Date of Award


Document Type

Thesis - Open Access

Degree Name

Master of Science in Aerospace Engineering


Aerospace Engineering

Committee Chair

Dr. Morad Nazari

First Committee Member

Dr. Troy Henderson

Second Committee Member

Dr. Richard Prazenica

Third Committee Member

Dr. William MacKunis


This thesis studies the constrained motion for a spacecraft hovering over an asteroid, where the Udwadia-Kalaba (UK) formulation is applied for nominal control, and an adaptive controller is developed to account for unknowns in the dynamics. Then, the formulation is extended in the geometric mechanics framework to account for rigid body spacecraft asteroid hovering. Constraints are developed and applied for fully constrained and under-constrained asteroid hovering. The fully constrained solutions provided by the UK fundamental equation are compared to an optimal linear quadratic regulator. An adaptive controller is designed using the UK fundamental equation as a basis in the form of a model reference adaptive controller. The controller is proven to have asymptotic tracking of the reference system designed by the desired constraints on the spacecraft. The convergence of the tracking error dynamics is studied using the Lyapunov’s direct method. It is shown that the controller, with accurate estimation of the unknown parameters, results in the minimum required control response due to its basis on the UK equation. The parameters are successfully estimated using a finite-time estimation method.

Furthermore, the extension of the UK formulation into the geometric mechanics framework is developed to account for rigid-body spacecraft, where the formulation also allows orientation constraints to be applied on the spacecraft. Constraints with a basis on the Lie algebra of special Euclidean group SE(3) are developed to fully constrain a spacecraft’s position and orientation for hovering over an asteroid. The geometric mechanics UK formulation successfully gives the required angular and translational accelerations to maintain the desired configuration (pose) of the rigid-body spacecraft. The developments above are discussed for a spacecraft hovering over the asteroid Bennu and the closed-loop response of the system, control inputs, and control efforts are provided and discussed.