Laser communications has been highlighted in space applications because of its great potential compared to radio-frequency [1], [2], [3]. This advantage mainly stems from the beamwidth of the lasers, but the extremely narrow beamwidth presents a significant challenge for communication technology to guarantee the stable transmission to the receiver [4]. For example, the National Aeronautics and Space Administration (NASA) conducted a lunar-laser communication demonstration (LLCD) mission, which demonstrated that the laser channel between the Earth and Lunar orbits has a pointing accuracy estimated to be 2.5 μrad (0.5 arcsec) [5]. The NFIRE satellite, developed in the U.S., successfully established a laser communication link with the German SAR satellite, TerraSAR-X, resulting in the pointing accuracy of 141 μrad (29 arcsec) [6].

Recently, the nano-satellite form factor, which is known as CubeSat standard, has led to a new industry of space development to develop small and low-cost satellites [7]. CubeSat projects can support stand-alone missions, often involving substantial quantities of data. Laser communication systems have a great capability to transmit a large amount of data at much higher data rates than conventional RF systems, while working within much smaller mass and power that are suitable for CubeSat systems [8]. For CubeSat applications, the laser communication system should be supported by the satellite attitude control system. For example, NASA’s CubeSat AC7-B&C for the laser downlink experiment in the OCSD mission implemented a body pointing approach not to use heavy gimbal structures. For body pointing, sun, Earth-nadir, Earth-horizon sensors, and star trackers are developed for the attitude control system, with an expected pointing error of approximately 417 μrad (86 arcsec) [9].

Researchers who are developing laser communication systems have to pay attention to meet strict requirements for pointing accuracy. There have been several researches to analyze pointing performance of laser communication. Arnon et al. Barry et al. Yang et al. and Rui analyzed the probability density functions of vibrations that can influence communication stability [10], [11], [12], [13]. Toyoshima et al. tested the fine-pointing system in the experimental satellite ETS-VI from Japan and calculated the frequency component of the pointing error [14]. Algrain attempted to use sensor fusion to reject both low and high frequency pointing jitter [15]. Though these methodologies have been helpful in achieving required pointing in practice, the previous researches provided little insight into the fundamentals of pointing control systems. Antonello et al. analyzed the control system of LaserCube, a laser communication terminal, and proposed a theoretical analysis of the pointing error of the laser beam stabilization device [16]. The study effectively analyzed the system, and experiments have proven the validity of their analysis and development approaches. However, they treated the satellite attitude as an independent external jitter source. For nano-satellites equipped with a laser communication terminal, the attitude control system should also contribute to laser pointing control. Neglecting spacecraft dynamics hinders achieving reproducibility and obtaining valuable insights in developing laser communication systems.

This work analytically analyzes the laser pointing control systems for nano-satellites, which has two kinds of sensor/actuator systems designed to control the satellite attitude and the laser beam. The noises from sensors are considered to be the main error sources. Two systems are described in this paper: the body pointing stage and the fine pointing stage, each operating with different sampling frequencies. Their 3-dimensional motions are approximated as one-dimensional motion under proper assumptions to clarify the error transfer function. The final goal, the laser pointing error, is derived as a combined analysis of two stages, which include proportional and derivative (PD) controls with Kalman filter estimator in the body pointing stage and integral (I) controls with sensor/actuator models in the fine pointing stage. The transfer functions are converted into power spectral density (PSD) of the pointing errors, obtaining the root-mean-square error (RMSE) of the pointing. In the combining process, the PSD of the body pointing stage is upsampled to synchronize with the higher sampling frequency of the fine pointing stage. Since the linear interpolation can be achieved through a convolution manner, the PSD in the frequency domain can be properly upsampled. We compared the analyzed pointing error PSD with Monte-Carlo simulations and experiment to verify the validity of the proposed approach.

The remainder of this work is organized as follows: In Section 2, the body pointing stage is described and analyzed in detail. Section 3 introduces the structure of the fine pointing stage and analyzes the control system connected with disturbance. Next, we present the comparison between the simulations results and our analysis in Section 4. The experiment for practical validation is presented in Section 5. The RMSE prediction and the relationship with controller gain is presented in Section 6. Finally, Section 7 concludes our work.