A High-Gain Observer Approach to Robust Trajectory Estimation and Tracking for a Multi-rotor UAV

TL;DR

This work adopts an extended high-gain observer (EHGO) estimation framework to estimate the unmeasured multi-rotor states, modeling errors, external disturbances, and the reference trajectory and designs a robust output feedback system for trajectory tracking that comprises a feedback linearizing controller and the EHGO.

Abstract

Using the context of trajectory estimation and tracking for multi-rotor unmanned aerial vehicles (UAVs), we explore the challenges in applying high-gain observers to highly dynamic systems. The multi-rotor will operate in the presence of external disturbances and modeling errors. At the same time, the reference trajectory is unknown and generated from a reference system with unknown or partially known dynamics. We assume the only measurements that are available are the position and orientation of the multi-rotor and the position of the reference system. We adopt an extended high-gain observer (EHGO) estimation framework to estimate the unmeasured multi-rotor states, modeling errors, external disturbances, and the reference trajectory. We design a robust output feedback controller for trajectory tracking that comprises a feedback linearizing controller and the EHGO. The proposed control method is rigorously analyzed to establish its stability properties. Finally, we illustrate our theoretical results through numerical simulation and experimental validation in which a multi-rotor tracks a moving ground vehicle with an unknown trajectory and dynamics and successfully lands on the vehicle while in motion.

Figures (9)

• Figure 1: Simulated rotational system response with and without actuator dynamics included in the EHGO. The disturbance estimate, $\hat{\sigma}_2$, when actuator dynamics are omitted oscillates between the saturation bounds (top), inducing oscillations in the tracking performance of $\phi_2$ (bottom). The disturbance estimate, $\hat{\sigma}_1$, and tracking, $\phi_1$, show excellent performance when actuator dynamics are included in the EHGO for this example.
• Figure 2: The trajectory of the multi-rotor UAV (dashed) and the trajectory of the ground vehicle (solid). The red points are the initial conditions and the green point signifies the occurrence of the landing.
• Figure 3: Estimation errors of both rotational disturbance and translational disturbance during the simulation.
• Figure 4: Experimental multi-rotor on ground vehicle landing platform.
• Figure 5: Experimental landing on moving ground vehicle.

Theorems & Definitions (13)

• Definition 1: Prime Canonical Form
• Remark 1
• Lemma 1: Restricting Domain of Operation
• proof
• Remark 2
• Theorem 1: Stability Under State Feedback
• proof
• Lemma 2: Stability of Actuator Dynamics
• proof
• Theorem 2: Convergence of EHGO Estimates