Related papers: A Motion Planning Algorithm in a Figure Eight Trac…
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…
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…
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 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,…
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 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 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…
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…
Instabilities of robot motion are caused by topological reasons. In this paper we find a relation between the topological properties of a configuration space (the structure of its cohomology algebra) and the character of instabilities,…
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…
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 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.…
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…
Motion planning is a difficult problem in robot control. The complexity of the problem is directly related to the dimension of the robot's configuration space. While in many theoretical calculations and practical applications the…
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…
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…
A fundamental challenge in multi-robot motion planning is achieving sufficient coordination to avoid inter-robot conflicts without incurring the large computational expense of searching the joint configuration space of the robot group. In…
Planning for multi-robot teams in complex environments is a challenging problem, especially when these teams must coordinate to accomplish a common objective. In general, optimal solutions to these planning problems are computationally…
We study the topological complexity of work maps with respect to some subspaces of the configuration space and a workspace considered as the target set of the motion of robots. The motivation is to optimize and reduce the number of motion…
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…