Related papers: Configuration Spaces and Robot Motion Planning Alg…
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…
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 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…
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 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…
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…
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 robotics, a topological theory of motion planning was initiated by M. Farber. The multitasking motion planning problem is new and its theoretical part via topological complexity has hardly been developed, but the concrete implementations…
We consider the problem of multi-robot path planning in a complex, cluttered environment with the aim of reducing overall congestion in the environment, while avoiding any inter-robot communication or coordination. Such limitations may…
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,…
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…
Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of robots. The purpose of this survey is threefold. Firstly, we…
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…
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…
Motion path planning is an intrinsically geometric problem which is central for design of robot systems. Since the early years of AI, robotics together with computer vision have been the areas of computer science that drove its development.…
Navigating mobile robots through environments shared with humans is challenging. From the perspective of the robot, humans are dynamic obstacles that must be avoided. These obstacles make the collision-free space nonconvex, which leads to…
We address the problem of planning robot motions in constrained configuration spaces where the constraints change throughout the motion. The problem is formulated as a fixed sequence of intersecting manifolds, which the robot needs to…
We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on…
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…