scholarly journals A Novel Cooperative Path Planning for Multi-robot Persistent Coverage with Obstacles and Coverage Period Constraints

Sensors ◽  
2019 ◽  
Vol 19 (9) ◽  
pp. 1994 ◽  
Author(s):  
Guibin Sun ◽  
Rui Zhou ◽  
Bin Di ◽  
Zhuoning Dong ◽  
Yingxun Wang
Keyword(s):  
Path Planning ◽  
Numerical Simulations ◽  
Obstacle Avoidance ◽  
Travelling Salesman Problem ◽  
Region Of Interest ◽  
Minimum Cost ◽  
Closed Path ◽  
Combinatorial Approach ◽  
Travelling Salesman ◽  
Multi Robot

In this paper, a multi-robot persistent coverage of the region of interest is considered, where persistent coverage and cooperative coverage are addressed simultaneously. Previous works have mainly concentrated on the paths that allow for repeated coverage, but ignored the coverage period requirements of each sub-region. In contrast, this paper presents a combinatorial approach for path planning, which aims to cover mission domains with different task periods while guaranteeing both obstacle avoidance and minimizing the number of robots used. The algorithm first deploys the sensors in the region to satisfy coverage requirements with minimum cost. Then it solves the travelling salesman problem to obtain the frame of the closed path. Finally, the approach partitions the closed path into the fewest segments under the coverage period constraints, and it generates the closed route for each robot on the basis of portioned segments of the closed path. Therefore, each robot can circumnavigate one closed route to cover the different task areas completely and persistently. The numerical simulations show that the proposed approach is feasible to implement the cooperative coverage in consideration of obstacles and coverage period constraints, and the number of robots used is also minimized.

The Travelling Salesman Problem in symmetric circulant matrices with two stripes

2008 ◽  
Vol 18 (1) ◽  
pp. 165-175 ◽  
Author(s):  
IVAN GERACE ◽  
FEDERICO GRECO
Keyword(s):  
Computational Complexity ◽  
Lower Bound ◽  
Lower Bounds ◽  
Travelling Salesman Problem ◽  
Minimum Cost ◽  
Circulant Matrix ◽  
Upper And Lower Bounds ◽  
Circulant Matrices ◽  
Travelling Salesman ◽  
New Construction

The Symmetric Circulant Travelling Salesman Problem asks for the minimum cost tour in a symmetric circulant matrix. The computational complexity of this problem is not known – only upper and lower bounds have been determined. This paper provides a characterisation of the two-stripe case. Instances where the minimum cost of a tour is equal to either the upper or lower bound are recognised. A new construction providing a tour is proposed for the remaining instances, and this leads to a new upper bound that is closer than the previous one.

scholarly journals Decentralized Path Planning for Multi-Objective Robot Swarm System

2021 ◽  
Vol 2113 (1) ◽  
pp. 012002
Author(s):  
Zhuokai Wu
Keyword(s):  
Path Planning ◽  
Obstacle Avoidance ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Planning Problem ◽  
Robot Swarm ◽  
Planning Algorithm ◽  
Path Planning Algorithm ◽  
Path Planning Problem ◽  
Multi Robot

Abstract The multi-robot path planning aims to explore a set of non-colliding paths with the shortest sum of lengths for multiple robots. The most popular approach is to artificially decompose the map into discrete small grids before applying heuristic algorithms. To solve the path planning in continuous environments, we propose a decentralized two-stage algorithm to solve the path-planning problem, where the obstacle and inter-robot collisions are both considered. In the first stage, an obstacle- avoidance path-planning problem is mathematically developed by minimizing the travel length of each robot. Specifically, the obstacle-avoidance trajectories are generated by approximating the obstacles as convex-concave constraints. In the second stage, with the given trajectories, we formulate a quadratic programming (QP) problem for velocity control using the control barrier and Lyapunov function (CBF-CLF). In this way, the multi-robot collision avoidance as well as time efficiency are satisfied by adapting the velocities of robots. In sharp contrast to the conventional heuristic methods, path length, smoothness and safety are fully considered by mathematically formulating the optimization problems in continuous environments. Extensive experiments as well as computer simulations are conducted to validate the effectiveness of the proposed path-planning algorithm.

ON THE VERTEX-CONNECTIVITY PROBLEM FOR GRAPHS WITH SHARPENED TRIANGLE INEQUALITY

2004 ◽  
Vol 15 (05) ◽  
pp. 701-715
Author(s):  
ALESSANDRO FERRANTE ◽  
MIMMO PARENTE
Keyword(s):  
Triangle Inequality ◽  
Travelling Salesman Problem ◽  
Minimum Cost ◽  
Time Algorithm ◽  
Performance Ratio ◽  
Travelling Salesman ◽  
Vertex Connectivity ◽  
Worst Case ◽  
Spanning Subgraph ◽  
Np Hard Problem

Given a graph with the edge costs satisfying the β-sharpened triangle inequality: cost(u,v)≤β(cost(u,x)+cost(x,v)), for l/2≤β<1, we study the NP-hard problem of finding a minimum cost spanning subgraph which is k-vertex-connected, k≥2. We analyze an approximation quadratic-time algorithm whose performance ratio is [Formula: see text]. The main motivation of this study is to provide an algorithm with a good performance ratio and a practical worst case running time for significative subclasses of the metric Travelling Salesman Problem and the naturally related to it connectivity problems.

The shortest path through many points

1959 ◽  
Vol 55 (4) ◽  
pp. 299-327 ◽  
Author(s):  
Jillian Beardwood ◽  
J. H. Halton ◽  
J. M. Hammersley
Keyword(s):  
Euclidean Space ◽  
Shortest Path ◽  
Travelling Salesman Problem ◽  
Dimensional Euclidean Space ◽  
Closed Path ◽  
Street Network ◽  
Plane Region ◽  
Travelling Salesman ◽  
Plateau’S Problem ◽  
Network Problem

ABSTRACTWe prove that the length of the shortest closed path throughnpoints in a bounded plane region of areavis ‘almost always’ asymptotically proportional to √(nv) for largen; and we extend this result to bounded Lebesgue sets ink–dimensional Euclidean space. The constants of proportionality depend only upon the dimensionality of the space, and are independent of the shape of the region. We give numerical bounds for these constants for various values ofk; and we estimate the constant in the particular casek= 2. The results are relevant to the travelling-salesman problem, Steiner's street network problem, and the Loberman—Weinberger wiring problem. They have possible generalizations in the direction of Plateau's problem and Douglas' problem.

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