Related papers: Sequential collision-free optimal motion planning …
We present optimal motion planning algorithms which can be used in designing practical systems controlling objects moving in Euclidean space without collisions. Our algorithms are optimal in a very concrete sense, namely, they have the…
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}…
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 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…
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…
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 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 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 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…
Motion planning in the presence of multiple dynamic obstacles is an important research problem from the perspective of autonomous vehicles as well as space-constrained multi-robot work environment. In this paper, we address the motion…
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 work we will review the notion of topological complexity, introduced by Michael Farber in 2003. We will use this theory of topological complexity to solve the motion planning problem of a mobile robot that navigates in the Euclidean…
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…
We consider the problem of cooperative intersection management. It arises in automated transportation systems for people or goods but also in multi-robots environment. Therefore many solutions have been proposed to avoid collisions. The…
Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent…
Learning motion planners to move robot from one point to another within an obstacle-occupied space in a collision-free manner requires either an extensive amount of data or high-quality demonstrations. This requirement is caused by the fact…
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…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
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…