Wide-Range Relative Velocity Sensor Using Laser Interferometry for Ultra-Precision Formation Flying

The realization of ultra-precision formation flying, which controls the relative positions of multiple satellites with micrometer accuracy, is anticipated to enable new scientific missions using inter-satellite laser interferometry, such as space-based gravitational wave telescopes. Achieving such precision requires transitioning from coarse relative position control using the Global Navigation Satellite System (GNSS), accurate to sub-centimeter levels, to ultra-precision control at the micrometer level. This necessitates the development of a satellite-to-satellite relative velocity sensor capable of wide-range measurements from sub-centimeters per second to micrometers per second. We have developed a novel method using the Doppler effect in an asymmetric Michelson interferometer to measure relative velocity between satellites. This method involves modulating the laser frequency to introduce an effective offset to the frequency of signal, enabling signed velocity measurements. In our research, we conducted tabletop experiments to validate the proposed method. The setup included a laser source, a delay line, and mirrors suspended on a stage and controlled by electromagnetic actuators to simulate the relative motion between satellites in a space mission. The results demonstrated that our approach could accurately measure velocities ranging from sub-centimeters per second to micrometers per second. We also compared offline and online analysis results of the output signal to investigate the accuracy and limitations of our method. Our research demonstrates that this method can measure satellite-to-satellite relative velocities from sub-millimeter levels to micrometer level, significantly advancing the feasibility of ultra-precision formation flying missions. Future work will involve on-orbit verification to confirm its effectiveness, with the expectation of practical applications in various scientific missions.