arXiv subjects

Yuda Chen

Publications and source records attributed to Yuda Chen.

9 recordsLinked to original sources

arXiv2026

Uniform Resolvent Estimates for the Discrete Schr\"odinger Operator in Higher Dimensions

Let $H_0$ be the standard discrete Laplacian on $\mathbb Z^d$, $d\geq4$, let $R_0(z)=(H_0-z)^{-1}$, and let $p'$ denote the H\"older conjugate of $p$, with $p'=\infty$ when $p=1$. We establish uniform diagonal resolvent estimates from $\ell^p(\mathbb Z^d)$ to $\ell^{p'}(\mathbb Z^d)$ by proving local Fourier-decay bounds for surface measure on the Fermi surfaces of the lattice dispersion relation. At a regular point, the decay is governed by the number of coordinate directions in which the quadratic term vanishes: after a local change of variables, these directions produce cubic one-dimensional phases, while the remaining directions are quadratic. For $d\geq5$, we prove the sharp global range \[ 1\leq p\leq\frac{2(d+2)}{d+5}. \] Away from the threshold energies, this range remains sharp in odd dimensions, whereas for even $d\geq6$ the sharp range improves to \[ 1\leq p\leq\frac{2(2d+5)}{2d+11}. \] In dimension four, we obtain uniform estimates for $1\leq p<4/3$ and an $\ell^{4/3}$-to-$\ell^4$ endpoint estimate with a square-root logarithmic loss. Matching anisotropic Knapp-type constructions give the corresponding necessary conditions. We also derive Birman--Schwinger and Kato smoothing bounds, complex-eigenvalue estimates, and improved thin spectral projection estimates.

math.SP↗

arXiv2026

Decoupling and Discrete Strichartz Estimates for Dispersive Equations on the Torus

This paper proves weighted discrete Strichartz, or equivalently discrete restriction, estimates for two-dimensional exponential sums with fractional and perturbed polynomial phases. The new results cover three related classes of curves: the fractional Schr\"odinger-type curve $(n,n^{1+\nu})$, the fully fractional curve $(n^{1+\mu},n^{1+\nu})$ with $0<\mu<\nu$, and bounded perturbations of the polynomial curve $(n,n^k)$. In each case we obtain $\ell^2$-weighted $L^p$ estimates with decoupling-type dependence on the frequency scale, including both low- and high-$p$ regimes. The proofs are based on finite-type decoupling, together with localization and rescaling arguments adapted to curvature degeneracy, anisotropic homogeneity, and bounded perturbations of the phase. The introduction frames these estimates from the viewpoint of decoupling theory, with arithmetic results obtained by efficient congruencing used only as comparison points for the known cases.

math.CA↗

arXiv2025

Multi-UAV Deployment in Obstacle-Cluttered Environments with LOS Connectivity

A reliable communication network is essential for multiple UAVs operating within obstacle-cluttered environments, where limited communication due to obstructions often occurs. A common solution is to deploy intermediate UAVs to relay information via a multi-hop network, which introduces two challenges: (i) how to design the structure of multihop networks; and (ii) how to maintain connectivity during collaborative motion. To this end, this work first proposes an efficient constrained search method based on the minimumedge RRT? algorithm, to find a spanning-tree topology that requires a less number of UAVs for the deployment task. Then, to achieve this deployment, a distributed model predictive control strategy is proposed for the online motion coordination. It explicitly incorporates not only the inter-UAV and UAVobstacle distance constraints, but also the line-of-sight (LOS) connectivity constraint. These constraints are well-known to be nonlinear and often tackled by various approximations. In contrast, this work provides a theoretical guarantee that all agent trajectories are ensured to be collision-free with a teamwise LOS connectivity at all time. Numerous simulations are performed in 3D valley-like environments, while hardware experiments validate its dynamic adaptation when the deployment position changes online.

cs.RO↗

arXiv2024

Some results on a conjecture of de Polignac about numbers of the form $p + 2^k$

We have primarily obtained three results on numbers of the form $p + 2^k$. Firstly, we have constructed many arithmetic progressions, each of which does not contain numbers of the form $p + 2^k$, disproving a conjecture by Erd\H{o}s as Chen did recently. Secondly, we have verified a conjecture by Chen that any arithmetic progression that do not contain numbers of the from $p + 2^k$ must have a common difference which is at least 11184810. Thirdly, we have improved the existing upper bound estimate for the density of numbers that can be expressed in the form $p + 2^k$ to $0.490341088858244$.

math.NT↗

arXiv2023

Asynchronous Spatial-Temporal Allocation for Trajectory Planning of Heterogeneous Multi-Agent Systems

