Data-driven Feedback Control of Lattice Structures with Localized Actuation and Sensing

TL;DR

This work addresses feedback control of digital lattice structures built from modular cuboctahedron voxels using a data-driven modeling approach. It employs Extended Dynamic Mode Decomposition to learn a linear predictor in lifted coordinates via Koopman theory, yielding a model of the form $z_{k+1}=Az_k+Bu_k$, $\,\hat{y}_k=Cz_k$ suitable for linear control. Two regulators, discrete-time LQR and Koopman Model Predictive Control (KMPC), are then used to achieve stabilization, disturbance rejection, and reference tracking, validated on a physically implemented Voxel Tower. The results demonstrate that high-performance control of complex, nonlinear lattice dynamics is achievable without prior analytic models, enabling robust, reconfigurable digital metamaterials in practical applications.

Abstract

Assembling lattices from discrete building blocks enables the composition of large, heterogeneous, and easily reconfigurable objects with desirable mass-to-stiffness ratios. This type of building system may also be referred to as a digital material, as it is constituted from discrete, error-correcting components. Researchers have demonstrated various active structures and even robotic systems that take advantage of the reconfigurable, mass-efficient properties of discrete lattice structures. However, the existing literature has predominantly used open-loop control strategies, limiting the performance of the presented systems. In this paper, we present a novel approach to feedback control of digital lattice structures, leveraging real-time measurements of the system dynamics. We introduce an actuated voxel which constitutes a novel means for actuation of lattice structures. Our control method is based on the Extended Dynamical Mode Decomposition algorithm in conjunction with the Linear Quadratic Regulator and the Koopman Model Predictive Control. The key advantage of our approach lies in its purely data-driven nature, without the need for any prior knowledge of a system's structure. We illustrate the developed method via real experiments with custom-built flexible lattice beam, showing its ability to accomplish various tasks even with minimal sensing and actuation resources. In particular, we address two problems: stabilization together with disturbance attenuation, and reference tracking.

Figures (9)

• Figure 1: (\ref{['fig::rig_face']}) The rigid face, (\ref{['fig::cmp_face']}) the compliant face, an assembled voxel (\ref{['fig::rig_voxel']}), and larger structure (\ref{['fig::rig_struct']})
• Figure 2: Render of the actuated voxel: (\ref{['fig::act_vox']}) assembled; (\ref{['fig::act_vox_disas']}) individual parts
• Figure 3: Demonstration of the real actuated voxel (\ref{['fig::AV_untilted']}) at rest; (\ref{['fig::AV_left']}) tilted to the left; (\ref{['fig::AV_right']}) tilted to the right
• Figure 4: Comparison of actuator types
• Figure 5: Sensing Voxel

Theorems & Definitions (2)

• Remark 1
• Remark 2