Page 661 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 661
OPTIMIZATION AND CONTROL
cost functional andexpress it by means of support functions, using the formulas proposed in
[Boulkhemair, A. and Chakib, A., 2014. On a shape derivative formulawith respect to convex
domains. Journal of Convex Analysis, 21(1), pp.67-87.], for a family of convex domains. Then
the numerical discretization is performed using the boundary element method in order to avert
the remeshingtask required when one use the finite element method. Finally, we give somenu-
merical results, based on the gradient method, showing the efficiency ofthe proposed approach.
Real-time planning for the cooperative discovery of unknown graph by
the multi-agent dynamical system
Mila Zovko, mila.zovko@fpmoz.sum.ba
Faculty of Science and Education, University of Mostar, Mostar, Bosnia and Herzegovina
Coauthors: Bojan Crnkovic´, Stefan Ivic´
We propose a solution to the problem of discovering an unknown graph by the multi-agent
dynamical system.
The basic idea for the proposed algorithm comes from the HEDAC (Heat Equation Driven
Area Coverage) method introduced by Ivic´, Crnkovic´ and Mezic´ in [1]. This method has al-
ready been successfully applied for motion control for multi-agent non-uniform spraying [2]
and for motion control for autonomous heterogeneous multi-agent area search in uncertain con-
ditions [3].
The proposed algorithm uses a potential field to discover an unknown graph with a built-
in cooperative behavior of agents which includes collision avoidance, coverage coordination,
and optimal path planning. The algorithm is robust, adaptive, scalable and computationally
inexpensive which enables real-time planning.
We will present the application of the proposed algorithm for discovering different types of
graphs.
As the problem of discovering an unknown graph is related to the examination of social
networks, computer networks and maze exploration, the proposed algorithm will be applied in
solving problems in this area.
References
[1] Ivic´, S., Crnkovic´, B., Mezic´, I.: Ergodicity-based cooperative multiagent area coverage
via a potential field, IEEE Transactions on Cybernetics, vol. 47, no. 8, pp. 1983-1993,
(2017).
[2] Ivic´, S., Andrejcˇuk, A., Družeta, S.: Autonomous control for multi-agent non-uniform
spraying. Applied Soft Computing, 80, 742-760.(2019.)
[3] Ivic´, S.: Motion control for autonomous heterogeneous multi-agent area search in uncer-
tain conditions, IEEE Transactions on Cybernetics, (2020.)
659
cost functional andexpress it by means of support functions, using the formulas proposed in
[Boulkhemair, A. and Chakib, A., 2014. On a shape derivative formulawith respect to convex
domains. Journal of Convex Analysis, 21(1), pp.67-87.], for a family of convex domains. Then
the numerical discretization is performed using the boundary element method in order to avert
the remeshingtask required when one use the finite element method. Finally, we give somenu-
merical results, based on the gradient method, showing the efficiency ofthe proposed approach.
Real-time planning for the cooperative discovery of unknown graph by
the multi-agent dynamical system
Mila Zovko, mila.zovko@fpmoz.sum.ba
Faculty of Science and Education, University of Mostar, Mostar, Bosnia and Herzegovina
Coauthors: Bojan Crnkovic´, Stefan Ivic´
We propose a solution to the problem of discovering an unknown graph by the multi-agent
dynamical system.
The basic idea for the proposed algorithm comes from the HEDAC (Heat Equation Driven
Area Coverage) method introduced by Ivic´, Crnkovic´ and Mezic´ in [1]. This method has al-
ready been successfully applied for motion control for multi-agent non-uniform spraying [2]
and for motion control for autonomous heterogeneous multi-agent area search in uncertain con-
ditions [3].
The proposed algorithm uses a potential field to discover an unknown graph with a built-
in cooperative behavior of agents which includes collision avoidance, coverage coordination,
and optimal path planning. The algorithm is robust, adaptive, scalable and computationally
inexpensive which enables real-time planning.
We will present the application of the proposed algorithm for discovering different types of
graphs.
As the problem of discovering an unknown graph is related to the examination of social
networks, computer networks and maze exploration, the proposed algorithm will be applied in
solving problems in this area.
References
[1] Ivic´, S., Crnkovic´, B., Mezic´, I.: Ergodicity-based cooperative multiagent area coverage
via a potential field, IEEE Transactions on Cybernetics, vol. 47, no. 8, pp. 1983-1993,
(2017).
[2] Ivic´, S., Andrejcˇuk, A., Družeta, S.: Autonomous control for multi-agent non-uniform
spraying. Applied Soft Computing, 80, 742-760.(2019.)
[3] Ivic´, S.: Motion control for autonomous heterogeneous multi-agent area search in uncer-
tain conditions, IEEE Transactions on Cybernetics, (2020.)
659
