Effect of Quantization on Data-Driven Model Predictive Control of Quadcopters

The increasing reliance on autonomy in aerospace systems has created high demand for robust and computationally efficient control methods. Unmanned aerial vehicles (UAVs), such as drones, are among the most common autonomous systems due to their versatility and widespread applications. However, these drones can be heavily affected by the environmental conditions, e.g., wind gusts, which are difficult to model. Therefore, data-driven system identification and subsequent controller design have become increasingly important in UAV operation. Due to their limited onboard computation power and memory, small UAVs are not always able to perform the system identification onboard, and they need to communicate the acquired data to an edge server for system identification. This communication is done via a bandwidth limited wireless channel where the data needs to be quantized to make efficient use of the available bandwidth. Quantization, the process of discretizing continuous-valued data into a smaller subset of discrete values, addresses these constraints by reducing the bandwidth required to communicate the data and trading precision for efficiency. While theoretical studies have shown some degradation in system identification and control performance due to data quantization, its effects in experimental UAV settings remain minimally explored. This work investigates the effect of dither quantization on the Extended Dynamic Mode Decomposition (EDMD) method, a Koopman operator-based method for data-driven system identification and the subsequent Model Predictive Control (MPC) framework. The goal is to characterize and quantify the performance loss during experimental testing. The methodology of this research includes numerical simulations and future plans to incorporate software-in-the-loop (SITL) simulations in Gazebo. These testing phases aim to determine the effects of quantization on model accuracy, control fidelity, and real-world UAV flight performance. Results from numerical simulations indicate that higher levels of quantization degrade both system identification and subsequent MPC performance while defining a potentially beneficial trade-off word-length of 12 to 14 bits. By bridging the gap between theory and application, this research advances the understanding of how communication bandwidth affects resource limited data-driven MPC for multirotor UAVs. The findings contribute to the development of efficient, data-driven control strategies with broader implications in sensor fusion algorithms, real-time embedded systems, and wireless communications.