An Efficient Follow-the-Leader Strategy for Continuum Robot Navigation and Coiling

Aims and Objective: The idea of partition and resolving sets plays an important role in various areas of engineering, chemistry and computer science such as robot navigation, facility location, pharmaceutical chemistry, combinatorial optimization, networking, and mastermind game. Method: In a graph to obtain the exact location of a required vertex which is unique from all the vertices, several vertices are selected this is called resolving set and its generalization is called resolving partition, where selected vertices are in the form of subsets. Minimum number of partitions of the vertices into sets is called partition dimension. Results: It was proved that determining the partition dimension a graph is nondeterministic polynomial time (NP) problem. In this article, we find the partition dimension of convex polytopes and provide their bounds. Conclusion: The major contribution of this article is that, due to the complexity of computing the exact partition dimension we provides the bounds and show that all the graphs discussed in results have partition dimension either less or equals to 4, but it cannot been be greater than 4.

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Real-time road edge following for mobile robot navigation

Electronics & Communications Engineering Journal ◽

10.1049/ecej:19900010 ◽

1990 ◽

Vol 2 (1) ◽

pp. 35 ◽

Cited By ~ 5

Author(s):

R.A. Lotufo ◽

A.D. Morgan ◽

E.L. Dagless ◽

D.J. Milford ◽

J.F. Morrissey ◽

...

Keyword(s):

Mobile Robot ◽

Real Time ◽

Robot Navigation ◽

Mobile Robot Navigation

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Power graphs and exchange property for resolving sets

Open Mathematics ◽

10.1515/math-2019-0093 ◽

2019 ◽

Vol 17 (1) ◽

pp. 1303-1309 ◽

Cited By ~ 1

Author(s):

Ghulam Abbas ◽

Usman Ali ◽

Mobeen Munir ◽

Syed Ahtsham Ul Haq Bokhary ◽

Shin Min Kang

Keyword(s):

Present Article ◽

Linear Algebra ◽

Finite Groups ◽

Robot Navigation ◽

Simple Graph ◽

Exchange Property ◽

Metric Dimension ◽

Sufficient Condition ◽

Resolving Set ◽

Dihedral Groups

Abstract Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton twins is given. A sufficient condition for the graph to have the exchange property for resolving sets is found. Consequently, every minimal resolving set in the graph forms a basis for a matriod in the context of independence defined by Boutin [Determining sets, resolving set and the exchange property, Graphs Combin., 2009, 25, 789-806]. Also, a new way to define a matroid on finite ground is deduced. It is proved that the matroid is strongly base orderable and hence satisfies the conjecture of White [An unique exchange property for bases, Linear Algebra Appl., 1980, 31, 81-91]. As an application, it is shown that the power graphs of some finite groups can define a matroid. Moreover, we also compute the metric dimension of the power graphs of dihedral groups.

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THÖR: Human-Robot Navigation Data Collection and Accurate Motion Trajectories Dataset

IEEE Robotics and Automation Letters ◽

10.1109/lra.2020.2965416 ◽

2020 ◽

Vol 5 (2) ◽

pp. 676-682

Author(s):

Andrey Rudenko ◽

Tomasz P. Kucner ◽

Chittaranjan S. Swaminathan ◽

Ravi T. Chadalavada ◽

Kai O. Arras ◽

...

Keyword(s):

Data Collection ◽

Robot Navigation ◽

Motion Trajectories ◽

Navigation Data

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Path Planning and Replanning for Mobile Robot Navigation on 3D Terrain: An Approach Based on Geodesic

Mathematical Problems in Engineering ◽

10.1155/2016/2539761 ◽

2016 ◽

Vol 2016 ◽

pp. 1-12 ◽

Cited By ~ 2

Author(s):

Kun-Lin Wu ◽

Ting-Jui Ho ◽

Sean A. Huang ◽

Kuo-Hui Lin ◽

Yueh-Chen Lin ◽

...

Keyword(s):

Mobile Robot ◽

Robot Navigation ◽

Tangent Plane ◽

Intersection Point ◽

Mobile Robot Navigation ◽

Complete Manifold ◽

Geodesic Triangle ◽

Planning Stage ◽

3D Terrain ◽

Bonnet Theorem

In this paper, mobile robot navigation on a 3D terrain with a single obstacle is addressed. The terrain is modelled as a smooth, complete manifold with well-defined tangent planes and the hazardous region is modelled as an enclosing circle with a hazard grade tuned radius representing the obstacle projected onto the terrain to allow efficient path-obstacle intersection checking. To resolve the intersections along the initial geodesic, by resorting to the geodesic ideas from differential geometry on surfaces and manifolds, we present a geodesic-based planning and replanning algorithm as a new method for obstacle avoidance on a 3D terrain without using boundary following on the obstacle surface. The replanning algorithm generates two new paths, each a composition of two geodesics, connected via critical points whose locations are found to be heavily relying on the exploration of the terrain via directional scanning on the tangent plane at the first intersection point of the initial geodesic with the circle. An advantage of this geodesic path replanning procedure is that traversability of terrain on which the detour path traverses could be explored based on the local Gauss-Bonnet Theorem of the geodesic triangle at the planning stage. A simulation demonstrates the practicality of the analytical geodesic replanning procedure for navigating a constant speed point robot on a 3D hill-like terrain.

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Perception-action map learning in controlled multiscroll systems applied to robot navigation

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.3005783 ◽

2008 ◽

Vol 18 (4) ◽

pp. 043119 ◽

Cited By ~ 9

Author(s):

Paolo Arena ◽

Sebastiano De Fiore ◽

Luigi Fortuna ◽

Luca Patané

Keyword(s):

Robot Navigation ◽

Map Learning ◽

Perception Action

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