RingNav: Task-Shaped Circular Memory for Visual Heading

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.