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 (S1). 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 27.3Hz on Raspberry Pi Zero 2W and can be deployed on an ultra-low power GAP8 processor at 33.4Hz.