Inspection of critical infrastructure with drones is experiencing an increasing uptake in the industry driven by a demand for reduced cost, time, and risk for inspectors. Early deployments of drone inspection services involve manual drone operations with a pilot and do not obtain the technological benefits concerning autonomy, coordination, and cooperation. In this paper, we study the design needed to handle the complexity of an Unmanned Aerial System (UAS) to support autonomous inspection of safety-critical infrastructure. We apply a constructive research approach to link innovation needs with concepts, designs, and validations that include simulation and demonstration of key design parts. Our design approach addresses the complexity of the UAS and provides a selection of technology components for drone and ground control hardware and software including algorithms for autonomous operation and interaction with cloud services. The paper presents a drone perception system with accelerated onboard computing, communication technologies of the UAS, as well as algorithms for swarm membership, formation flying, object detection, and fault detection with artificial intelligence. We find that the design of a cooperative drone swarm and its integration into a custom-built UAS for infrastructure inspection is highly feasible given the current state of the art in electronic components, software, and communication technology.