Adaptive state-space model approximation for quadcopter using Fast Orthogonal Search

This paper presents a novel application of Fast Orthogonal Search (FOS) to select the basis and coefficients for a linear, state-space model representing the dynamics of a quadcopter. This is developed in the context of Model Predictive Control (MPC) by evaluating the performance of the approximate model over finite prediction horizons in different flight regimes. A time-varying model is implemented using sliding window (SW-FOS) and recursive (R-FOS) techniques. FOS was selected because it provides a numerically efficient technique for selecting which basis terms are important in the model while simultaneously solving for their coefficients. Based on experimental data from an actual quadcopter, SW-FOS provided mean squared error performance similar to Least Squares (LS) while requiring on average 5 fewer states in the state-space model. R-FOS produced more accurate results with significantly reduced computation times. Both SW-FOS and R-FOS provided linear, time-varying models that adapted to various flight regimes.