of on-chip memory; its persistent heading state occupies 8 bytes.The deployment uses 320 × 240 grayscale input; Visual Gyro is excluded from the on-chip comparison because its current GAP8 implementation requires external HyperRAM.Source: F. Edge Deployment · p. 7
V. CONCLUSION
- RingNav fixes heading memory to S1, updates it by SO(2) rotation, and learns only visual turn; its constraints give exact zero turn for identical frames and sign reversal when image order is reversed.The conclusion describes RingNav as a 10.6k-parameter estimator.Source: §V · p. 8
- The frozen model transfers from synthetic training to real Crazyflie flights without fine-tuning and returns estimates under tested motion-blur, low-light, and low-contrast degradations.The conclusion reports 33.4 Hz on GAP8 with the complete runtime in 0.49 MiB of on-chip memory.Source: §V · p. 8
- Visual turn accuracy remains the main limitation: the fixed geometric update cannot correct an inaccurate or unobservable increment.Future work aims to improve the visual estimator while preserving the compact structured state and to extend task-shaped memory to richer navigation manifolds.Source: §V · p. 8