Description

• Title:
  Motion planning algorithms for configuration spaces in the higher dimensional case
• Creator:
  Borat, Ayşe
• Description:
  The topological approach to the motion planning problem was introduced by Farber in \cite{F} and \cite{F2}. A motion planning problem is a rule assigning a continuous path to given two configurations - initial point and desired final point of a robot. Farber introduced the notion of topological complexity which measures the discontinuity of any motion planner in a configuration space. In \cite{Ru}, Rudyak introduced higher topological complexity, the concept fully developed in \cite{B}. Higher topological complexity is related to motion planning problem which assigns a continuous path (with $n$-legs) to given $n$ configurations. More precisely, it can be understood as a motion planning algorithm when a robot travels from the initial point $A_{1}$ to $A_{2}$, then from $A_{2}$ to $A_{3}$, and this keeps going until it reaches at the desired final point $A_{n}$. This paper is based on the work of Mas-Ku and Torres-Giese who gave an explicit motion planning algorithm for configuration spaces $F(\mathbb{R}^{2},k)$ and $F(\mathbb{R}^{n},k)$, in \cite{MT}. In the last section, we will consider the higher dimensional case in the sense of Rudyak in \cite{Ru}, and give an explicit motion planning algorithm for this case.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 47, No 2 (June 2016); 763 - 767;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.030/8099 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.030/8100
• Subject:
  Motion planning algorithm;
  configuration spaces;
  55R80
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.030
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other