To plan the trajectories of a large-scale heterogeneous swarm, sequentially or synchronously distributed methods usually become intractable due to the lack of global clock synchronization. To this end, we provide a novel asynchronous spatial-temporal allocation method. Specifically, between a pair of agents, the allocation is proposed to determine their corresponding derivable time-stamped space and can be updated in an asynchronous way, by inserting a waiting duration between two consecutive replanning steps. Via theoretical analysis, the inter-agent collision is proved to be avoided and the allocation ensures timely updates. Comprehensive simulations and comparisons with five baselines validate the effectiveness of the proposed method and illustrate its improvement in completion time and moving distance. Finally, hardware experiments are carried out, where $8$ heterogeneous unmanned ground vehicles with onboard computation navigate in cluttered scenarios with high agility.

cs.RO↗

arXiv2023

Multi-UAV Deployment in Obstacle-Cluttered Environments with LOS Connectivity

A reliable communication network is essential for multiple UAVs operating within obstacle-cluttered environments, where limited communication due to obstructions often occurs. A common solution is to deploy intermediate UAVs to relay information via a multi-hop network, which introduces two challenges: (i) how to design the structure of multi-hop networks; and (ii) how to maintain connectivity during collaborative motion. To this end, this work first proposes an efficient constrained search method based on the minimum-edge RRT$^\star$ algorithm, to find a spanning-tree topology that requires a less number of UAVs for the deployment task. To achieve this deployment, a distributed model predictive control strategy is proposed for the online motion coordination. It explicitly incorporates not only the inter-UAV and UAV-obstacle distance constraints, but also the line-of-sight (LOS) connectivity constraint. These constraints are well-known to be nonlinear and often tackled by various approximations. In contrast, this work provides a theoretical guarantee that all agent trajectories are ensured to be collision-free with a team-wise LOS connectivity at all time. Numerous simulations are performed in 3D valley-like environments, while hardware experiments validate its dynamic adaptation when the deployment position changes online.

cs.RO↗

arXiv2022

Multi-Robot Trajectory Planning with Feasibility Guarantee and Deadlock Resolution: An Obstacle-Dense Environment

This article presents a multi-robot trajectory planning method which not only guarantees optimization feasibility and but also resolves deadlocks in obstacle-dense environments. The method is proposed via formulating a recursive optimization problem, where a novel safe corridor is generated online to ensure obstacle avoidance in trajectory planning. A dynamic-priority mechanism is combined with the right-hand rule to handle potential deadlocks that are much harder to resolve due to static obstacles. Comparisons with other state-of-the-art results are conducted to validate the improved safety and success rate. Additional hardware experiments are carried out with up to eight nano-quadrotors in various cluttered scenarios.

cs.RO↗

arXiv2022

Deadlock Resolution and Recursive Feasibility in MPC-based Multi-robot Trajectory Generation

Online collision-free trajectory generation within a shared workspace is fundamental for most multi-robot applications. However, many widely-used methods based on model predictive control (MPC) lack theoretical guarantees on the feasibility of underlying optimization. Furthermore, when applied in a distributed manner without a central coordinator, deadlocks often occur where several robots block each other indefinitely. Whereas heuristic methods such as introducing random perturbations exist, no profound analyses are given to validate these measures. Towards this end, we propose a systematic method called infinite-horizon model predictive control with deadlock resolution. The MPC is formulated as a convex optimization over the proposed modified buffered Voronoi with warning band. Based on this formulation, the condition of deadlocks is formally analyzed and proven to be analogous to a force equilibrium. A detection-resolution scheme is proposed, which can effectively detect deadlocks online before they even happen. Once detected, it utilizes an adaptive resolution scheme to resolve deadlocks, under which no stable deadlocks can exist under minor conditions. In addition, the proposed planning algorithm ensures recursive feasibility of the underlying optimization at each time step under both input and model constraints, is concurrent for all robots and requires only local communication. Comprehensive simulation and experiment studies are conducted over large-scale multi-robot systems. Significant improvements on success rate are reported, in comparison with other state-of-the-art methods and especially in crowded and high-speed scenarios.

cs.RO↗

arXiv2019

A*3D Dataset: Towards Autonomous Driving in Challenging Environments

With the increasing global popularity of self-driving cars, there is an immediate need for challenging real-world datasets for benchmarking and training various computer vision tasks such as 3D object detection. Existing datasets either represent simple scenarios or provide only day-time data. In this paper, we introduce a new challenging A*3D dataset which consists of RGB images and LiDAR data with significant diversity of scene, time, and weather. The dataset consists of high-density images ($\approx~10$ times more than the pioneering KITTI dataset), heavy occlusions, a large number of night-time frames ($\approx~3$ times the nuScenes dataset), addressing the gaps in the existing datasets to push the boundaries of tasks in autonomous driving research to more challenging highly diverse environments. The dataset contains $39\text{K}$ frames, $7$ classes, and $230\text{K}$ 3D object annotations. An extensive 3D object detection benchmark evaluation on the A*3D dataset for various attributes such as high density, day-time/night-time, gives interesting insights into the advantages and limitations of training and testing 3D object detection in real-world setting.

cs.CV↗