相关论文: Harmonic Field-based Provable Exploration of 3D In…

This paper presents a robust computationally efficient real-time collision avoidance algorithm for Unmanned Aerial Vehicle (UAV), namely Memory-based Wall Following-Artificial Potential Field (MWF-APF) method. The new algorithm switches…

This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…

Autonomous exploration using unmanned aerial vehicles (UAVs) is essential for various tasks such as building inspections, rescue operations, deliveries, and warehousing. However, there are two main limitations to previous approaches: they…

In this paper, a safety-critical control strategy for a nonholonomic robot is developed to generate control signals that result in optimal, obstacle-free paths through dynamic environments. We formulate the control synthesis problem as an…

We present a framework for a ground-aerial robotic team to explore large, unstructured, and unknown environments. In such exploration problems, the effectiveness of existing exploration-boosting heuristics often scales poorly with the…

Using properties of harmonic functions in multidimensional space, we transform the Hartree-Fock eigenvalue problem into a more tractable eigenvalue problem in which the Laplacian is eliminated. This new formulation may facilitate the…

Optimal control problems with constraints ensuring safety and convergence to desired states can be mapped onto a sequence of real time optimization problems through the use of Control Barrier Functions (CBFs) and Control Lyapunov Functions…

Exploration and collision-free navigation through an unknown environment is a fundamental task for autonomous robots. In this paper, a novel exploration strategy for Micro Aerial Vehicles (MAVs) is presented. The goal of the exploration…

We study the $h$- and $p$-versions of non-conforming harmonic virtual element methods (VEM) for the approximation of the Dirichlet-Laplace problem on a 2D polygonal domain, providing quasi-optimal error bounds. Harmonic VEM do not make use…

Efficient path planning for autonomous mobile robots is a critical problem across numerous domains, where optimizing both time and energy consumption is paramount. This paper introduces a novel methodology that considers the dynamic…

3-D astrophysical atmospheres will have random velocity fields. We seek to combine the methods we have developed for solving the 1-D problem with arbitrary flows to those that we have developed for solving the fully 3-D relativistic…

We introduce an enriched immersed finite element method for addressing interface problems characterized by general non-homogeneous jump conditions. Unlike many existing unfitted mesh methods, our approach incorporates a homogenization…

We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than…

This paper focuses on the motion planning for mobile robots in 3D, which are modelled by 6-DOF rigid body systems with nonholonomic kinematics constraints. We not only specify the target position, but also bring in the requirement of the…

In this paper we address planning problems in high-dimensional hybrid configuration spaces, with a particular focus on manipulation planning problems involving many objects. We present the hybrid backward-forward (HBF) planning algorithm…

In this paper, we will use the interior functions of an hierarchical basis for high order $BDM_p$ elements to enforce the divergence-free condition of a magnetic field $B$ approximated by the H(div) $BDM_p$ basis. The resulting constrained…

This paper introduces harmonic control Lyapunov barrier functions (harmonic CLBF) that aid in constrained control problems such as reach-avoid problems. Harmonic CLBFs exploit the maximum principle that harmonic functions satisfy to encode…

A simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a Hamiltonian H with singular potentials. Closed-form analytic expressions in N dimensions are obtained for the matrix…

We investigate a hybrid numerical algorithm aimed at the large-scale cosmological N-body simulation for the on-going and the future high precious sky surveys. It makes use of a truncated Fast Multiple Method (FMM) for short-range gravity,…

In this paper, we propose an integrated framework for the autonomous robotic exploration in indoor environments. Specially, we present a hybrid map, named Semantic Road Map (SRM), to represent the topological structure of the explored…