  Decentralized heading control is crucial for robotic network operations such
as surveillance, exploration, and cooperative construction. However, few
results consider decentralized heading control when the speed of heading
adjustment is restricted. In this paper, we propose a simple hybrid-dynamical
model based on pulse-coupled oscillators for decentralized heading control in
mobile robots while accounting for the constraint on the rate of heading
change. The pulse-coupled oscillator model is effective in coordinating the
phase of oscillator networks and hence is promising for robotic heading
coordination given that both phase and heading evolve on the same
one-dimensional torus. However, existing pulse-coupled oscillator results
require the phase adjustment to be instantaneous, which cannot hold for robot
heading adjustment due to physical limitations. We propose a generalization to
the standard pulse-coupled oscillator model to allow for the phase to adjust at
a finite rate, yet still have the oscillator network converge to the desired
state, making our approach applicable to robotic heading coordination under
rate constraints. We provide rigorous mathematical proof for the achievement of
both synchronized and desynchronized heading relationships, and experimentally
verify the results using extensive tests on a multi-robot platform.
