Abstract-This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the use of the Koopman operator towards augmenting modelbased control. Specifically, we illustrate how the operator can be used to obtain a linearizable data-driven model for an unknown dynamical process that is useful for model-based control synthesis. Simulated results show that with increasing complexity in the choice of the basis functions, a closed-loop controller is able to invert and stabilize a cart-and VTOL-pendulum systems. Furthermore, the specification of the basis function are shown to be of importance when generating a Koopman operator for specific robotic systems. Experimental results with the Sphero SPRK robot explore the utility of the Koopman operator in a reduced state representation setting where increased complexity in the basis function improve open-and closed-loop controller performance in various terrains, including sand. Modeling for complex dynamical systems has typically been the first step when designing, control, planning, or stateestimation algorithms. System design and specifications have been dependent on the use of high-fidelity models. However, any derivation of a dynamical model from first principles is typically a demanding task when the complexity of state interactions is high. Moreover, analytical models do not capture external disturbances. As a result, derived models, for use in model-based control settings, often have limited use or poor prediction over longer time spans. Nevertheless, a representation of the behavior of a dynamical system is central to most model-based engineering and scientific application. Within the field of systems and control theory, model uncertainty has typically been mitigated with the use of robust and adaptive control architectures. Typically, adaptive controllers are self tuning and reactive to incoming state information while robust controllers are designed to be invariant to model uncertainty [1]-[4]. Motion planning for uncertain dynamical systems have also been extensively investigated. Generally, in this approach, uncertainty is explicitly modeled and incorporated into the decision making process [5]- [7] . However, like robust and adaptive control approaches, the need for an explicit uncertainty model often limits its utility in general settings. Machine learning, offers a much more general approach [8]- [10] . In particular, recent advances have utilized large sets
In particular, recent work from the authors implemented a controller using a Koopman operator representation of a robotic system in an experimental setting of a robot in sand REF .
Model-Based Control Using Koopman Operators
Robotics: Science and Systems Proceedings, 2017
Computer Science Mathematics