Enhancement for Robustness of Koopman Operator-based Data-driven Mobile Robotic Systems

Abstract

Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. There is a growing interest in research to derive robustness (and/or safety) guarantees for systems the dynamics of which are extracted via the Koopman operator. In this paper, we propose a way to quantify the prediction error because of noisy measurements when the Koopman operator is approximated via Extended Dynamic Mode Decomposition. We further develop an enhanced robot control strategy to endow robustness to a class of data-driven (robotic) systems that rely on Koopman operator theory, and we show how part of the strategy can happen offline in an effort to make our algorithm capable of real-time implementation. We perform a parametric study to evaluate the (theoretical) performance of the algorithm using a Van der Pol oscillator, and conduct a series of simulated experiments in Gazebo using a non-holonomic wheeled robot.