Coordination with the leader in a robotic team without active communication

We propose a coordination algorithm for robotic multi-agent systems with leader-follower structures so that when a leader moves with a constant velocity, its followers can compute the leader's velocity after measuring their distances to the leader for a finite number of times. One feature of the proposed algorithm is that no active communication is needed, and as a result, the algorithm becomes advantageous in the application of robotic sensor networks where energy efficient algorithms are highly desirable to maximize network lifespan. The algorithm makes use of the Cayley-Menger determinant which is a powerful tool from distance geometry. It is shown that the proposed algorithm has the potential to be applied to robotic swarms in a challenging scenario where each robot is installed with only range sensors and cannot measure the position of a target directly.