This paper addresses the problem of collaborative formation control for multi-agent systems with limited resources. We consider a team of robots tasked with achieving a desired formation from an arbitrary initial configuration. To reduce unnecessary control updates and conserve resources, we propose a distributed event-triggered formation controller. Unlike the well-studied linear formation control strategies, the proposed controller is nonlinear and relies on inter-agent distance measurements. Control updates are triggered only when the measurement error exceeds a predefined threshold, ensuring system stability while minimizing actuation effort. We also employ a distributed control barrier function to guarantee inter-agent collision avoidance. The proposed controller is validated through extensive simulations and real-world experiments involving different formations, communication topologies, scalability tests, and variations in design parameters, while also being compared against periodic triggering strategies. Results demonstrate that the event-triggered approach significantly reduces control effort while preserving formation performance.