相关论文: The sequential (distributional) topological comple…
How hard is it to program $n$ robots to move about a long narrow aisle such that only $w$ of them can fit across the width of the aisle? In this paper, we answer that question by calculating the topological complexity of $\text{conf}(n,w)$,…
We consider the ordered configuration space of $n$ open unit-diameter disks in the infinite strip of width $w$. In the spirit of Arnol'd and Cohen, we provide a finite presentation for the rational homology groups of this ordered…
We give $\mathbb{Z}$-bases for the homology and cohomology of the configuration space $\operatorname{config}(n,w)$ of $n$ unit disks in an infinite strip of width $w$, first studied by Alpert, Kahle and MacPherson. We also study the way…
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 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…
This paper is concerned with problems relevant to motion planning in robotics. Configuration spaces are of practical relevance in designing safe control schemes for robots moving on a track. The topological complexity of a configuration…
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 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 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…
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…
In this paper we generalize the discrete r-homotopy to the discrete (s, r)-homotopy. Then by this notion, we introduce the discrete motion planning for robots which can move discreetly. Moreover, in this case the number of motion planning,…
We study the topology of the configuration spaces $C(n,w)$ of $n$ hard disks of unit diameter in an infinite strip of width $w$. We describe ranges of parameter or "regimes", where homology $H_j [C(n,w)]$ behaves in qualitatively different…
It has been observed that the very important motion planning problem of robotics mathematically speaking boils down to the problem of finding a section to the path-space fibration, raising the notion of topological complexity, as introduced…
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…
Despite the attention that the problem of path planning for tethered robots has garnered in the past few decades, the approaches proposed to solve it typically rely on a discrete representation of the configuration space and do not exploit…
We determine the topological complexity of unordered configuration spaces on almost all punctured surfaces (both orientable and non-orientable). We also give improved bounds for the topological complexity of unordered configuration spaces…
The topological complexity TC(X) is a homotopy invariant which reflects the complexity of the problem of constructing a motion planning algorithm in the space X, viewed as configuration space of a mechanical system. In this paper we…
In this paper we determine the topological complexity of configuration spaces of graphs which are not necessarily trees, which is a crucial assumption in previous results. We do this for two very different classes of graphs: fully…
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…
The unordered configuration space of $n$ points on a graph $\Gamma,$ denoted here by $UC^n(\Gamma),$ can be viewed as the space of all configurations of $n$ unlabeled robots on a system of one-dimensional tracks, which is interpreted as a…