Quadrotor Trajectory Tracking with Learned Dynamics: Joint Koopman-based Learning of System Models and Function Dictionaries

TL;DR

This paper introduces a neural network-based approach that jointly learns a system model and function dictionary for quadrotor trajectory tracking, enabling robust control in ground-effect regimes where traditional models fail.

Contribution

The authors propose a novel joint learning method combining Koopman-based models and neural networks to improve quadrotor control in complex aerodynamic conditions.

Findings

Achieves trajectory tracking comparable to nominal models at medium altitude.

Successfully tracks trajectories in ground-effect regimes where nominal models fail.

Demonstrates real-time applicability of learned models for agile drone control.

Abstract

Nonlinear dynamical effects are crucial to the operation of many agile robotic systems. Koopman-based model learning methods can capture these nonlinear dynamical system effects in higher dimensional lifted bilinear models that are amenable to optimal control. However, standard methods that lift the system state using a fixed function dictionary before model learning result in high dimensional models that are intractable for real time control. This paper presents a novel method that jointly learns a function dictionary and lifted bilinear model purely from data by incorporating the Koopman model in a neural network architecture. Nonlinear MPC design utilizing the learned model can be performed readily. We experimentally realized this method on a multirotor drone for agile trajectory tracking at low altitudes where the aerodynamic ground effect influences the system's behavior. Experimental results demonstrate that the learning-based controller achieves similar performance as a nonlinear MPC based on a nominal dynamics model in medium altitude. However, our learning-based system can reliably track trajectories in near-ground flight regimes while the nominal controller crashes due to unmodeled dynamical effects that are captured by our method.