Exact range and bearing control of many differential-drive robots with uniform control inputs

In this paper we investigate controlling many nonholonomic unicycles that each receive exactly the same inputs. The robots are almost homogeneous, but each robot has a unique parameter that scales its turning rate. Previous work showed that such a collection of robots can be approximately steered to arbitrary Cartesian positions, but not to arbitrary heading angles in a global reference frame. We extend this work by proving we can always steer such a collection of robots exactly to arbitrary range and bearing locations relative to targets in R² in a finite number of steps. We also provide existence proofs for controlling the final heading angles of many robots. This work addresses a fundamental challenge in micro-and nanorobotics with possible applications in targeted therapy, sensing, and actuation. Scale hardware experiments validate the control policy. All code is provided online.