Having gained recent popularity with the successful missions of the robotic Mission Extension Vehicle and the Crew Dragon flights to the ISS, autonomous rendezvous and docking systems are one of the principal enabling technologies for the continued commercialization and exploration of space. As in other fields of spaceflight, the push for the reduction of system cost is driving designers of space debris removal systems, on-orbit servicing robots, and in-space assembly systems towards the use of smaller platforms and cheaper off-the-shelf components. With off-the-shelf thrusters and sensor systems being less well-characterized than traditional space hardware, and with lower cost requirements also putting pressure on extensive verification and validation test campaigns, this approach introduces system uncertainties. Uncertainties in navigation solution and knowledge of thruster performance and characteristics can lead to problems when feedback control laws such as Proportional-Integral-Derivative (PID) or Linear Quadratic Regulator (LQR) controllers are used. An alternative is to use simple, bang-bang limit-cycle controllers to maintain relative positioning within operational bounds, and to follow trajectories. Limit-cycle controllers are robust against uncertainties in system modeling and component characterization. They present a simple, effective and robust minimum control capability, even in mission-critical proximity maneuvering. The paper presents the results of a study evaluating a limit-cycle controller for formation flight and capture maneuvers using air bearing vehicles in the Florida Tech ORION hardware-in-the-loop testbed. The experiments were conducted with two air-bearing vehicles performing formation flight maneuvers at ranges between 3 m and 0.1 m, controlled by sets of on/off cold-gas thrusters. The paper discusses challenges with the characterization of thruster performance, presents details on the implementation of the limit-cycle controller, describes the design of the experiments in the testbed environment, and discusses the results of the experiments.