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Research Papers

A Noise Based Distributed Optimization Method for Multirobot Task Allocation With Multimodal Utility

[+] Author and Article Information
Baisravan HomChaudhuri

Mem. ASME
Department of Mechanical, Industrial
and Manufacturing Engineering,
University of Toledo,
Toledo, OH 43606
e-mail: baisravan.hc@gmail.com

Manish Kumar

Associate Professor
Mem. ASME
Department of Mechanical, Industrial
and Manufacturing Engineering,
University of Toledo,
Toledo, OH 43606
e-mail: manish.kumar2@utoledo.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 30, 2014; final manuscript received June 12, 2014; published online October 21, 2014. Assoc. Editor: Dejan Milutinovic.

J. Dyn. Sys., Meas., Control 137(3), 031010 (Oct 21, 2014) (8 pages) Paper No: DS-14-1047; doi: 10.1115/1.4028553 History: Received January 30, 2014; Revised June 12, 2014

Distributed optimization methods have been used extensively in multirobot task allocation (MRTA) problems. In distributed optimization domain, most of the algorithms are developed for solving convex optimization problems. However, for complex MRTA problems, the cost function can be nonconvex and multimodal in nature with more than one minimum or maximum points. In this paper, an effort has been made to address these complex MRTA problems with multimodal cost functions in a distributed manner. The approach used in this paper is a distributed primal–dual interior point method where noise is added in the search direction as a mechanism to allow the algorithm to escape from suboptimal solutions. The search direction from the distributed primal–dual interior point method and the weighted variable updates help in the generation of feasible primal and dual solutions and in faster convergence while the noise added in the search direction helps in avoiding local optima. The optimality and the computation time of this proposed method are compared with that of the genetic algorithm (GA) and the numerical results are provided in this paper.

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Figures

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Fig. 2

Multimodal cost function

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Fig. 3

Geometric interpretation of the approach

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Fig. 4

Evolution of system utility with the number of iterations for Case 1 using the proposed distributed approach

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Fig. 5

Case 1: comparison of utility for 50 different runs for 50 tasks and 80 robots

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Fig. 6

Evolution of system utility with the number of iterations for Case 2 using the proposed distributed approach

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Fig. 7

Case 2: comparison of utility for 50 different runs for 200 tasks and 500 robots

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Fig. 8

Evolution of system utility with the number of iterations for Case 3 using the proposed distributed approach

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Fig. 9

Total utility versus σ

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