Monocular distance estimation with optical flow maneuvers and efference copies: a stability-based strategy

The visual cue of optical flow plays an important role in the navigation of flying insects, and is increasingly studied for use by small flying robots as well. A major problem is that successful optical flow control seems to require distance estimates, while optical flow is known to provide only the ratio of velocity to distance. In this article, a novel, stability-based strategy is proposed for monocular distance estimation, relying on optical flow maneuvers and knowledge of the control inputs (efference copies). It is shown analytically that given a fixed control gain, the stability of a constant divergence control loop only depends on the distance to the approached surface. At close distances, the control loop starts to exhibit self-induced oscillations. The robot can detect these oscillations and hence be aware of the distance to the surface. The proposed stability-based strategy for estimating distances has two main attractive characteristics. First, self-induced oscillations can be detected robustly by the robot and are hardly influenced by wind. Second, the distance can be estimated during a zero divergence maneuver, i.e., around hover. The stability-based strategy is implemented and tested both in simulation and on board a Parrot AR drone 2.0. It is shown that the strategy can be used to: (1) trigger a final approach response during a constant divergence landing with fixed gain, (2) estimate the distance in hover, and (3) estimate distances during an entire landing if the robot uses adaptive gain control to continuously stay on the 'edge of oscillation.'