Koopman-Based Control System for Quadrotors in Noisy Environments

Abstract

It is well known that identification of the complete system dynamics is challenging, especially in noisy environments. The Koopman operator theory provides a linear representation of a nonlinear system using only the input/output data acquired from the system, which does not need the exact model dynamics. Since the data is collected from the real-world, noise is inherent in that collected data. Therefore, the identified model with the Koopman operator can consider noise appeared in the real-world. In this paper, we propose the Koopman-based control system for quadrotors with the environment selector under varying noisy environments. We consider varying noisy environments of the quadrotor changing from nominal to windy, and construct two different quadrotor dynamics depending on the environment by using the Koopman operator theory. Then the proposed environment selector identifies whether the current environment is nominal or windy, by which an appropriate quadrotor dynamics obtained by the Koopman operator is determined. The selected Koopman dynamics is used in the Model Predictive Control (MPC) to obtain the optimal control input for the quadrotor. Note that by the proposed environment selector and the MPC-based control input, the quadrotor is able to follow the optimal reference trajectory generated by the Soft Actor-Critic (SAC) algorithm even in suddenly varying noisy environments. To verify the effectiveness of the proposed control system, we provide the simulation and experiment results of the quadrotor under various environment situations. In particular, we verify that by the proposed method, the quadrotor is able to follow the optimal reference trajectory even under varying noisy environments.

Keywords

• Koopman operator theory
• data-driven control
• linear control system application
• soft actor-critic (SAC)
• quadrotor