Koopman Operators in Robot Learning

Koopman operator theory offers a rigorous treatment of dynamics and has been emerging as a powerful modeling and learning-based control method enabling significant advancements across various domains of robotics. Due to its ability to represent nonlinear dynamics as a linear operator, Koopman theory offers a fresh lens through which to understand and tackle the modeling and control of complex robotic systems. Moreover, it enables incremental updates and is computationally inexpensive making it particularly appealing for real-time applications and online active learning. This review comprehensively presents recent research results on advancing Koopman operator theory across diverse domains of robotics, encompassing aerial, legged, wheeled, underwater, soft, and manipulator robotics. Furthermore, it offers practical tutorials to help new users get started as well as a treatise of more advanced topics leading to an outlook on future directions and open research questions. Taken together, these provide insights into the potential evolution of Koopman theory as applied to the field of robotics.