Ambiguity Remediation in Launch Vehicles and Morse-Lyapunov-Based Control with Parameter Uncertainties

Conventional methods for launch vehicle estimation and control are performed primarily using quaternions, which outperform minimal attitude parameterization sets since quaternions have no singularities. Yet quaternions exhibit the disadvantage of non-uniqueness, leaving room for improvement. Launch vehicle attitude dynamics are known to be especially noisy, while position and velocity measurements are usually known with a high degree of precision. In this work, a launch problem is simulated using the dynamic formulation on the special Euclidean group (SE(3)) considering varying mass properties. State and parameter estimates are filtered on SE(3) using an unscented Kalman filter (UKF). A state-and-parameter-estimation-error-based Morse-Lyapunov tracking law controller with backstepping is introduced and demonstrated. Finally, the ability of the UKF on SE(3) to overcome ambiguity in attitude and attitude rate estimates is demonstrated in a simulated launch to low Earth orbit, where precise position and velocity estimates are obtained using the coupled formulation.