Bearing Invariance and Robust Disturbance Thresholds for Hybrid Camera-Based Unicycle Stabilization

Abstract

A recent hybrid camera-based stabilizer regulates a unicycle robot by switching between front and rear onboard camera-coordinate representations. We analyze whether the active-camera bearing can reach the field-of-view (FOV) boundary under nominal closed-loop dynamics and additive yaw-rate disturbances. Using a range-independent two-state bearing model, we first recover the known result that the bearing remains within $|\theta |\le \pi /2$ . We then derive a gain condition that keeps the bearing strictly inside the FOV, an initial-condition safe set valid for every initial range, and the largest persistent yaw-rate disturbance bound that preserves $|\theta |\le \pi /2$ . We also show that any larger bound can violate this property and give explicit error and sampling-age limits that prevent false camera switching. Numerical sweeps support the analytical results and illustrate their disturbance limits.