Is it possible to dock CubeSats in Low Earth Orbit? Challenges are associated with the level of miniaturisation: the docking accuracy is driven by the docking mechanism dimensions. The achievable docking performance with the Guidance, Navigation and Control (GNC) subsystem is constrained by the use of small sensors and actuators. A docking mechanism prototype, tailored for CubeSats was designed, built and tested in the laboratory using a simple experimental setup. Results showed that a lateral precision of 1 cm and a relative angular alignment better than 2 degrees are required to guarantee successful docking. A filtered monocular camera on the chaser satellite and various arrays of light-emitting diodes on the target vehicle were selected for the metrology, due to their potential to achieve a high relative navigation accuracy and to ensure the observability of the system throughout the final approach trajectory. Both docking mechanism and metrology system are contained within 0.5U volume and can thus be used on a wide span of satellite types. The chaser and target have a complete 3-axis attitude pointing capability and are equipped with off-the-shelf CubeSats attitude sensors and actuators, including star trackers and reaction wheels. The chaser is further equipped with a six degrees of freedom low-thrust cold gas propulsion system. The navigation and control functions rely on a linearised coupled dynamic, which includes fuel sloshing effects, and describes the 6 degrees of freedom relative motion between the chaser and target docking ports. Using this dynamic, LQR, LQI, H-Infinity and Mu-Synthesis controllers were investigated and their stability and performance assessed by mean of Mu-Analysis. A comprehensive simulation framework was developed to evaluate the performances of the navigation and control functions and the impact of actuator and sensor errors on the overall docking performance. The environmental and internal perturbations, such as atmospheric drag and fuel sloshing were taken into account. All sensors and actuators required for the docking were modelled, including realistic errors and noise characteristics. Different docking scenarios were investigated based on the different behaviour of the coupled dynamics. Worst-case scenarios such as the loss of sensor signals prior to docking are also tackled. The robustness of the proposed control schemes was assessed by the use of structured singular values. Complementary non-linear Monte-Carlo simulations were also performed to determine the complete GNC performances as well as fuel consumption. Results show that the proposed GNC is robust to the modelled sensor and actuator noises, fuel sloshing, dynamics uncertainties and that a lateral position accuracy better than 5 mm can always be obtained at docking. Furthermore, docking is not affected by the loss of star tracker signals nor by harsh illumination conditions, and can thus take place on a variety of orbits.