Leveling the head relative to ground slope improves visual odometry in simulated bees

In honeybees, foragers use the waggle dance to communicate the direction and ``a distance" to a food source from the hive to other members of the colony. Behavioral studies indicate that dancing foragers estimate this ``distance" during outward flights (from the hive to the food source) based on visual cues, in particular optic flow, even over mountain slopes. While optic flow-based biologically plausible models for the honeybee visual odometer were previously presented, their robustness with respect to uneven terrain has not yet been investigated. In this study, we present a new model for the honeybee visual odometer, called Surf, which combines vertical oscillations with the constant reorientation of the honeybee's compound eye with respect to the slope overflown. As the simulated honeybee's compound eye is typically kept level with the surface below, the direction of perception of ventral and divergent optic flow tends to remain perpendicular to the surface, enhancing the robustness of their detection across terrain irregularities. Tested in open field simulations across uneven terrain and varied wind conditions, the Surf model demonstrated greater accuracy compared to previous models evaluated under the same conditions, while keeping precision. The reliability of the Surf model accounts for the observed ``mountain slopes" (uphill and downhill) behaviors in honeybees and offers promising applications for minimalistic aerial robots navigating uneven terrain and indoor spaces.