Safe and reliable autonomous inspection tasks using \ac{MAVs} in cluttered environments are challenging due uncertainties encountered during inspections. In general, algorithms consist of pre-planning paths and executing them. These precomputed inspection paths do not consider potential occlusion by obstacles. In turn, this could render the path infeasible and result in an incomplete inspection of the object to inspect. In order to solve this, a robust method is required, defined as the mitigation of viewing disturbances. This thesis presents an on-line inspection method for occluded environments with static obstacles. The proposed method splits an off-line computed global inspection path into segments and treats each segment as a separate inspection problem. By using an information-based cost function, an \ac{MPC} allows for robust on-line inspection of each of these segments by rejecting obstacle occlusion and collision, if necessary. Additionally, the cost function is designed to be submodular, a mathematical property describing diminishing returns and allowing greedy optimisation while obtaining performance guarantees. Properties of the method are demonstrated in two different environments: with and without obstacles. Due to many sigmoid functions within the cost function, it is a complex optimisation problem. For this reason, scalability is tested and measured in amount of triangles to determine feasible-sized inspection segments. It is shown that for $16$ triangles with one obstacle (both of arbitrary sizes), the calculation time for each \acs{MPC} iteration starts to exceed $15Hz$, becoming more unstable with each added triangle. This effect can be mitigated by discarding information cost of the intermediate cost function. Finally, it is shown that, where the global inspection path is partly occluded, the proposed method handles occlusion by obstacles during inspection at the cost of increased duration of the inspection, while maintaining quality of the solution. However, the predicted performance guarantee by submodularity does not always hold in practice. Future work can explore the integration of sensor measurements to the method or use learning-based approaches to reduce the required on-line computational resources.