Related papers: Collision free motion planning on a wedge of circl…
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 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 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…
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…
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 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…
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…
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…
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…
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…
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…
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 study the problem of determining optimal coordinated motions for two disc robots in an otherwise obstacle-free plane. Using the total path length traced by the two disc centres as a measure of distance, we give an exact characterization…
We study the problem of motion-planning for free-flying multi-link robots and develop a sampling-based algorithm that is specifically tailored for the task. Our work is based on the simple observation that the set of configurations for…
Tendon-driven continuum robots (TDCRs), with their flexible backbones, offer the advantage of being used for navigating complex, cluttered environments. However, to do so, they typically require multiple segments, often leading to complex…
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…
If we give a robot the task of moving an object from its current position to another location in an unknown environment, the robot must explore the map, identify all types of obstacles, and then determine the best route to complete the…
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…
Path planning in dynamic environments is essential to high-risk applications such as unmanned aerial vehicles, self-driving cars, and autonomous underwater vehicles. In this paper, we generate collision-free trajectories for a robot within…
We study the path planning problem for continuum-arm robots, in which we are given a starting and an end point, and we need to compute a path for the tip of the continuum arm between the two points. We consider both cases where obstacles…