Related papers: KoopMotion: Learning Almost Divergence Free Koopma…
Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this work, we attempt to provide a consistent framework through Koopman theory and its related…
This paper presents a unified and scalable framework for predictive and safe autonomous navigation in dynamic transportation environments by integrating model predictive control (MPC) with distributed Koopman operator learning.…
Manipulation has long been a challenging task for robots, while humans can effortlessly perform complex interactions with objects, such as hanging a cup on the mug rack. A key reason is the lack of a large and uniform dataset for teaching…
An outstanding challenge in nonlinear systems theory is identification or learning of a given nonlinear system's Koopman operator directly from data or models. Advances in extended dynamic mode decomposition approaches and machine learning…
A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in…
We present a low-rank Koopman operator formulation for accelerating deformable subspace simulation. Using a Dynamic Mode Decomposition (DMD) parameterization of the Koopman operator, our method learns the temporal evolution of deformable…
For dynamical systems involving decision making, the success of the system greatly depends on its ability to make good decisions with incomplete and uncertain information. By leveraging the Koopman operator and its adjoint property, we…
Humanoid robots could benefit from using their upper bodies for support contacts, enhancing their workspace, stability, and ability to perform contact-rich and pushing tasks. In this paper, we propose a unified approach that combines an…
This paper investigates the generalisability of Koopman-based representations for chaotic dynamical systems, focusing on their transferability across prediction and control tasks. Using the Lorenz system as a testbed, we propose a…
A new approach to data-driven discovery of Koopman eigenfunctions without a pre-defined set of basis functions is proposed. The approach is based on a reference trajectory, for which the Koopman mode amplitudes are first identified, and the…
Soft robots are challenging to model due in large part to the nonlinear properties of soft materials. Fortunately, this softness makes it possible to safely observe their behavior under random control inputs, making them amenable to…
We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. Each epoch is an application of the map induced by the optimization algorithm and the loss function. Using this induced…
The accurate simulation of complex dynamics in fluid flows demands a substantial number of degrees of freedom, i.e. a high-dimensional state space. Nevertheless, the swift attenuation of small-scale perturbations due to viscous diffusion…
In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation…
Planning whole-body motions while taking into account the terrain conditions is a challenging problem for legged robots since the terrain model might produce many local minima. Our coupled planning method uses stochastic and…
Controlling nonlinear dynamical systems remains a central challenge in a wide range of applications, particularly when accurate first-principle models are unavailable. Data-driven approaches offer a promising alternative by designing…
The Bellman equation and its continuous form, the Hamilton-Jacobi-Bellman equation, are ubiquitous in reinforcement learning and control theory. However, these equations become intractable for high-dimensional or nonlinear systems. This…
In data-driven modelling of complex dynamic processes, it is often desirable to combine different classes of models to enhance performance. Examples include coupled models of different fidelities, or hybrid models based on physical…
In this paper, we describe an approach to achieve dynamic legged locomotion on physical robots which combines existing methods for control with reinforcement learning. Specifically, our goal is a control hierarchy in which highest-level…
This paper presents a novel feedback method on the motion planning for unicycle robots in environments with static obstacles, along with an extension to the distributed planning and coordination in multi-robot systems. The method employs a…