arXiv subjects

Chenyang Sun

Publications and source records attributed to Chenyang Sun.

11 recordsLinked to original sources

arXiv2026

HaptiNet: Networked Haptic Robots Enable Physical Co-presence in Geographically-Unconstrained Rehabilitation

Cooperative rehabilitation enhances engagement, task performance, and social-motor interaction, yet it demands physical co-presence: users must transmit forces, coordinate movements, and infer intent through haptic contact. Telerehabilitation promises to expand access for patients constrained by distance, mobility, or clinical disparities, yet current techniques remain predominantly audiovisual while leaving users haptically and physically isolated. Here, we introduce HaptiNet, a networked haptic robotic system enabling physical co-presence for geographically distributed users via force-mediated interaction. Each robotic terminal features a low-inertia, long-stroke design with high force-feedback capacity, tailored for haptic rendering in upper-limb training. Building on these terminals, HaptiNet creates a distributed haptic network with an imitation-learning-based delay compensator, enabling users to physically perceive and coordinate with one another over distance. We validated HaptiNet in 284 healthy participants and 111 patients with neurological impairments across progressively realistic settings, including laboratory tests, cross-city deployments, and clinical applications. HaptiNet preserved task-level force rendering consistency across single-user and multi-user scenarios. Compared with solo and visual cooperative training, haptic cooperation improved task performance by 24% and 22%, respectively, while also boosting engagement and interpersonal motor synchrony. Across three intercity links totaling approximately 4,000 km, HaptiNet maintained stable haptic interaction among patients with neurological impairments, producing a 3.87-fold greater baseline-to-training score improvement and a 106% higher patient-applied effort over the solo condition.

cs.RO↗

arXiv2026

Disturbance-Aware Flight for Aerial Robots in Narrow Space

Autonomous flight of aerial robots in narrow space remains challenging due to strong aerodynamic disturbances and limited flying space. Existing approaches mainly address aerodynamic disturbances at the control level, while motion planning typically relies on geometric constraints and fixed speed limits, leading to conservative or unsafe behaviors in confined environments. This paper presents a disturbance-aware planning and control framework (DAPCF) that integrates online disturbance estimation into the planning-control loop for quadrotor flight in narrow space. First, the dual-loop observers estimate 6-degree-of-freedom disturbance forces and torques in real time based on odometry and motor speed measurements. Then, a disturbance risk function is introduced that adaptively modulates the reference speed of the planner based on disturbance estimation, reducing velocity when disturbances exceed a threshold and restoring it under low-disturbance conditions. Finally, a motor-dynamics-based nonlinear model predictive controller (MDNMPC) with disturbance compensation is designed to ensure robust trajectory tracking under perturbed conditions. Experiments demonstrate that a quadrotor with a diagonal length of 0.39~m can traverse straight, sloped, and curved tunnels as narrow as 0.6~m, outperforming human pilots in both success rate and flight efficiency.

cs.RO↗

arXiv2026

Large-Scale Tunnel Air-Ground Collaboration With FLISP: Fast LiDAR-IMU Synchronized Path Planner

Hydropower tunnel inspection is critical for infrastructure integrity yet remains inefficient and hazardous using manual methods. We propose FLISP (Fast LiDAR-IMU Synchronized Path Planner), a mapless planning framework for cooperative UGV-UAV inspection. Unlike traditional map-based paradigms, FLISP features three core contributions: (1) a unified architecture where a single UGV-mounted LiDAR-IMU suite drives synchronized path generation for both platforms; (2) platform-specific solvers utilizing an enhanced Firefly Algorithm for UGV obstacle avoidance and a dynamic iterative optimizer for UAV flight; and (3) a hierarchical refinement strategy ensuring kinematic feasibility without state estimation drift. Benchmarks in a 1.2 km operational tunnel demonstrate that FLISP circumvents structural bottlenecks of map-based methods, eliminating map rasterization overhead (Fast-LIO2 + A*) and sampling instability (LIO-SAM + RRT*). FLISP achieves a 100% success rate with 7 ms latency, representing a 7-fold speedup over grid-based and a three-order-of-magnitude improvement over sampling-based baselines. Validated in operational hydropower tunnels, this approach offers a scalable solution for robotic inspection in feature-degraded linear infrastructure. A demonstration video is available at https://youtu.be/Y_ezs1PfLJ4, and the code at https://github.com/ArchibaldGuo/FLISP.git.

