Koopman NMPC: Koopman-based Learning and Nonlinear Model Predictive Control of Control-affine Systems

TL;DR

This paper introduces a Koopman-based learning and control approach that models control-affine systems as bilinear models, enabling efficient nonlinear model predictive control with improved accuracy, demonstrated on a simulated quadrotor.

Contribution

It presents a novel Koopman canonical transform that captures control-affine dynamics as bilinear models for enhanced control and computational efficiency.

Findings

Prediction error significantly reduced.

Closed-loop performance comparable to full model NMPC.

Effective on simulated planar quadrotor.

Abstract

Koopman-based learning methods can potentially be practical and powerful tools for dynamical robotic systems. However, common methods to construct Koopman representations seek to learn lifted linear models that cannot capture nonlinear actuation effects inherent in many robotic systems. This paper presents a learning and control methodology that is a first step towards overcoming this limitation. Using the Koopman canonical transform, control-affine dynamics can be expressed by a lifted bilinear model. The learned model is used for nonlinear model predictive control (NMPC) design where the bilinear structure can be exploited to improve computational efficiency. The benefits for control-affine dynamics compared to existing Koopman-based methods are highlighted through an example of a simulated planar quadrotor. Prediction error is greatly reduced and closed loop performance similar to NMPC with full model knowledge is achieved.