Koopman Operator Based Time-Delay Embeddings and State History Augmented LQR for Periodic Hybrid Systems: Bouncing Pendulum and Bipedal Walking

Fuente: arXiv
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Main Authors: Yang, Chun-Ming, Bhounsule, Pranav A.
Format: Preprint
Published: 2025
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author Yang, Chun-Ming
Bhounsule, Pranav A.
author_facet Yang, Chun-Ming
Bhounsule, Pranav A.
contents Time-delay embedding is a technique that uses snapshots of state history over time to build a linear state space model of a nonlinear smooth system. We demonstrate that periodic non-smooth or hybrid system can also be modeled as a linear state space system using this approach as long as its behavior is consistent in modes and timings. We extend time-delay embeddings to generate a linear model of two periodic hybrid systems: the bouncing pendulum and the simplest walker with control inputs. This leads to a state history augmented linear quadratic regulator (LQR) which uses current and past state history for feedback control. Example code can be found at https://github.com/Chun-MingYang/koopman-timeDelay-lqr.git
format Preprint
id arxiv_https___arxiv_org_abs_2507_14455
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Koopman Operator Based Time-Delay Embeddings and State History Augmented LQR for Periodic Hybrid Systems: Bouncing Pendulum and Bipedal Walking
Yang, Chun-Ming
Bhounsule, Pranav A.
Robotics
Time-delay embedding is a technique that uses snapshots of state history over time to build a linear state space model of a nonlinear smooth system. We demonstrate that periodic non-smooth or hybrid system can also be modeled as a linear state space system using this approach as long as its behavior is consistent in modes and timings. We extend time-delay embeddings to generate a linear model of two periodic hybrid systems: the bouncing pendulum and the simplest walker with control inputs. This leads to a state history augmented linear quadratic regulator (LQR) which uses current and past state history for feedback control. Example code can be found at https://github.com/Chun-MingYang/koopman-timeDelay-lqr.git
title Koopman Operator Based Time-Delay Embeddings and State History Augmented LQR for Periodic Hybrid Systems: Bouncing Pendulum and Bipedal Walking
topic Robotics
url https://arxiv.org/abs/2507.14455