Related papers: Walk on Spheres for PDE-based Path Planning
We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of…
Planning collision-free motions for robots with many degrees of freedom is challenging in environments with complex obstacle geometries. Recent work introduced the idea of speeding up the planning by encoding prior experience of successful…
We present a number of breakthroughs for coordinated motion planning, in which the objective is to reconfigure a swarm of labeled convex objects by a combination of parallel, continuous, collision-free translations into a given target…
Markov chain Monte Carlo (MCMC) algorithms have played a significant role in statistics, physics, machine learning and others, and they are the only known general and efficient approach for some high-dimensional problems. The random walk…
Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to…
The approximation of data is a fundamental challenge encountered in various fields, including computer-aided geometric design, the numerical solution of partial differential equations, or the design of curves and surfaces. Numerous methods…
We propose an implementation of a quantum walk on a circle on an optomechanical system by encoding the walker on the phase space of a radiation field and the coin on a two-level state of a mechanical resonator. The dynamics of the system is…
We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically…
The weighted sum method is a simple and widely used technique that scalarizes multiple conflicting objectives into a single objective function. It suffers from the problem of determining the appropriate weights corresponding to the…
We study the problem of motion planning for a collection of $n$ labeled unit disc robots in a polygonal environment. We assume that the robots have revolving areas around their start and final positions: that each start and each final is…
In this work, we develop a probabilistic estimator for the voltage-to-current map arising in electrical impedance tomography. This novel so-called partially reflecting random walk on spheres estimator enables Monte Carlo methods to compute…
This paper presents a trajectory optimization and control approach for the guidance of an orbital four-arm robot in extravehicular activities. The robot operates near the target spacecraft, enabling its arm's end-effectors to reach the…
The Orthogonal Watchman Route Problem (OWRP) entails the search for the shortest path, known as the watchman route, that a robot must follow within a polygonal environment. The primary objective is to ensure that every point in the…
We propose a deep learning approach to the obstacle problem inspired by the first-order system least-squares (FOSLS) framework. This method reformulates the problem as a convex minimization task; by simultaneously approximating the…
Due to its invariance to rigid transformations such as rotations and reflections, Procrustes-Wasserstein (PW) was introduced in the literature as an optimal transport (OT) distance, alternative to Wasserstein and more suited to tasks such…
Robot motion planning involves computing a sequence of valid robot configurations that take the robot from its initial state to a goal state. Solving a motion planning problem optimally using analytical methods is proven to be PSPACE-Hard.…
In this article, two methods of addressing path planning for a Dubins vehicle moving on a sphere are considered, wherein either spherical coordinates or a moving frame are considered to describe the vehicle's motion. The primary…
In a multi-robot system, a number of autonomous robots would sense, communicate, and decide to move within a given domain to achieve a common goal. In this paper, we consider a new variant of the pursuit-evasion problem in which the robots…
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
We propose a scheme called MuNES for single mapping and trajectory planning including elevators and stairs. Optimized multifloor trajectories are important for optimal interfloor movements of robots. However, given two or more options of…