相关论文: Curve-Induced Dynamical Systems on Riemannian Mani…
The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…
Recent advances in Dense Simultaneous Localization and Mapping (SLAM) have demonstrated remarkable performance in static environments. However, dense SLAM in dynamic environments remains challenging. Most methods directly remove dynamic…
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…
We analyze convergence of gradient-descent methods on Riemannian manifolds. In particular, we study randomization of Riemannian gradient algorithms for minimizing smooth cost functions (of Morse-Bott type). We prove that randomized gradient…
Performing acrobatic maneuvers like dynamic jumping in bipedal robots presents significant challenges in terms of actuation, motion planning, and control. Traditional approaches to these tasks often simplify dynamics to enhance…
It is well-known that the class of piecewise smooth curves together with a smooth Riemannian metric induces a metric space structure on a manifold. However, little is known about the minimal regularity needed to analyze curves and…
Modeling 4D scenes requires capturing both spatial structure and temporal motion, which is challenging due to the need for physically consistent representations of complex rigid and non-rigid motions. Existing approaches mainly rely on…
Recent advances in mobile robotic platforms like quadruped robots and drones have spurred a demand for deploying visuomotor policies in increasingly dynamic environments. However, the collection of high-quality training data, the impact of…
Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…
Delineation of anatomical structures is often the first step of many medical image analysis workflows. While convolutional neural networks achieve high performance, these do not incorporate anatomical shape information. We introduce a novel…
We present a data-driven framework for learning dynamical systems on compact Riemannian manifolds based on the spectral exterior calculus (SEC). This approach represents vector fields as linear combinations of frame elements constructed…
Safe autonomous navigation in unknown environments is an important problem for mobile robots. This paper proposes techniques to learn the dynamics model of a mobile robot from trajectory data and synthesize a tracking controller with safety…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
Dynamical models estimate and predict the temporal evolution of physical systems. State Space Models (SSMs) in particular represent the system dynamics with many desirable properties, such as being able to model uncertainty in both the…
Matrix Lie groups are an important class of manifolds commonly used in control and robotics, and optimizing control policies on these manifolds is a fundamental problem. In this work, we propose a novel computationally efficient approach…
This paper introduces the Cable Robot Simulation and Control (CaRoSaC) Framework, which integrates a simulation environment with a model-free reinforcement learning control methodology for suspended Cable-Driven Parallel Robots (CDPRs),…
We present 3DScenePrompt, a framework that generates the next video chunk from arbitrary-length input while enabling precise camera control and preserving scene consistency. Unlike methods conditioned on a single image or a short clip, we…
Diffusion policies generate robot motions by learning to denoise action-space trajectories conditioned on observations. These observations are commonly streams of RGB images, whose high dimensionality includes substantial task-irrelevant…
Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…
Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.