Koopman NMPC: Koopman-based Learning and Nonlinear Model Predictive Control of Control-affine Systems
This work addresses a specific bottleneck in robotic control for researchers, presenting an incremental improvement over existing Koopman-based methods.
The paper tackled the limitation of Koopman-based methods in capturing nonlinear actuation effects in robotic systems by proposing a learning and control methodology that uses the Koopman canonical transform to express control-affine dynamics as a lifted bilinear model for nonlinear model predictive control (NMPC). The result showed greatly reduced prediction error and achieved closed-loop performance similar to NMPC with full model knowledge in a simulated planar quadrotor example.
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.