Numerical Simulation of Visually Guided Landing Based on a Honeybee Motion Model

Abstract

We verified the validity of a bio-inspired strategy for visually guided landing and its mathematical model proposed M.V. Srinivasan et al. by numerical simulation. We studied the influence of temporal discretization and the values of the supported optical flow on the landing duration and its result (from smooth to crash). An algorithm for landing simulation was developed taking into account accepted assumptions of the model. Two formulas (sine and tangent) were derived to calculate the distance and the speed of the flying robot, ensuring the constancy of the optical flow at given time steps. A limitation was found in the very value of the optical flow (threshold value), when exceeding this, the strategy leads to a hard touchdown or a crash (at near zero distance the speed is not close to zero). It was shown that the threshold value of the optical flow decreases with increasing time step in both formulas. However, calculating the distance using sine formula has a significantly lower threshold value of the optical flow than the calculation using the tangent formula. It was found that landing occurs faster if we use the sine formula at equal values of the optical flow. Nevertheless, the smooth landing ends at lower threshold values of the optical flow than using the tangent formula. As a result, using a larger value of the optical flow, a faster smooth landing can be achieved using the tangent formula.