Simulations of LQR Control on Linear Spacecraft Dynamics about Asteroid Equilibrium Points

Future exploratory missions to asteroids may require a spacecraft to perform attitude and position change maneuvers within small perturbations of the equilibrium point to conduct measurements and make observations based on mission requirements. The non-linear dynamics of the spacecraft can be approximated to be linear given that the system operates about an equilibrium point and the signals are small. Based on this, the linearized system is equivalent to the non-linear system within a limited operating range. This project follows this precedent and applies a closed loop LQR controller to perturbations of 1%, 2% and 5% from asteroid 101955 Bennu’s equilibrium points. The LQR controller methodology requires that weighting matrices Q and R which penalize the states and the controls respectively to be iterated for – depending on the application requirements. The iteration procedure is the primary objective of this project and is conducted for six different spacecraft orientations about eight different equilibrium points. The procedure examines the settling times and response plots to critique the performance of the controller. This paper presents the underlying control theory, the modelling scenario, the simulation procedure, results and some patterns discovered in the results. This project was conducted in conjunction with [3] and presents the results of simulations based on linearized spacecraft dynamics. The results of the non-linear spacecraft dynamics simulations can be found in [3].

Simulations of LQR Control on Linear Spacecraft Dynamics about Asteroid Equilibrium Points

Future exploratory missions to asteroids may require a spacecraft to perform attitude and position change maneuvers within small perturbations of the equilibrium point to conduct measurements and make observations based on mission requirements. The non-linear dynamics of the spacecraft can be approximated to be linear given that the system operates about an equilibrium point and the signals are small. Based on this, the linearized system is equivalent to the non-linear system within a limited operating range. This project follows this precedent and applies a closed loop LQR controller to perturbations of 1%, 2% and 5% from asteroid 101955 Bennu’s equilibrium points. The LQR controller methodology requires that weighting matrices Q and R which penalize the states and the controls respectively to be iterated for – depending on the application requirements. The iteration procedure is the primary objective of this project and is conducted for six different spacecraft orientations about eight different equilibrium points. The procedure examines the settling times and response plots to critique the performance of the controller. This paper presents the underlying control theory, the modelling scenario, the simulation procedure, results and some patterns discovered in the results. This project was conducted in conjunction with [3] and presents the results of simulations based on linearized spacecraft dynamics. The results of the non-linear spacecraft dynamics simulations can be found in [3].

Unscented Kalman Filter and Control in TSE(3) with Applications to Spacecraft Dynamics

This paper presents a novel rigid-body spacecraft navigation and control architecture within the framework of special Euclidean group SE(3) and its tangent bundle TSE(3) while considering stochastic processes in the system. The proposed framework combines the orbit-attitude motions of the spacecraft into a single, compact set. The stochastic state filter is designed based on the unscented Kalman filter which uses a special retraction function to encode the sigma points onto the manifold. The navigation system is then integrated to an almost globally asymptotically stabilizing Morse-Lyapunov-based control system with backstepping. Numerical simulations are conducted to demonstrate the effectiveness of the proposed navigation filter for the full state estimation. In addition, the navigation and control system is tested in the nonlinear gravity field of a small celestial body with an irregular shape. In particular, the performance of the closed-loop system is studied in a tracking problem of spacecraft motion near the asteroid Bennu based on the OSIRIS-REx's mission data.

High spectral resolution multi-tone Spacecraft Doppler tracking software: Algorithms and implementations

We present a software package for single-dish data processing of spacecraft signals observed with VLBI-equipped radio telescopes. The Spacecraft Doppler tracking (SDtracker) software allows one to obtain topocentric frequency detections with a sub-Hz precision and reconstructed and residual phases of the carrier signal of any spacecraft or landing vehicle at any location in the Solar System. These data products are estimated using the ground-based telescope’s highly stable oscillator as a reference, without requiring an a priori model of the spacecraft dynamics nor the downlink transmission carrier frequency. The software has been extensively validated in multiple observing campaigns of various deep space missions and is compatible with the raw sample data acquired by any standard VLBI radio telescope worldwide. In this paper, we report the numerical methodology of SDtracker, the technical operations for deployment and usage, and a summary of use cases and scientific results produced since its initial release.