Real-Time Surrogate for Quadcopter Attitude Control: A Least-Squares Quadratic Imitation Learning Approach

Imitation Learning (IL) has shown considerable promise in enabling automated systems to replicate expert behavior with reduced computational overhead. However, many IL techniques often suffer from limited interpretability, generalization, and the need for vast quantities of high-quality expert data. This paper presents Least-Squares based Quadratic Imitation Learning (LS-QIL), a simple yet powerful IL framework designed to overcome these limitations through a transparent and analytically tractable policy structure. LS-QIL learns a quadratic control policy using linear least-squares optimization, resulting in a closed-form mapping between system states and control actions that enables efficient and reliable deployment in real-time environments. Leveraging high-performance Nonlinear Model Predictive Control (NMPC) as the expert, LS-QIL captures complex, optimal behavior while significantly reducing online computational demands. The framework is applied to quaternion-based quadrotor attitude control, leveraging its compact and singularity-free representation to ensure robustness and stability. Through extensive simulation and analysis, the imitation learning-based framework demonstrates strong performance, adaptability, and practical feasibility, making it a promising surrogate for real-time control tasks. This research strengthens the foundations of imitation learning by bridging the gap between model-based control and learning-based methods. It offers a stable, scalable, and interpretable solution for real-time applications, highlighting a path toward scalable autonomy in aerial robotics and beyond.