Date of Award


Document Type


Degree Name

Master of Science (MS)


Aerospace, Physics, and Space Sciences

First Advisor

Madhur Tiwari

Second Advisor

Xianqi Li

Third Advisor

Eric D. Swenson

Fourth Advisor

David Fleming


As interest in Moon exploration grows and efforts to establish an orbiting outpost intensify, accurate modeling of spacecraft dynamics in cis-lunar space is becoming increasingly important. Contrary to satellites in Low Earth Orbit (LEO) where it takes around 5 ms to communicate back and forth with a ground station, in the Moon’s orbit it can take up to 2.4 seconds to do so. This delay in communication can make the difference between a successful docking and a catastrophic collision for a remotely controlled satellite. Moreover, due to the unstable nature of trajectories in cis-lunar space, it is necessary to design spacecraft that can make the frequent and needed maneuvers to stay on track. The communication delay and unstable trajectories are exactly why autonomous navigation is critical for proximity operations and rendezvous and docking missions in cis-lunar space. In this paper, the relative equations of motion are derived, linearized, and a simulation is performed to compare state estimation results obtained from using the linearized dynamics equations of motion along with a Kalman filter and the nonlinear equations of motion along with an Unscented Kalman filter. After it was shown that the linearized model was sufficient for state estimation in the presence of noisy measurements, an LQR (Linear Quadratic Regulator) controller was added to optimally control a spacecraft and successfully dock with another. The contribution of this work is twofold: to compare the results obtained from the linearized model and the nonlinear model as well as to simulate an optimal docking maneuver in cis-lunar space using the linearized equations of motion in the presence of measurement noise.


Copyright held by author