相关论文: Curve-Induced Dynamical Systems on Riemannian Mani…

Symmetric positive definite (SPD) matrix has been demonstrated to be an effective feature descriptor in many scientific areas, as it can encode spatiotemporal statistics of the data adequately on a curved Riemannian manifold, i.e., SPD…

Human motion generation is often learned in Euclidean spaces, although valid motions follow structured non-Euclidean geometry. We present Riemannian Motion Generation (RMG), a unified framework that represents motion on a product manifold…

We present Stochastic Dynamic Mode Decomposition (SDMD), a novel data-driven framework for approximating the Koopman semigroup in stochastic dynamical systems. Unlike existing methods, SDMD explicitly incorporates sampling time into its…

Estimating accurate camera poses, 3D scene geometry, and object motion from in-the-wild videos is a long-standing challenge for classical structure from motion pipelines due to the presence of dynamic objects. Recent learning-based methods…

We derive low-dimensional, data-driven models for transitions among exact coherent states (ECSs) in one of the most studied canonical shear flows, the plane Couette flow. These one- or two-dimensional nonlinear models represent the…

Video-based human pose transfer is a video-to-video generation task that animates a plain source human image based on a series of target human poses. Considering the difficulties in transferring highly structural patterns on the garments…

In this work, we address the design of tracking controllers that drive a mechanical system's state asymptotically towards a reference trajectory. Motivated by aerospace and robotics applications, we consider fully-actuated systems evolving…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

Developing mathematical models of dynamic systems is central to many disciplines of engineering and science. Models facilitate simulations, analysis of the system's behavior, decision making and design of automatic control algorithms. Even…

Strictly enforcing orthonormality constraints on parameter matrices has been shown advantageous in deep learning. This amounts to Riemannian optimization on the Stiefel manifold, which, however, is computationally expensive. To address this…

Determining the reachable set for a given nonlinear system is critically important for autonomous trajectory planning for reach-avoid applications and safety critical scenarios. Providing the reachable set is generally impossible when the…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

Human motion synthesis is an important task in computer graphics and computer vision. While focusing on various conditioning signals such as text, action class, or audio to guide the generation process, most existing methods utilize…

Learning from Demonstration (LfD) has shown to provide robots with fundamental motion skills for a variety of domains. Various branches of LfD research (e.g., learned dynamical systems and movement primitives) can generally be classified…

Visual SLAM algorithms achieve significant improvements through the exploration of 3D Gaussian Splatting (3DGS) representations, particularly in generating high-fidelity dense maps. However, they depend on a static environment assumption…

Traditional Visual Simultaneous Localization and Mapping (vSLAM) systems focus solely on static scene structures, overlooking dynamic elements in the environment. Although effective for accurate visual odometry in complex scenarios, these…

Learning robot motions from demonstration requires models able to specify vector fields for the full robot pose when the task is defined in operational space. Recent advances in reactive motion generation have shown that learning adaptive,…

Safe operation of systems such as robots requires them to plan and execute trajectories subject to safety constraints. When those systems are subject to uncertainties in their dynamics, it is challenging to ensure that the constraints are…

Data-Driven Computational Mechanics is a novel computing paradigm that enables the transition from standard data-starved approaches to modern data-rich approaches. At this early stage of development, one can distinguish two mainstream…

Dynamic movement primitives are widely used for learning skills which can be demonstrated to a robot by a skilled human or controller. While their generalization capabilities and simple formulation make them very appealing to use, they…