cs.RO↗

arXiv2025

Noise Quantification and Control in Circuits via Strong Data-Processing Inequalities

This essay explores strong data-processing inequalities (SPDI's) as they appear in the work of Evans and Schulman \cite{ES} and von Neumann \cite{vN} on computing with noisy circuits. We first develop the framework in \cite{ES}, which leads to lower bounds on depth and upper bounds on noise that permit reliable computation. We then introduce the $3$-majority gate, introduced by \cite{vN} for the purpose of controlling noise, and obtain an upper bound on noise necessary for its function. We end by generalizing von Neumann's analysis to majority gates of any order, proving an analogous noise threshold and giving a sufficient upper bound for order given a desired level of reliability. The presentation of material has been modified in a way deemed more natural by the author, occasionally leading to simplifications of existing proofs. Furthermore, many computations omitted from the original works have been worked out, and some new commentary added. The intended audience has a rudimentary understanding of information theory similar to that of the author.

cs.IT↗

arXiv2024

Optimal Doubling Thresholds in Backgammon-like Stochastic Games

We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different multipliers to the stake. We determine the optimal game state for proposing and accepting, giving analytic solutions in many variants. We also introduce a 3-player generalization of the game and prove basic results about its behavior, in addition to providing a simulation.

math.OC↗

arXiv2023

Asymptotics of Reciprocal Supernorm Partition Statistics

We consider two multiplicative statistics on the set of integer partitions: the norm of a partition, which is the product of its parts, and the supernorm of a partition, which is the product of the prime numbers $p_i$ indexed by its parts $i$. We introduce and study new statistics that are sums of reciprocals of supernorms on three statistical ensembles of partitions, labelled by their size $|\lambda|=n$, their perimeter equaling $n$, and their largest part equaling $n$. We show that the cumulative statistics of the reciprocal supernorm for each of the three ensembles are asymptotic to $e^{\gamma} \log n$ as $n \to \infty$.

math.CO↗

arXiv2021

Hyperbolic Staircases: Periodic Paths on $2g+1$-gons

The study of polygonal billiards, particularly those in the regular pentagon, has been the subject of two recent papers. One of these papers approaches the problem of discovering the periodic trajectories on the pentagon by identifying slopes of periodic directions with points in the Poincar\'e disk generated by hyperbolic isometric transformations. The other approach, coming from the other paper, transforms the double pentagon into a rectilinear translation surface called the 'golden L', where periodic directions are generated by a set of matrices associated with this surface in a special way. We connect and unify these two approaches, and use our unification of these results to generalize them to arbitrary $2g+1$-sided regular polygons.

math.DS↗

arXiv2020

Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, II

Zeckendorf's theorem states that every positive integer can be written uniquely as the sum of non-consecutive shifted Fibonacci numbers $\{F_n\}$, where we take $F_1=1$ and $F_2=2$. This has been generalized for any Positive Linear Recurrence Sequence (PLRS), which informally is a sequence satisfying a homogeneous linear recurrence with a positive leading coefficient and non-negative integer coefficients. In this and the preceding paper we provide two approaches to investigate linear recurrences with leading coefficient zero, followed by non-negative integer coefficients, with differences between indices relatively prime (abbreviated ZLRR), via two different approaches. The first approach involves generalizing the definition of a legal decomposition for a PLRS found in Kolo\u{g}lu, Kopp, Miller and Wang. We prove that every positive integer $N$ has a legal decomposition for any ZLRR using the greedy algorithm. We also show that a specific family of ZLRRs lost uniqueness of decompositions. The second approach converts a ZLRR to a PLRR that has the same growth rate. We develop the Zeroing Algorithm, a powerful helper tool for analyzing the behavior of linear recurrence sequences. We use it to prove a very general result that guarantees the possibility of conversion between certain recurrences, and develop a method to quickly determine whether a sequence diverges to $+\infty$ or $-\infty$, given any real initial values. This paper investigates the second approach.

