Related papers: Topology of parametrised motion planning algorithm…
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 study a generalized motion planning problem involving multiple autonomous robots navigating in a $d$-dimensional Euclidean space in the presence of a set of obstacles whose positions are unknown a priori. Each robot is required to visit…
In this paper we study paramertized motion planning algorithms which provide universal and flexible solutions to diverse motion planning problems. Such algorithms are intended to function under a variety of external conditions which are…
The paper surveys topological problems relevant to the motion planning problem of robotics and includes some new results and constructions. First we analyse the notion of topological complexity of configuration spaces which is responsible…
We study motion planning algorithms for collision free control of multiple objects in the presence of moving obstacles. We compute the topological complexity of algorithms solving this problem. We apply topological tools and use information…
We study an elementary problem of the topological robotics: collective motion of a set of $n$ distinct particles which one has to move from an initial configuration to a final configuration, with the requirement that no collisions occur in…
We design a motion planning algorithm to coordinate the movements of two robots along a figure eight track, in such a way that no collisions occur. We use a topological approach to robot motion planning that relates instabilities in motion…
A topological theory initiated recently by the author uses methods of algebraic topology to estimate numerically the character of instabilities arising in motion planning algorithms. The present paper studies random motion planning…
This is a continuation of our recent paper in which we developed the theory of sequential parametrized motion planning. A sequential parametrized motion planning algorithm produced a motion of the system which is required to visit a…
We describe parametrised motion planning algorithms for systems controlling objects represented by points that move without collisions in an even dimensional Euclidean space and in the presence of up to three obstacles with \emph{a priori}…
Multi-robot motion planning (MRMP) is the problem of finding collision-free paths for a set of robots in a continuous state space. The difficulty of MRMP increases with the number of robots and is exacerbated in environments with narrow…
We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the…
Sequential parametrized topological complexity is a numerical homotopy invariant of a fibration, which arose in the robot motion planning problem with external constraints. In this paper, we study sequential parametrized topological…
We consider the problem of robot motion planning in an oriented Riemannian manifold as a topological motion planning problem in its oriented frame bundle. For this purpose, we study the topological complexity of oriented frame bundles,…
The Topological complexity a la Farber $\text{TC}(-)$ is a homotopy invariant which have interesting applications in Robotics, specifically, in the robot motion planning problem. In this work we calculate the topological complexity of the…
In this paper we study a notion of topological complexity for the motion planning problem. The topological complexity is a number which measures discontinuity of the process of motion planning in the configuration space X. More precisely,…
The topological complexity TC(X) is a numerical homotopy invariant of a topological space X which is motivated by robotics and is similar in spirit to the classical Lusternik-Schnirelmann category of X. Given a mechanical system with…
Effective motion planning in high dimensional spaces is a long-standing open problem in robotics. One class of traditional motion planning algorithms corresponds to potential-based motion planning. An advantage of potential based motion…
In terms of Rudyak's generalization of Farber's topological complexity of the path motion planning problem in robotics, we give a complete description of the topological instabilities in any sequential motion planning algorithm for a system…
To control how a robot moves, motion planning algorithms must compute paths in high-dimensional state spaces while accounting for physical constraints related to motors and joints, generating smooth and stable motions, avoiding obstacles,…