Honeybees foraging and recruiting nest-mates by performing the waggle dance need to be able to gauge the flight distance to the food source regardless of the wind and terrain conditions. Previous authors have hypothesized that the foragers’ visual odometer mathematically integrates the angular velocity of the ground image sweeping backward across their ventral viewfield, known as translational optic flow. The question arises as to how mathematical integration of optic flow (usually expressed in radians/s) can reliably encode distances, regardless of the height and speed of flight. The vertical self-oscillatory movements observed in honeybees trigger expansions and contractions of the optic flow vector field, yielding an additional visual cue called optic flow divergence. We have developed a self-scaled model for the visual odometer in which the translational optic flow is scaled by the visually estimated current clearance from the ground. In simulation, this model, which we have called SOFIa, was found to be reliable in a large range of flight trajectories, terrains and wind conditions. It reduced the statistical dispersion of the estimated flight distances approximately 10-fold in comparison with the mathematically integrated raw optic flow model. The SOFIa model can be directly implemented in robotic applications based on minimalistic visual equipment.

无论风和地形条件如何，蜜蜂通过摆动舞觅食和招募巢友都需要能够测量到食物来源的飞行距离。以前的作者假设觅食者的视觉里程计在数学上整合了地面图像向后扫过他们腹侧视场的角速度，称为平移光流。问题是光流的数学积分（通常以弧度/秒表示）如何可靠地编码距离，而不管飞行的高度和速度如何。在蜜蜂中观察到的垂直自振荡运动触发了光流矢量场的膨胀和收缩，产生了一个额外的视觉线索，称为光流发散。我们为视觉里程计开发了一个自缩放模型，其中平移光流由视觉估计的离地电流间隙缩放。在仿真中，我们发现这个模型（我们称之为 SOFIa）在大范围的飞行轨迹、地形和风力条件下都是可靠的。与数学集成的原始光流模型相比，它减少了估计飞行距离的统计离散度大约 10 倍。SOFIa 模型可以直接在基于极简视觉设备的机器人应用中实现。与数学集成的原始光流模型相比，它减少了估计飞行距离的统计离散度大约 10 倍。SOFIa 模型可以直接在基于极简视觉设备的机器人应用中实现。与数学集成的原始光流模型相比，它减少了估计飞行距离的统计离散度大约 10 倍。SOFIa 模型可以直接在基于极简视觉设备的机器人应用中实现。