相关论文: Motion planning in tori
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…
The complexity of algorithms solving the motion planning problem is measured by a homotopy invariant TC(X) of the configuration space X of the system. Previously known lower bounds for TC(X) use the structure of the cohomology algebra of X.…
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 provide explicit motion planners for Euiclidean configuration spaces. This allows us to recover some known values of the topological complexity and the Lusternik-Schinirelman category of these spaces.
We study an elementary problem of topological robotics: rotation of a line, which is fixed by a revolving joint at a base point: one wants to bring the line from its initial position to a final position by a continuous motion in the space.…
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…
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 establish sharp upper bounds for the topological complexity of motion planning problem in spaces with small fundamental group, i.e. when it is finite of small order or has small cohomological dimension.
The topological complexity ${\sf TC}(X)$ is a homotopy invariant of a topological space $X$, motivated by robotics, and providing a measure of the navigational complexity of $X$. The topological complexity of a connected sum of real…
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…
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…
Farber and Rudyak introduced topological complexity $\mathbf{TC}(X)$ of motion planning and its higher analogs $\mathbf{TC}_n(X)$ to measure the complexity of assigning paths to point tuples. Motivated by motion planning where a robotic…
We prove that the topological complexity of (a motion planning algorithm on) the complement of generic complex essential hyperplane arrangement of $n$ hyperplanes in an $r$-dimensional linear space is min$\{n+1,2r\}$.
In this paper, we introduce the notion of transversal topological complexity (TTC) for a smooth manifold $X$ with respect to a submanifold of codimension 1 together with basic results about this numerical invariant. In addition, we present…
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…
In this paper we introduce and study a new concept of parametrised topological complexity, a topological invariant motivated by the motion planning problem of robotics. In the parametrised setting, a motion planning algorithm has high…
We compute the higher topological complexity of ordered configuration spaces of orientable surfaces, thus extending Cohen-Farber's description of the ordinary topological complexity of those spaces.
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…
In this paper we study symmetric motion planning algorithms, i.e. such that the motion from one state A to another B, prescribed by the algorithm, is the time reverse of the motion from B to A. We experiment with several different notions…