A light curve is a plot of brightness versus time of an object. Light curves are dependent on orbit, attitude, surface area, size, and shape of the observed object. Using light curve data, several analysis methods have been developed to derive these parameters. These parameters can be used for tracking orbital debris, monitoring satellite health, and determining the mission of an unknown spacecraft. This paper discusses the development, verification, and utilization of a tool that simulates light curve data. This tool models ground-based observations, space-based observations, self-shadowing geometry, tumbling debris, and controlled spacecraft. The main output from the tool is the pass prediction plot and the light curve plot. The author intends to publish the tool and supporting documents for future researchers to utilize. This will save researchers time developing their own models and the tool can act as a baseline for comparisons between analysis methods. For clarity, this paper does not develop nor implement a light curve analysis method, but rather creates a tool to simulate light curve observations and data. Each section of the tool was verified independently to ensure that the simulated light curves were correct. The tool was verified with STK, matlab, and simulink. It predicts the start and end times of passes, eclipses, and ground-site night cycles within 1% of the total event duration, when compared to STK. The attitude propagator predicts the attitude of the target with offsets less than 0.06 degrees on average and a maximum offset less than 0.6 degrees when compared to provided attitude code.

Attitude determination and estimation algorithms are developed and implemented in simulation for the Exocube satellite currently under development by PolySat at Cal Poly. A mission requirement of ±5˚ of attitude knowledge has been flowed down from the NASA Goddard developed payload, and this requirement is to be met with a basic sensor suite and the appropriate algorithms. The algorithms selected in this work are TRIAD and an Extended Kalman Filter, both of which are placed in a simulation structure along with models for orbit propagation, spacecraft kinematics and dynamics, and sensor and reference vector models. Errors inherent from sensors, orbit position knowledge, and reference vector generation are modeled as well. Simulations are then run for anticipated dynamic states of Exocube while varying parameters for the spacecraft, attitude algorithms, and level of error. The nominal case shows steady state convergence to within 1˚ of attitude knowledge, with sensor errors set to 3.5˚ and reference vector errors set to 2˚. The algorithms employed have their functionality confirmed with the use of STK, and the simulations have been structured to be used as tools to help evaluate attitude knowledge capabilities for the Exocube mission and future PolySat missions.

This graduate project compares legacy simplified general perturbation model (SGP4) code developed by NASA Johnson Space Center, Orbital Debris Program Office, to a recent public release of SGP4 code by David Vallado. The legacy code is a subroutine in a larger program named PREDICT, which is used to predict the location of orbital debris in GEO. Direct comparison of the codes showed that the new code yields better results for GEO objects, which are more accurate by orders of magnitude (error in meters rather than kilometers). The public release of SGP4 also provides effective results for LEO and MEO objects on a short time scale. The public release code was debugged and modified to provide instant functionality to the Orbital Debris Program Office. Code is provided in an appendix to this paper along with an accompanying CD. A User’s Guide is presented in Chapter 7.

The low size and budget of typical nanosatellite missions limit the available sensors for attitude estimation. Relatively high noise MEMS gyroscopes often must be employed when accurate knowledge of the spacecraft’s angular velocity is necessary for attitude determination and control. This thesis derived and tested in simulation the “Virtual Gyroscope” algorithm, which replaced a standard gyroscope with an array of spatially distributed accelerometers for a 1U CubeSat mission. A MEMS accelerometer model was developed and validated using Root Allan Variance, and the Virtual Gyroscope was tested both in the open loop configuration and as a replacement for a gyroscope in a Multiplicative Extended Kalman Filter. It was found that the quality of the Virtual Gyroscope’s rate measurement improved with a larger and higher quality array, but the error in the estimate was very large. The low signal-to-noise ratio and the unknown bias in the accelerometers caused the angular velocity estimate from the accelerometer array to be too poor for use in the propagation step of the Kalman filter. The Kalman filter performed better with attitude measurements alone than with the Virtual Gyroscope, even when the attitude were delivered at a low rate with added noise. Overall, the current Virtual Gyroscope algorithm that is presented in this thesis is not suitable to replace a MEMS gyroscope in a nanosatellite mission, although there is room for future improvements using bias prediction for the individual accelerometers in the array.

Legged robots have the potential to be a valuable technology that provides agile and adaptive locomotion over complex terrain. To realize legged locomotion's full abilities a control design must consider the nonlinear piecewise dynamics of the systems. This paper aims to develop a controller for the planar bounding of a quadrupedal robot. The bounding of the quadruped robot is characterized by a simplified hybrid model that consists of two subsystems for stance and flight phases and the switching laws between the two states. An additional model, the Multibody model, with fewer simplifications, is used concurrently to best approximate real-world behavior. The bounding gait (periodic orbit) of the robot is predicted by an optimization method based on the numerical integration of the differential equations of subsystems. To stabilize the gait, a switching controller is applied which can be split into two separate phases: stance-phase and swing-phase control. The stance phase implements reaction force control utilizing a body state feedback controller and a gait stabilizer, while the swing phase deploys position control in conjunction with a trajectory planning algorithm to ensure proper footfall. Numerical simulations are carried out for the system with/without control. The control strategy is further validated by simulations of the Simscape multibody model. The overall simulated controller results are promising and demonstrate stable bounding for four system cycles.

