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This paper describes a vision-based relative navigation and control strategy for inspecting an unknown, noncooperative, and possibly spinning object in space using a visual-inertial system that is designed to minimize the computational requirements while maintaining a safe relative distance. The proposed spacecraft inspection system relies solely on a calibrated stereo camera and a three-axis gyroscope to maintain a safe inspection distance while following a circular trajectory around the object. The navigation system is based on image processing algorithms, which extract the relative position and velocity between the inspector and the object, and a simple control approach is used to ensure that the desired range and bearing are maintained throughout the inspection maneuver. The hardware implementation details of the system are provided. Computer simulation results and experiments conducted aboard the International Space Station during Expedition 34 are reported to demonstrate the performance and applicability of the proposed hardware, and related navigation and control systems to inspect an unknown spacecraft.