Modification of the hopfield neural network model for solving the task of optimal task allocation in a group of mobile robots

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Abstract

In the context of group interaction among mobile robots, there arises the challenge of task distribution within the group, considering the robots' characteristics and the working environment. This study aims to modify the Hopfield neural network and develop methodologies for its application in solving the task allocation problem for an arbitrary number of tasks within a group of mobile robots. To achieve this, the Hopfield neural network is represented as a graph. An algorithm is presented, demonstrating the transition from the initial problem to the Traveling Salesman Problem (TSP). The application of the Hopfield model to the task distribution problem in a group of robots is described, along with the development of an optimization function calculation algorithm. An assessment is conducted to evaluate the impact of neural network parameters on the quality and speed of solving the optimization problem. By comparing it with other heuristic methods (genetic and ant colony algorithms), the domains of application for the modified algorithm are determined.

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About the authors

O. V. Darintsev

Mavlyutov Institute of Mechanics of the Ufa Federal Research Centre of the Russian Academy of Sciences; Ufa University of Science and Technology

Author for correspondence.
Email: ovd@uimech.org
Russian Federation, Ufa; Ufa

A. B. Migranov

Mavlyutov Institute of Mechanics of the Ufa Federal Research Centre of the Russian Academy of Sciences

Email: abm.imech.anrb@mail.ru
Russian Federation, Ufa

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Supplementary files

Supplementary Files
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2. Fig. 1. Graphical representation of robots and tasks arrangement on the working field

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3. Fig. 2. GVRP graph for the considered example

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4. Fig. 3. Block diagram of the optimisation algorithm

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5. Fig. 4. Result of calculating the behavioural strategy of a group of robots

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6. Fig. 5. Test problem for dimensionality N = 20 (5 robots, 15 tasks) and its solution with initial parameters (u0 = 0.2; A = B = D = 500; C = 200)

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7. Fig. 6. Dependence of the minimum route length on the threshold level of potential (250 runs of the neural network for each point)

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8. Fig. 7. Meta-optimisation of total route length by weight coefficients (250 runs of neural network for each point)

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9. Fig. 8. Test problem and its solution after step 2 of meta-optimisation

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10. Fig. 9. Dependence of the minimum route length on the threshold level of potential at stage 3 of meta-optimisation (250 runs of the neural network for each point)

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11. Fig. 10. Test problem and its solution after meta-optimisation step 3

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12. Fig. 11. Examples of test problems solved by the modified neural network under different initial conditions (N = 20)

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13. Fig. 12. Examples of polygons of types 1, 2, 3, 4, 5

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