Small Satellite Attitude Determination and Control

This overall objective of this research was to design and validate high-precision pointing and attitude estimation and control algorithms for spacecraft under severe hardware constraints. This was done by using ExoplanetSat, a 3U CubeSat designed to detect exoplanets around bright stars via the transit method, as a case study. This report summarizes the main contributions of this research and is organized in terms of the operational modes of the spacecraft: detumbling, Sun acquisition, slewing, and precision pointing. The first set of algorithms was developed to support detumbling the spacecraft after initial deployment using a magnetometer and magnetorquers. Without gyros or coarse Sun sensors with full-sky coverage, this mode becomes complicated since it cannot directly measure or calculate the angular rate of the spacecraft. A literature review was performed, which showed that while it is possible to estimate angular rate from magnetometer measurements alone, there are observability singularities associated with this estimation scheme. However, no method of avoiding these observability singularities was found in the literature. A set of control laws were then developed, which are able to simultaneously detumble the spacecraft while exciting nutation. By exciting nutation in the spacecraft, the conditions for losing observability are avoided. Simulations were then used to show that a standard b-dot control algorithm actually tends to drive the system to these observability singularities, which can cause a premature transition to the next mode. However, with the nutation excitation, these observability singularities are avoided, the angular rate is properly estimated, and the spacecraft transitions to the next mode at the appropriate time. See Chapter 3 of the thesis for further details. After the spacecraft has detumbled, the Sun must now be acquired within the field of view (FOV) of a Sun sensor. Without full-sky coverage of the Sun sensors, the spacecraft must navigate with a magnetometer alone. A literature review showed that many simple algorithms exist for searching for the Sun, but mostly rely on knowledge of the angular rate of the spacecraft. While the previously developed angular rate estimator can be used, the observability singularities must still be avoided. A novel guidance and control law is developed to slew the boresight of the Sun sensor around to search for the Sun, which does not require full three-axis attitude knowledge, rather just a single vector measurement. This guidance and control law is demonstrated to be useful for many general pointing, tracking, and searching tasks. It is then applied to the Sun acquisition problem where it is shown how the search space can be reduced to a circle of a sphere (versus the entire 4π-steradian sky) using knowledge of time and position of the spacecraft. Simulations show that this algorithm can properly search for the Sun, while some tweaks to the guidance law are necessary to ensure that observability singularities, while rare, are avoided. Further details can be found in Chapter 4 of the thesis. The spacecraft can now transition to operating with its main payload—a star camera. A complete software architecture for initializing a star camera and operating it in a windowed mode is outlined. This operation of the star camera greatly reduces the processing time and allows it to be used during slews. The literature review revealed many algorithms to support attitude determination from a star camera that have been developed and refined to decrease processing time. In addition, with the transition to CMOS detectors, it became possible to output small windows around each star, further decreasing image processing time. However, there are no existing algorithms for efficiently generating new windows to ensure that enough stars are tracked as the spacecraft slews and stars fall out of the FOV. A star neighbor table is generated to fill this purpose. Robustness of this approach requires careful construction of this star neighbor catalog, including steps to merge and prune stars as well as force neighbors to be distributed. Monte Carlo simulations show that this algorithm can efficiently find new stars to track for 20,000 random slews with a 100% success rate using a star neighbor catalog with five or more neighbors (and on rare occasion, using neighbors of neighbors). An air bearing testbed was used to demonstrate, in hardware, the entire star camera software architecture, including initialization, transitioning to a windowed mode, performing a slew, and acquiring the target star. The details of these algorithms and this testing can be found in Chapter 5. Finally, algorithms to perform high-precision pointing during science observations of the target star were developed. To achieve this high-precision pointing, the spacecraft employs a staged control approach where reaction wheels, desaturated, by magnetorquers, provide coarse attitude control and a piezo stage provides fine pointing control. A literature review revealed that pointing precision is normally obtained from hardware performance and a careful accounting of the various error sources. On ExoplanetSat and many other missions, higher precision pointing results in better science measurements. Due to the stringent constraints on the spacecraft, better hardware cannot be used to improve pointing. This research explored the possibility of improving the pointing precision with software improvements alone. A linear model of the system is developed to determine the contributions of various noise sources to the overall pointing error. Stochastic linearization techniques were employed to linearize the torque quantization of the reaction wheel since the relatively large torque bit compared to the inertia of the spacecraft significantly effects the pointing at the arcsecond level. This linear model is used to determine that both attitude noise and external torque disturbances contribute the most to pointing error. Based on this, software improvements were developed to further improve the pointing of the system, which is predicted to be 4.6 arcsec (3σ) by the nonlinear simulation. These improvements include feeding back the quantized torque values into the estimator, augmenting the estimator to estimate disturbance torques, and using a model of the dynamics to propagate the state forward in time to mitigate the effects of time delay in the system. The linear analysis was used to provide a classical, frequency domain interpretation of how these software changes are able to improve the pointing. With these changes, the nonlinear simulation predicts a pointing of 2.3 arcsec (3σ), a 50% improvement over the baseline. Finally, the air bearing testbed was used to demonstrate 12 arcsec (3σ) pointing with flight-equivalent hardware. This falls within 10% of the pointing predicted by the nonlinear simulation, with parameters changed to match the testbed environment. This validates the nonlinear simulation and increases the pointing technology readiness level to 6. Further details of this analysis and testing can be found in Chapter 6 of the thesis.