Robust Station-keeping and High-Precision Attitude Control for a Spacecraft on Sun–Earth L1 Halo Orbit

Abstract

The halo orbits around the Sun-Earth L1 Lagrange point form an ideal location for deploying a solar observation spacecraft as they offer uninterrupted, long-duration visibility of the Sun. However, the complex orbital and attitude dynamics near the Sun-Earth L1 region pose distinct challenges for maintaining the spacecraft trajectory and achieving a precise Sun-pointing attitude. This thesis aims to address these challenges by focusing on the development of an advanced station-keeping guidance algorithm and constrained adaptive attitude control strategies.

An optimal station-keeping guidance strategy is proposed to regulate a spacecraft around a reference L1 quasi-halo orbit in the Sun-Earth elliptical restricted n-body problem. The inherent instability of the quasi-halo orbit, coupled with disturbance forces and navigational uncertainties, cause the spacecraft to rapidly deviate from the reference trajectory. The station-keeping problem is formulated as a finite-time, nonlinear optimal control problem, incorporating hard boundary constraints on the terminal state and accounting for switched spacecraft dynamics during the coasting and maneuver execution phases as path constraints. A computationally efficient algorithm based on prediction-correction philosophy, namely the Impulsive Model Predictive Static Programming (I-MPSP) technique, is used to solve the optimal control problem and obtain the station-keeping maneuvers. The algorithm is iterative and applied in a receding horizon fashion, where a set of guess maneuvers are updated using a simple closed-form equation until an output terminal constraint is satisfied. The technique involves the calculation of sensitivity matrices, which are efficiently computed due to their recursive nature. Extensive simulations demonstrate the superior station-keeping performance of I-MPSP based guidance compared to traditional strategies, resulting in a spacecraft trajectory that is tightly bound to the reference orbit over the entire mission duration.

In parallel, a Barrier Lyapunov Function (BLF) based model-following neuro-adaptive control design approach is also presented using the back-stepping philosophy to maintain the required Sun-pointing accuracy. In the presence of parametric uncertainties and unknown torques, the proposed method effectively learns the disturbances using a neural network based function approximation strategy and adapts the control action to achieve its objective of meeting the pointing accuracy requirements. Furthermore, the controller incorporates when to learn and when to switch-off by leveraging the principles of meta-cognitive learning. The adaptation process is activated only when necessary, as the controller continuously monitors the Sun-pointing errors to adjust the learning strategy. The efficacy of the proposed control law is demonstrated by carrying out extensive simulations and also by comparing it with a Quadratic Lyapunov Function (QLF) based unconstrained adaptive control law.

An adaptive attitude control law capable of enforcing time-varying attitude constraints is synthesized using a BLF based back-stepping philosophy to address the challenge posed by initial attitude errors lying outside the Sun-pointing constraint. A set of time-varying attitude constraints are formulated as a fixed-time prescribed performance function, enabling the apriori setting of the convergence time, transient and steady-state behaviour to meet the precision requirements for Sun-pointing. The design philosophy incorporates fault tolerance, allowing a single control law to handle both regular and faulty cases. Moreover, the controller guarantees constraint satisfaction in the presence of parametric uncertainties, unknown exogenous disturbances, time-varying inertia, actuator saturation and faults. The control constraints are handled by approximating actuator saturation using a smooth hyperbolic tangent function. The computational requirements are minimized during control synthesis by employing a norm based disturbance approximation strategy. The effectiveness of the control law is demonstrated via extensive simulations and by comparing it with a QLF based unconstrained adaptive control law.

Finally, a six degree-of-freedom simulation of the spacecraft with both guidance and control implementation in the Sun-Earth L1 quasi-halo orbit is carried out. The continuous rejection of the solar radiation pressure torque by the reaction wheels periodically causes the spin rates to increase beyond a maximum allowable threshold. A simple momentum desaturation law is formulated while stabilizing the spacecraft using a set of canted reaction control system thrusters. Given the on-off functionality of the thrusters, a linear programming based thruster allocation scheme is proposed to determine the optimal firing times. Additionally, the process of implementing the station-keeping maneuvers, including achieving the desired attitude and determining the execution time, is explained in detail. The ideas are demonstrated using numerical simulations.