Related papers: Topological robotics: motion planning in projectiv…
We study the geodesic complexity of the ordered and unordered configuration spaces of graphs in both the $\ell_1$ and $\ell_2$ metrics. We determine the geodesic complexity of the ordered two-point $\varepsilon$-configuration space of any…
Recent advancements in robotics have transformed industries such as manufacturing, logistics, surgery, and planetary exploration. A key challenge is developing efficient motion planning algorithms that allow robots to navigate complex…
For positive integers $m$ and $s$, let $\mathbf{m}_s$ stand for the $s$-th tuple $(m,\ldots,m)$. We show that, for large enough $s$, the higher topological complexity $TC_s$ of an even dimensional real projective space $RP^m$ is…
Deformable objects present a formidable challenge for robotic manipulation due to the lack of canonical low-dimensional representations and the difficulty of capturing, predicting, and controlling such objects. We construct compact…
We consider a distributed system of n identical mobile robots operating in the two dimensional Euclidian plane. As in the previous studies, we consider the robots to be anonymous, oblivious, dis-oriented, and without any communication…
Task-motion planning (TMP) addresses the problem of efficiently generating executable and low-cost task plans in a discrete space such that the (initially unknown) action costs are determined by motion plans in a corresponding continuous…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external conditions, which are viewed as parameters and form part of the input of the underlying…
We introduce a bivariate version of topological complexity, $\mathrm{TC}(f,g)$, associated with two continuous maps $f\colon X\to Z$ and $g\colon Y\to Z$. This invariant measures the minimal number of continuous motion planning rules…
Autonomous motion of a system (robot) is controlled by a motion planning algorithm. A sequential parametrized motion planning algorithm \cite{FP22} works under variable external conditions and generates continuous motions of the system to…
Autonomous robotic inspection, where a robot moves through its environment and inspects points of interest, has applications in industrial settings, structural health monitoring, and medicine. Planning the paths for a robot to safely and…
We exhibit an algorithm with continuous instructions for two robots moving without collisions on a track shaped as a wedge of three circles. We show that the topological complexity of the configuration space associated with this problem is…
Systems of networked mobile robots, such as unmanned aerial or ground vehicles, will play important roles in future military and commercial applications. The communications for such systems will typically be over wireless links and may…
In many robot motion planning problems, task objectives and physical constraints induce non-Euclidean geometry on the configuration space, yet many planners operate using Euclidean distances that ignore this structure. We address the…
We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…
This work is motivated by the question of whether there are spaces $X$ for which the Farber-Grant symmetric topological complexity $TC^S(X)$ differs from the Basabe-Gonz\'alez-Rudyak-Tamaki symmetric topological complexity $TC^\Sigma(X)$.…
In this series of papers, we present a motion planning framework for planning comfortable and customizable motion of nonholonomic mobile robots such as intelligent wheelchairs and autonomous cars. In Part I, we presented the mathematical…
Humanoid robots are machines built with an anthropomorphic shape. Despite decades of research into the subject, it is still challenging to tackle the robot locomotion problem from an algorithmic point of view. For example, these machines…
This study investigates the problem of traveling salesman problem with circular neighborhood (TSPCN). Instead of cities there are circles and each point on circle can be a potential visiting node. The problem is to find the minimum length…
Assembly of large scale structural systems in space is understood as critical to serving applications that cannot be deployed from a single launch. Recent literature proposes the use of discrete modular structures for in-space assembly and…