math.NT↗

arXiv2020

Deterministic Zeckendorf Games

Zeckendorf proved that every positive integer can be written uniquely as the sum of non-adjacent Fibonacci numbers. We further explore a two-player Zeckendorf game introduced in Baird-Smith, Epstein, Flint, and Miller: Given a fixed integer $n$ and an initial decomposition of $n = nF_1$, players alternate using moves related to the recurrence relation $F_{n+1} = F_n + F_{n_1}$, and the last player to move wins. We improve the upper bound on the number of moves possible and show that it is of the same order in $n$ as the lower bound; this is an improvement by a logarithm over previous work. The new upper bound is $3n - 3Z(n) - IZ(n) + 1$, and the existing lower bound is sharp at $n - Z(n)$ moves, where $Z(n)$ is the number of terms in the Zeckendorf decomposition of $n$ and $IZ(n)$ is the sum of indices in the same Zeckendorf decomposition of $n$. We also studied four deterministic variants of the game, where there was a fixed order on which available move one takes: Combine Largest, Split Largest, Combine Smallest and Split Smallest. We prove that Combine Largest and Split Largest realize the lower bound. Split Smallest has the largest number of moves over all possible games, and is close to the new upper bound. For Combine Split games, the number of moves grows linearly with $n$.

math.NT↗

arXiv2020

Generalizing the Distribution of Missing Sums in Sumsets

Given a finite set of integers $A$, its sumset is $A+A:= \{a_i+a_j \mid a_i,a_j\in A\}$. We examine $|A+A|$ as a random variable, where $A\subset I_n = [0,n-1]$, the set of integers from 0 to $n-1$, so that each element of $I_n$ is in $A$ with a fixed probability $p \in (0,1)$. Recently, Martin and O'Bryant studied the case in which $p=1/2$ and found a closed form for $\mathbb{E}[|A+A|]$. Lazarev, Miller, and O'Bryant extended the result to find a numerical estimate for $\text{Var}(|A+A|)$ and bounds on the number of missing sums in $A+A$, $m_{n\,;\,p}(k) := \mathbb{P}(2n-1-|A+A|=k)$. Their primary tool was a graph-theoretic framework which we now generalize to provide a closed form for $\mathbb{E}[|A+A|]$ and $\text{Var}(|A+A|)$ for all $p\in (0,1)$ and establish good bounds for $\mathbb{E}[|A+A|]$ and $m_{n\,;\,p}(k)$. We continue to investigate $m_{n\,;\,p}(k)$ by studying $m_p(k) = \lim_{n\to\infty}m_{n\,;\,p}(k)$, proven to exist by Zhao. Lazarev, Miller, and O'Bryant proved that, for $p=1/2$, $m_{1/2}(6)>m_{1/2}(7) m_{p}(1)<m_{p}(2)$. Finally, we extend the graph-theoretic framework originally introduced by Lazarev, Miller, and O'Bryant to correlated sumsets $A+B$ where $B$ is correlated to $A$ by the probabilities $\mathbb{P}(i\in B \mid i\in A) = p_1$ and $\mathbb{P}(i\in B \mid i\not\in A) = p_2$. We provide some preliminary results using the extension of this framework.

math.NT↗

arXiv2020

Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, I

Zeckendorf's theorem states that every positive integer can be written uniquely as the sum of non-consecutive shifted Fibonacci numbers $\{F_n\}$, where we take $F_1=1$ and $F_2=2$. This has been generalized for any Positive Linear Recurrence Sequence (PLRS), which informally is a sequence satisfying a homogeneous linear recurrence with a positive leading coefficient and non-negative integer coefficients. These decompositions are generalizations of base $B$ decompositions. In this and the follow-up paper, we provide two approaches to investigate linear recurrences with leading coefficient zero, followed by non-negative integer coefficients, with differences between indices relatively prime (abbreviated ZLRR). The first approach involves generalizing the definition of a legal decomposition for a PLRS found in Kolo\u{g}lu, Kopp, Miller and Wang. We prove that every positive integer $N$ has a legal decomposition for any ZLRR using the greedy algorithm. We also show that a specific family of ZLRRs loses uniqueness of decompositions. The second approach converts a ZLRR to a PLRR that has the same growth rate. We develop the Zeroing Algorithm, a powerful helper tool for analyzing the behavior of linear recurrence sequences. We use it to prove a very general result that guarantees the possibility of conversion between certain recurrences, and develop a method to quickly determine whether certain sequences diverge to $+\infty$ or $-\infty$, given any real initial values. This paper investigates the first approach.

math.NT↗