PD-Based and SINDy Nonlinear Dynamics Identification of UAVs for MPC Design

TL;DR

A fusion of data-driven approaches and theoretical modeling enhances the system's robustness and adaptability in real-world conditions, offering a detailed analysis of the UAV's dynamic behavior.

Abstract

This paper presents a comprehensive approach to nonlinear dynamics identification for UAVs using a combination of data-driven techniques and theoretical modeling. Two key methodologies are explored: Proportional-Derivative (PD) approximation and Sparse Identification of Nonlinear Dynamics (SINDy). The UAV dynamics are first modeled using the Euler-Lagrange formulation, providing a set of generalized coordinates. However, platform constraints limit the control inputs to attitude angles, and linear and angular velocities along the z-axis. To accommodate these limitations, thrust and torque inputs are approximated using a PD controller, serving as the foundation for nonlinear system identification. In parallel, SINDy, a data-driven method, is employed to derive a compact and interpretable model of the UAV dynamics from experimental data. Both identified models are then integrated into a Model Predictive Control (MPC) framework for accurate trajectory tracking, where model accuracy, informed by data-driven insights, plays a critical role in optimizing control performance. This fusion of data-driven approaches and theoretical modeling enhances the system's robustness and adaptability in real-world conditions, offering a detailed analysis of the UAV's dynamic behavior.

Figures (7)

• Figure 1: UAV reference frame DJI Matrice 100
• Figure 2: Comparison of the UAV's linear and angular positions with respect to the reference values.
• Figure 3: Comparison of the UAV's linear and angular velocities with respect to the reference values.
• Figure 4: System identification process for the UAV.
• Figure 5: Spatial behavior of the UAV under the PD-Euler Lagrange and SINDy models for three different reference trajectories: (a) Sinusoidal, (b) Circular, and (c) Spiral. The black dashed line represents the desired reference trajectory, while the blue and green lines correspond to the actual trajectories tracked.