Related papers: RM-Dijkstra: A surface optimal path planning algor…

Study the general single-source shortest path problem. Firstly, define a path function on a set of some path with same source on a graph, and develop a kind of general single-source shortest path problem (GSSSP) on the defined path…

We consider decentralized optimization over a compact Riemannian submanifold in a network of $n$ agents, where each agent holds a smooth, nonconvex local objective defined by its private data. The goal is to collaboratively minimize the sum…

Robotic surgery for minimally invasive surgery can reduce the surgeon's workload by autonomously guiding robotic forceps. Movement of the robot is restricted around a fixed insertion port. The robot often encounters angle limitations during…

An algorithm for robot formation path planning is presented in this paper. Given a map of the working environment, the algorithm finds a path for a formation taking into account possible split of the formation and its consecutive merge. The…

The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…

We consider a distributed non-convex optimization where a network of agents aims at minimizing a global function over the Stiefel manifold. The global function is represented as a finite sum of smooth local functions, where each local…

Many exciting robotic applications require multiple robots with many degrees of freedom, such as manipulators, to coordinate their motion in a shared workspace. Discovering high-quality paths in such scenarios can be achieved, in principle,…

Hierarchical, multi-resolution volumetric mapping approaches are widely used to represent large and complex environments as they can efficiently capture their occupancy and connectivity information. Yet widely used path planning methods…

Given a multidimensional free-energy or potential-energy landscape, finding reaction paths that connect an initial (or reactant) state and a final (or product) state is important for biophysics and materials science. The likelihood of a…

Finding the shortest route in wireless mesh networks is an important aspect. Many techniques are used to solve this problem like dynamic programming, evolutionary algorithms, weighted-sum techniques, and others. In this paper, we use…

We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding…

We propose an inexact optimization algorithm on Riemannian manifolds, motivated by quadratic discrimination tasks in high-dimensional, low-sample-size (HDLSS) imaging settings. In such applications, gradient evaluations are often biased due…

By starting with the assumption that motion is fundamentally a decision making problem, we use the world-line concept from Special Relativity as the inspiration for a novel multi-agent path planning method. We have identified a particular…

Trajectory planning for robotic manipulators operating in dynamic orbital debris environments poses significant challenges due to complex obstacle movements and uncertainties. This paper presents Deep Koopman RRT (DK-RRT), an advanced…

Motivated by efforts to incorporate sheaves into networking, we seek to reinterpret pathfinding algorithms in terms of cellular sheaves, using Dijkstra's algorithm as an example. We construct sheaves on a graph with distinguished source and…

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…

We show how to combine two techniques for efficiently computing shortest paths in directed planar graphs. The first is the linear-time shortest-path algorithm of Henzinger, Klein, Subramanian, and Rao [STOC'94]. The second is Fakcharoenphol…

Path planning is an important problem with the the applications in many aspects, such as video games, robotics etc. This paper proposes a novel method to address the problem of Deep Reinforcement Learning (DRL) based path planning for a…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

Covariance matrices have attracted attention for machine learning applications due to their capacity to capture interesting structure in the data. The main challenge is that one needs to take into account the particular geometry of the…