We consider a swarm-intelligent inspection system concerned with the inspection of blades in a jet turbine. The system is based on a swarm of autonomous, miniature robots, using only on-board, local sensors. We capture the dynamics of the system at a higher abstraction level using non-spatial, probabilistic, discrete-time macroscopic models, which we use in an optimal control framework to find an optimal collaboration policy minimizing time to completion and overall energy consumption of the swarm. We consider time-invariant and time-variant decision variables for various stage constraints (energy consumption), and find optimal profiles using an extremum-seeking control scheme. In particular, we show that using a communication-based policy exclusively towards the end of the inspection progress decreases time to task completion, but only if there are at least as many robots as blades.