Feedback control of many differential-drive robots with uniform control inputs

In this paper, we derive a globally asymptotically stabilizing feedback control policy for a collection of differential-drive robots under the constraint that every robot receives exactly the same control inputs. We begin by assuming that each robot has a slightly different wheel size, which scales its forward speed and turning rate by a constant that can be found by offline or online calibration. The resulting feedback policy is easy to implement, is robust to standard models of noise, and scales to an arbitrary number (even a continuous ensemble) of robots. We validate this policy with hardware experiments, which additionally reveal that our feedback policy still works when the wheel sizes are unknown and even when the wheel sizes are all approximately identical. These results have possible future application to control of micro- and nano-scale robotic systems, which are often subject to similar constraints.