Related papers: Nonlinear System Identification of Soft Robot Dyna…
In this paper, we propose a Koopman operator based approach to describe the nonlinear dynamics of a quadrotor on SE(3) in terms of an infinite-dimensional linear system which evolves in the space of observable functions (lifted space) and…
We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their…
A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincar\'e's geometric picture that focuses on "dynamics of states". While this picture has fueled our field for a century, it has shown…
Offline reinforcement learning leverages large datasets to train policies without interactions with the environment. The learned policies may then be deployed in real-world settings where interactions are costly or dangerous. Current…
Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. The Koopman operator has…
Effective rehabilitation methods are essential for the recovery of lower limb dysfunction caused by stroke. Nowadays, robotic exoskeletons have shown great potentials in rehabilitation. Nevertheless, traditional rigid exoskeletons are…
This paper addresses the problem of nonlinear state estimation for dynamical systems whose governing equations are approximated through Koopman operator liftings. While Koopman-based predictors have demonstrated broad approximation…
Soft robots offer unmatched adaptability and safety in unstructured environments, yet their compliant, high-dimensional, and nonlinear dynamics make modeling for control notoriously difficult. Existing data-driven approaches often fail to…
The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions.…
With the advancement of sensing and communication in power networks, high-frequency real-time data from a power network can be used as a resource to develop better monitoring capabilities. In this work, a systematic approach based on…
We present a theory of causality in dynamical systems using Koopman operators. Our theory is grounded on a rigorous definition of causal mechanism in dynamical systems given in terms of flow maps. In the Koopman framework, we prove that…
Collaborative robots (cobots) are machines designed to work safely alongside people in human-centric environments. Providing cobots with the ability to quickly infer the inertial parameters of manipulated objects will improve their…
Formation control of multi-agent systems has been a prominent research topic, spanning both theoretical and practical domains over the past two decades. Our study delves into the leader-follower framework, addressing two critical,…
The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…
In Koopman operator theory, a finite-dimensional nonlinear system is transformed into an infinite but linear system using a set of observable functions. However, manually selecting observable functions that span the invariant subspace of…
To avoid complex constraints of the traditional nonlinear method for tethered space robot (TSR) deployment, this paper proposes a data-driven optimal control framework with an improved deep learning based Koopman operator that could be…
Quadrotor systems are common and beneficial for many fields, but their intricate behavior often makes it challenging to design effective and optimal control strategies. Some traditional approaches to nonlinear control often rely on local…
Soft robotic manipulators provide numerous advantages over conventional rigid manipulators in fragile environments such as the marine environment. However, developing analytic inverse models necessary for shape, motion, and force control of…
Koopman spectral analysis has attracted attention for understanding nonlinear dynamical systems by which we can analyze nonlinear dynamics with a linear regime by lifting observations using a nonlinear function. For analysis, we need to…
The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function space is closed under…