Constrained Quaternion Attitude Control of Satellites via \\Semi‑Definite Programming

Abstract

Spacecraft attitude control is critical for mission success in communication, navigation, and payload safety, requiring maneuvers that respect complex geometric and hardware constraints. Classical quaternion-based PD/PID controllers provide robust unconstrained attitude regulation but lack systematic enforcement of constraints such as sun-avoidance zones and actuator saturation limits. This thesis presents a hybrid control framework that leverages semi-definite programming (SDP) to generate constraint-compliant, globally optimal attitude trajectories offline, integrating keep-in/out cones and actuator bounds via linear matrix inequalities (LMIs). A quaternion-feedback PD regulator then robustly tracks these trajectories in real time, enabling efficient onboard implementation. MATLAB and Simulink simulations demonstrate that the proposed SDP-guided control outperforms classical PD/PID methods by rigorously respecting all constraints and improving maneuver safety and accuracy. The results suggest strong potential for future small-satellite missions requiring high-performance constrained attitude control.