Answer 8—Yes, of course. In three dimensions, the full locus of points defined by the beacon and two sensors is a toriodal shape with the center hole closed off. The minor radius is greater than the major radius. The axis of this shape is the baseline joining the two sensors. Three or more sensors define multiple shapes whose intersections narrow down the beacon location to a small number of possible points. These points can be disambiguated a number of ways like using sensors that can see only a portion of the space around them (a hemisphere or less).

The missing item in the preceding discussion is the fact that the geometry of the system is invariant with respect to rotation around the beacon. In other words, the robot can tell where the beacon is relative to its own orientation, but it doesn’t learn anything about its own absolute position or orientation in space.

The robot needs another source of information. This could be in the form of a second beacon (with a different rotation rate so that the robot can tell them apart) or some sort of timing reference pulse that allows the robot to determine its absolute direction from the beacon’s idea of north. This is analogous to how aircraft VOR systems work.

Contributor: David Tweed