Koopman-based Learning and Control of Agile Robotic Systems

Citation

Folkestad, Carl A. A. (2022) Koopman-based Learning and Control of Agile Robotic Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2t6d-j206. https://resolver.caltech.edu/CaltechTHESIS:10122021-213903517

Abstract

Learning methods to enable high performance control systems have recently shown promising results in selected environments and applications. These advances promote the next generation of autonomous robots capable of significantly improving efficiency, cost, and safety in their respective domains. Importantly, these systems are safety-critical and operate in proximity to humans in diverse and uncertain environments. As a result, operational failures may cause significant material and societal losses. Additionally, robot learning and control are further complicated by requiring fast controller update rates and operational constraint satisfaction.

To address these challenges, this thesis presents multiple methods based on Koopman operator theory. The first approach develops algorithms to learn lifted-dimensional models of nonlinear systems and leverages the models in model predictive control (MPC) design. Koopman-based methods typically employ hand-crafted observable functions to "lift" the state variables to the higher dimensional space. For most systems, this leads to poor prediction performance and inefficient use of data and computational resources. Instead, I present methods that generate observable functions from data, both based on underlying theory and by incorporating the observable functions and model structure in a neural network model. This allows lower dimensional models, important for real-time control, and enables the nonlinearities of control-affine dynamics to be captured, crucial to describing many robotic systems. I use quadrotor drones to experimentally demonstrate that the learned models combined with MPC can achieve close to optimal behavior while respecting important operational constraints.

The last part of the thesis is concerned with endowing systems with an arbitrary nominal control policy with safety guarantees. Control barrier functions (CBFs) are a powerful tool to achieve this, yet they rely on the computation of control invariant sets, which is notoriously difficult. To avoid this, a backup strategy can be used to implicitly define a control invariant set. However, this requires forward integration of the system dynamics under a backup controller, which is prohibitively expensive for realistic systems. I present a method that replaces the expensive integration using learned Koopman operators of the closed-loop dynamics. As a result, the online computation time required to evaluate the controller is drastically reduced, enabling real-time use. I also derive an error bound on the unmodeled dynamics in order to robustify the CBF controller and demonstrate the method on multi-agent collision avoidance for wheeled robots and quadrotors.

Thesis Files