SE(3) Koopman-MPC: Data-driven Learning and Control of Quadrotor UAVs

TL;DR

This paper uses rotation matrices to directly represent the orientation dynamics and obtain a lifted linear representation of the nonlinear quadrotor dynamics in the SE(3) manifold and designs a linear model predictive controller (MPC) based on the proposed EDMD model to track agile reference trajectories.

Abstract

In this paper, we propose a novel data-driven approach for learning and control of quadrotor UAVs based on the Koopman operator and extended dynamic mode decomposition (EDMD). Building observables for EDMD based on conventional methods like Euler angles (to represent orientation) is known to involve singularities. To address this issue, we employ a set of physics-informed observables based on the underlying topology of the nonlinear system. We use rotation matrices to directly represent the orientation dynamics and obtain a lifted linear representation of the nonlinear quadrotor dynamics in the SE(3) manifold. This EDMD model leads to accurate prediction and can be generalized to several validation sets. Further, we design a linear model predictive controller (MPC) based on the proposed EDMD model to track agile reference trajectories. Simulation results show that the proposed MPC controller can run as fast as 100 Hz and is able to track arbitrary reference trajectories with good accuracy. Implementation details can be found in \url{https://github.com/sriram-2502/KoopmanMPC_Quadrotor}.

Figures (5)

• Figure 1: Quadrotor system.
• Figure 2: (a) Random trajectories, which represent the training dataset for EDMD, (b) Predicted trajectories using the learned linear Koopman predictors over 100 timesteps on the validation set.
• Figure 3: Trajectories obtained using SE(3) Koopman MPC can accurately track the reference trajectory.
• Figure 4: The state trajectories obtained from the MPC can accurately track the reference.
• Figure 5: The corresponding control inputs obtained from the MPC stay within the control limits.