Voronoi coverage control is a particular problem of importance in the area of multi-robot systems, which considers a network of multiple autonomous robots, tasked with optimally covering a large area. This is a common task for fleets of fixed-wing Unmanned Aerial Vehicles (UAVs), which are described in this work by a unicycle model with constant forward-speed constraints. We develop event-based control/communication algorithms to relax the resource requirements on wireless communication and control actuators, an important feature for battery-driven or otherwise energy-constrained systems. To overcome the drawback that the event-triggered algorithm requires continuous measurement of system states, we propose a self-triggered algorithm to estimate the next triggering time. Hardware experiments illustrate the theoretical results.