Data-Driven Predictive Control of Nonholonomic Robots Based on a Bilinear Koopman Realization: Data Does Not Replace Geometry

TL;DR

This paper explores data-driven predictive control of nonholonomic robots using Koopman-based models, demonstrating high accuracy but emphasizing the importance of geometric understanding alongside data for effective control.

Contribution

It introduces a data-driven control pipeline for nonholonomic robots using EDMD models within Koopman theory, highlighting the necessity of geometric insights.

Findings

Data-driven models enable high-precision control in experiments.

Purely data-centric approaches may fail without geometric understanding.

Koopman models can incorporate actuator dynamics for improved control.

Abstract

Advances in machine learning and the growing trend towards effortless data generation in real-world systems has led to an increasing interest for data-inferred models and data-based control in robotics. It seems appealing to govern robots solely based on data, bypassing the traditional, more elaborate pipeline of system modeling through first-principles and subsequent controller design. One promising data-driven approach is the Extended Dynamic Mode Decomposition (EDMD) for control-affine systems, a system class which contains many vehicles and machines of immense practical importance including, e.g., typical wheeled mobile robots. EDMD can be highly data-efficient, computationally inexpensive, can deal with nonlinear dynamics as prevalent in robotics and mechanics, and has a sound theoretical foundation rooted in Koopman theory. On this background, this present paper examines how EDMD models can be integrated into predictive controllers for nonholonomic mobile robots. In addition to the conventional kinematic mobile robot, we also cover the complete data-driven control pipeline - from data acquisition to control design - when the robot is not treated in terms of first-order kinematics but in a second-order manner, allowing to account for actuator dynamics. Using only real-world measurement data, it is shown in both simulations and hardware experiments that the surrogate models enable high-precision predictive controllers in the studied cases. However, the findings raise significant concerns about purely data-centric approaches that overlook the underlying geometry of nonholonomic systems, showing that, for nonholonomic systems, some geometric insight seems necessary and cannot be easily compensated for with large amounts of data.