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Multi-Robot Graph Exploration and Map Building with Collision Avoidance: A Decentralized Approach

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Abstract

This paper proposes a decentralized multi-robot graph exploration approach in which each robot takes independent decision for efficient exploration avoiding inter-robot collision without direct communication between them. The information exchange between the robots is possible through the beacons available at visited vertices of the graph. The proposed decentralized technique guarantees completion of exploration of an unknown environment in finite number of edge traversals where graph structure of the environment is incrementally constructed. New condition for declaring completion of exploration is obtained. The paper also proposes a modification in incidence matrix so that it can be used as a data structure for information exchange. The modified incidence matrix after completion represents map of the environment. The proposed technique requires either lesser or equal number of edge traversals compared to the existing strategy for a tree exploration. A predefined constant speed change approach is proposed to address the inter-robot collision avoidance using local sensor on a robot. Simulation results verify the performance of the algorithm on various trees and graphs. Experiments with multiple robots show multi-robot exploration avoiding inter-robot collision.

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Abbreviations

v i :

A vertex.

v r :

Root vertex.

e i j :

An edge between two vertices v i and v j .

R k :

k th Robot.

\(\mathcal {V}\) :

Set of vertices.

\(\mathcal {E}\) :

Set of edges.

\(G(\mathcal {V},\mathcal {E})\) :

Graph with vertices \(\mathcal {V}\) and edges \(\mathcal {E}\).

E :

Number of edges in the graph G.

V :

Number of vertices in the graph G.

K:

Number of robots exploring the graph G.

θ j i :

Incidence angle subtended by an edge e j i at the vertex v j .

\(\mathcal {E}_{c}^{n}(R_{k})\) :

Set of completed edges available with the robot R k after n th update.

\(\mathcal {E}_{c}^{n}(v_{j})\) :

Set of completed edges stored at the vertex v j after n th update.

\(\mathcal {E}_{o}^{n}(R_{k})\) :

Set of out edges available with the robot R k after n th update.

\(\mathcal {E}_{o}^{n}(v_{j})\) :

Set of out edges stored at the vertex v j after n th update.

\(\mathcal {E}_{u}^{n}(R_{k})\) :

Set of unexplored edges available with the robot R k after n th update.

\(\mathcal {E}_{u}^{n}(v_{j})\) :

Set of unexplored edges stored at the vertex v j after n th update.

\(\mathcal {E}_{m}^{n}(R_{k})\) :

Set of my-unexplored edges available with the robot R k after n th update.

\(\mathcal {E}_{m}^{n}(v_{j})\) :

Set of my-unexplored edges stored at the vertex v j after n th update.

\({G_{c}^{n}}(R_{k}\) :

Partially completed graph available with the robot R k after n th update.

\({G_{c}^{n}}(v_{j})\) :

Partially completed graph stored at the vertex v j after n th update.

\(\mathcal {V}_{c}^{n}(R_{k})\) :

Set of visited vertices available with the robot R k after n th update.

\(\mathcal {V}_{c}^{n}(v_{j})\) :

Set of visited vertices stored at the vertex v j after n th update.

I :

Proposed incidence matrix.

I n(R k ):

Incidence matrix available with the robot R k after n th update.

I n(v j ):

Incidence matrix stored at the vertex v j after n th update.

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Authors and Affiliations

  1. Systems and Control Engineering, Indian Institute of Technology Bombay, 400076, Mumbai, MH, India

    Sarat Chandra Nagavarapu, Leena Vachhani & Arpita Sinha

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  1. Sarat Chandra Nagavarapu
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  2. Leena Vachhani
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  3. Arpita Sinha
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Correspondence to Leena Vachhani.

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Nagavarapu, S.C., Vachhani, L. & Sinha, A. Multi-Robot Graph Exploration and Map Building with Collision Avoidance: A Decentralized Approach. J Intell Robot Syst 83, 503–523 (2016). https://doi.org/10.1007/s10846-015-0309-9

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