This paper presents a novel, sparse sensing motion planning algorithm for autonomous mobile robots in resource limited coverage problems. Optimizing usage of limited resources while effectively exploring an area is vital in scenarios where sensing is expensive, has adverse effects, or is exhaustive. We approach this problem using ergodic search techniques, which optimize how long a robot spends in a region based on the likelihood of obtaining informative measurements which guarantee coverage of a space. We recast the ergodic search problem to take into account when to take sensing measurements. This amounts to a mixed-integer program that optimizes when and where a sensor measurement should be taken while optimizing the agent’s paths for coverage. Using a continuous relaxation, we show that our formulation performs comparably to dense sampling methods, collecting information-rich measurements while adhering to limited sensing measurements. Multi-agent examples demonstrate the capability of our approach to automatically distribute sensor resources across the team. Further comparisons show comparable performance with the continuous relaxation of the mixed integer program while reducing computational resources.