Answer 7—At a range of 10 m and a rotation rate of 60 radians per second, the beam is sweeping past at 600 m per second. If two sensors are square-on to the beacon with 10-cm spacing, the pulses from them will be 166.7 µs apart, for an angle measurement of 0.01 radians or 0.57°.

A measurement resolution of 0.1 µs would translate into a quantization noise level of one part in 1667, or 600 ppm. This would translate to an error in the range measurement on the order of 10 m × 600 ppm = 6 cm, or roughly the same order of magnitude as the physical size of the robot, which isn’t too bad.

Obviously, square-on is the best-case situation. Other orientations require the measurement of smaller angles at the same range, and the proportional error will be higher. But if the robot has three sensors configured in an equilateral triangle, the beacon never will be more than 30° from being square-on to one pair of them, so the overall error should remain manageable.

Contributor: David Tweed