相关论文: Geometry-aware Dynamic Movement Primitives

We present a modular framework for solving a motion planning problem among a group of robots. The proposed framework utilizes a finite set of low level motion primitives to generate motions in a gridded workspace. The constraints on…

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…

Statistical inference for spatial processes from partially realized or scattered data has seen voluminous developments in diverse areas ranging from environmental sciences to business and economics. Inference on the associated rates of…

Riemannian geometry is a mathematical field which has been the cornerstone of revolutionary scientific discoveries such as the theory of general relativity. Despite early uses in robot design and recent applications for exploiting data with…

A Riemannian stochastic representation of model uncertainties in molecular dynamics is proposed. The approach relies on a reduced-order model, the projection basis of which is randomized on a subset of the Stiefel manifold characterized by…

Metric learning has been shown to be highly effective to improve the performance of nearest neighbor classification. In this paper, we address the problem of metric learning for Symmetric Positive Definite (SPD) matrices such as covariance…

We show that on the manifold of fixed-rank and symmetric positive semi-definite matrices, the Riemannian gradient descent algorithm almost surely escapes some spurious critical points on the boundary of the manifold. Our result is the first…

Many practically relevant robot grasping problems feature a target object for which all grasps are occluded, e.g., by the environment. Single-shot grasp planning invariably fails in such scenarios. Instead, it is necessary to first…

We present a novel framework for motion planning in dynamic environments that accounts for the predicted trajectories of moving objects in the scene. We explore the use of composite signed-distance fields in motion planning and detail how…

This paper proposes a vision-based framework for a 7-degree-of-freedom robotic manipulator, with the primary objective of facilitating its capacity to acquire information from human hand demonstrations for the execution of dexterous…

This paper presents a novel Representation-Free Model Predictive Control (RF-MPC) framework for controlling various dynamic motions of a quadrupedal robot in three dimensional (3D) space. Our formulation directly represents the rotational…

We construct an abstract framework in which the dynamic programming principle (DPP) can be readily proven. It encompasses a broad range of common stochastic control problems in the weak formulation, and deals with problems in the…

An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The…

Human-robot collaboration is on the rise. Robots need to increasingly improve the efficiency and smoothness with which they assist humans by properly anticipating a human's intention. To do so, prediction models need to increase their…

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The…

The realization of motion description is a challenging work for fixed-wing Unmanned Aerial Vehicle (UAV) acrobatic flight, due to the inherent coupling problem in ranslational-rotational motion. This paper aims to develop a novel maneuver…

Rectified Flow (RF) models achieve state-of-the-art generation quality, yet controlling them for precise tasks -- such as semantic editing or blind image recovery -- remains a challenge. Current approaches bifurcate into inversion-based…

Symmetric determinantal point processes (DPP's) are a class of probabilistic models that encode the random selection of items that exhibit a repulsive behavior. They have attracted a lot of attention in machine learning, when returning…

Fast and efficient sampling-based motion planning (SMP) is an integral component of many robotic systems, such as autonomous cars. A popular technique to improve the efficiency of these planners is to restrict search space in the planning…

In the realm of robotics, numerous downstream robotics tasks leverage machine learning methods for processing, modeling, or synthesizing data. Often, this data comprises variables that inherently carry geometric constraints, such as the…