Related papers: The Critical Radius in Sampling-based Motion Plann…
One-shot decision making is required in situations in which we can evaluate a fixed number of solution candidates but do not have any possibility for further, adaptive sampling. Such settings are frequently encountered in neural network…
Probabilistic collision detection (PCD) is essential in motion planning for robots operating in unstructured environments, where considering sensing uncertainty helps prevent damage. Existing PCD methods mainly used simplified geometric…
This paper proposes a novel sampling-based motion planner, which integrates in RRT* (Rapidly exploring Random Tree star) a database of pre-computed motion primitives to alleviate its computational load and allow for motion planning in a…
Let $\mathbb{T}^d$ denote the $d$-dimensional torus. We consider the problem of optimally recovering a target function $f^*:\mathbb{T}^d\rightarrow \mathbb{C}$ from samples of its Fourier coefficients. We make classical smoothness…
Despite the performance advantages of modern sampling-based motion planners, solving high dimensional planning problems in near real-time remains a challenge. Applications include hyper-redundant manipulators, snake-like and humanoid…
For a complete graph of size $n$, assign each edge an i.i.d.\ exponential variable with mean $n$. For $\lambda>0$, consider the length of the longest path whose average weight is at most $\lambda$. It was shown by Aldous (1998) that the…
Consider a random uniform sample of $n$ points in a compact region $A$ of Euclidean $d$-space, $d \geq 2$, with a smooth or (when $d=2$) polygonal boundary. Fix $k \in {\bf N}$. Let $T_{n,k}$ be the threshold $r$ at which the geometric…
We introduce a model of random interlacements made of a countable collection of doubly infinite paths on Z^d, d bigger or equal to 3. A non-negative parameter u measures how many trajectories enter the picture. This model describes in the…
Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate theory for optimal values and empirical…
Tendon-driven continuum robots (TDCRs), with their flexible backbones, offer the advantage of being used for navigating complex, cluttered environments. However, to do so, they typically require multiple segments, often leading to complex…
Modern sampling-based motion planning algorithms typically take between hundreds of milliseconds to dozens of seconds to find collision-free motions for high degree-of-freedom problems. This paper presents performance improvements of more…
Percolation theory has become a useful tool for the analysis of large-scale wireless networks. We investigate the fundamental problem of characterizing the critical density $\lambda_c^{(d)}$ for $d$-dimensional Poisson random geometric…
The contact process is a non-equilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the…
In experimental design, we are given $n$ vectors in $d$ dimensions, and our goal is to select $k\ll n$ of them to perform expensive measurements, e.g., to obtain labels/responses, for a linear regression task. Many statistical criteria have…
Let $(\{1,2,\ldots,n\},d)$ be a metric space. We analyze the expected value and the variance of $\sum_{i=1}^{\lfloor n/2\rfloor}\,d({\boldsymbol{\pi}}(2i-1),{\boldsymbol{\pi}}(2i))$ for a uniformly random permutation ${\boldsymbol{\pi}}$ of…
We consider the problem of maximizing $\langle c,x \rangle$ subject to the constraints $Ax \leq \mathbf{1}$, where $x\in R^n$, $A$ is an $m\times n$ matrix with mutually independent centered subgaussian entries of unit variance, and $c$ is…
The area of sublinear algorithms have recently received a lot of attention. In this setting, one has to choose specific access model for the input, as the algorithm does not have time to pre-process or even to see the whole input. A…
Generalizing the bounded kernel results of Borgs, Chayes, Lov\'asz, S\'os and Vesztergombi (2008), we prove two Sampling Lemmas for unbounded kernels with respect to the cut norm. On the one hand, we show that given a (symmetric) kernel…
We consider Kac's random walk on $n$-dimensional rotation matrices, where each step is a random rotation in the plane generated by two randomly picked coordinates. We show that this process converges to the Haar measure on $\mathit{SO}(n)$…
Informed sampling techniques accelerate the convergence of sampling-based motion planners by biasing sampling toward regions of the state space that are most likely to yield better solutions. However, when the current solution path contains…