Cooperative control of multi-UAV systems has attracted substantial research attention due to its significance in various application sectors such as emergency response, search and rescue missions, and critical infrastructure inspection. This paper proposes a distributed control algorithm to generate collision-free trajectories that drive the multi-UAV system to completely inspect a set of 3D points on the surface of an object of interest. The objective of the UAVs is to cooperatively inspect the object of interest in the minimum amount of time. Extensive numerical simulations for a team of quadrotor UAVs inspecting a real 3D structure illustrate the validity and effectiveness of the proposed approach.