This thesis proposes a set of methods for the purpose of improving the calibration of three-axis magnetometers. Specifically, these methods aim to improve the accuracy of the bias estimation methods currently in use. The first proposed method utilizes a constrained optimization problem based on norm preserving. The second proposed method finds the same bias estimate as the first method, but in a computationally more efficient manner. The last proposed method tackles the case where the value of the local geomagnetic field is only imprecisely known. Computer simulations demonstrate the viability of the proposed methods.

In the upcoming decade, the proliferation of high-LEO constellations is expected to exceed 20,000 objects, yet comprehensive Post Mission Disposal (PMD) strategies for these constellations are currently lacking. With the inherent challenges of efficiently deorbiting satellites from High-LEO orbits, there arises an urgent need to explore innovative approaches. Building upon insights garnered from the ReDSHIFT project and anticipating the proliferation of high-LEO constellations such as OneWeb, TeleSat, and GuoWang, this thesis delves into the potential viability of the Resonance Corridor Method for PMD. The investigation encompasses key metrics, including deorbit timelines and $\Delta v$ requirements to meet regulatory standards or recommendations, with comparisons drawn against alternative methods like Perigee Decrease and Graveyard Orbit solutions. Through this analysis, scenarios emerge where the Resonance Corridor method demonstrates advantages, offering feasible delta-v values while ensuring compliance with regulatory standards and recommendations. The findings yield categorizations of high-LEO constellation shells into specific disposal feasibility groups, thereby providing valuable insights into how space sustainability practices can be added into spacecraft design to align with evolving space debris mitigation standards. Additionally, certain altitude-inclination combinations are found to naturally align with the resonance corridor method, while others necessitate minor architectural adjustments to optimize effectiveness.

As the use of small satellites for advanced space missions continues to grow, the importance of low mass and cost three-axis attitude stabilization systems increases as well, with these systems requiring high accuracy attitude knowledge. Star trackers provide the most accurate attitude knowledge of any type of attitude sensor, but the high cost, size, and weight of commercial star trackers can be prohibitive to small satellite missions. Many simple star trackers have been developed using commercial off-the-shelf camera sensors and processing hardware, but the challenge remains in testing and characterizing these devices. A common solution is night sky tests, in which the star tracker is held up to the night sky to image the star field and perform attitude determination. Commercial star trackers, on the other hand, are regularly tested with manufacturer provided star field images that attach directly to the sensor. These methods, however, severely limit the sky conditions that can be used in testing. Night sky tests depend on weather and can only image regions of the sky the user has access to, while lab-based testing uses the few provided still images. This thesis presents a hardware-in-the-loop star tracker test bed developed for comprehensive ground-based testing of both in-house and commercial star trackers. The system consists of a small screen to display a star field, a simple in-house camera star tracker, and a microprocessor. This test bed allows any star field image to be simulated. The system is set up for use on a stationary tabletop, but its small size lends itself for use with a spacecraft dynamics platform, which can facilitate testing of control algorithms using real star tracker output.

The goal of this thesis is to use the Cal Poly Spacecraft Attitude Dynamics Simulator to provide proof of concept of two adaptive control theories developed by former Cal Poly students: Nonlinear Direct Model Reference Adaptive Control and Adaptive Output Feedback Control. The Spacecraft Attitude Dynamics Simulator is a student-built air bearing spacecraft simulator controlled by four reaction wheels in a pyramidal arrangement. Tests were performed to determine the effectiveness of the two adaptive control theories under nominal operating conditions, a “plug-and-play” spacecraft scenario, and under simulated actuator damage. Proof of concept of the adaptive control theories applied to attitude control of a spacecraft is provided. The adaptive control theories are shown to attain similar or improved performance over a Full State Feedback controller. However, the measurement capabilities of the simulator need to be improved before strong comparisons between the adaptive controllers and Full State Feedback can be achieved.

Fixed-wing unmanned aerial vehicles (UAVs) with the ability to hover combine the speed and endurance of traditional fixed-wing fight with the stable hovering and vertical takeoff and landing (VTOL) capabilities of helicopters and quadrotors. This combination of abilities can provide strategic advantages for UAV operators, especially when operating in urban environments where the airspace may be crowded with obstacles. Traditionally, fixed-wing UAVs with hovering capabilities had to be custom designed for specific payloads and missions, often requiring custom autopilots and unconventional airframe configurations. With recent government spending cuts, UAV operators like the military and law enforcement agencies have been urging UAV developers to make their aircraft cheaper, more versatile, and easier to repair. This thesis discusses the use of the commercially available ArduPilot open source autopilot, to autonomously transition a fixed-wing UAV to and from hover flight. Software modifications were made to the ArduPilot firmware to add hover flight modes using both Proportional, Integral, Derivative (PID) Control and Model Reference Adaptive Control (MRAC) with the goal of making the controllers robust enough so that anyone in the ArduPilot community could use their own ArduPilot board and their own fixed-wing airframe (as long as it has enough power to maintain stable hover) to achieve autonomous hover after some simple gain tuning. Three new hover flight modes were developed and tested first in simulation and then in flight using an E-Flight Carbon Z Yak 54 RC aircraft model, which was equipped with an ArduPilot 2.5 autopilot board. Results from both the simulations and flight test experiments where the airplane transitions both to and from autonomous hover flight are presented.