Graphs are mathematical objects that can describe the relations between the data of a combinatorial problem. The network structure and multi-robots are specific cases of a graph.
Hello,
Could you please provide more information of what exactly you need to do? Your question is too general. Thanks.
I need to develop a tracking system for a high order multi agent system of robots using graph theory. stability and robustness analysis are necessary. though how can i develop a mathematical analysis for these two issues. i need to find a way
You cannot simply find a way that can put all those keywords together unless you start study some literature about each keyword and what possibly has been done in the specific area. You can start by studying the Graph Theory in tracking system or image processing and then do some research in multi-agent system of robots and so on. Try to look at the articles below to have better idea about your problem statement and then try to narrow down your research. Good luck.
http://onlinelibrary.wiley.com/doi/10.1080/00241160500333415/pdf
http://greyc.stlo.unicaen.fr/lezoray/IPAG/files/IPAG-Chapter1.pdf
Hello,
possibly you have heared something about Petri nets. For Petri nets you find a lot of different alogorithms that can be usefull for analysis of robustness and stability. A god starting point is here: http://en.wikipedia.org/wiki/Petri-Net. Take a look on section "Mathematical properties of Petri nets".
Kind Regards
Heiko
Thank you Heiko for useful remark. I'll study the possibility of applying Petri nets.
And Thank you Hasan for useful references.
I already have a certain view of the problem. for the robots and graph theory i have a clear idea about how to develop the overall project. put for the point of the robustness and stability analysis i will start first by studying the option of using Petri nets as Heiko suggests.
Thanks again for very useful discussion
I guess the best thing is to start with ¨Information consensus in multivehicle cooperation control¨ by W. Ren et. al. In this article, you can find excellent problem formulation and stability analysis for the consensus of the rendevouz of multivehicle systems which is similar to multi-robot system. Other important article in this field are that of R. Olfati-Saber and R. M. Murray.
Hope this would help.
thank you Ibrahim. you are correct. in some of the literature that i reviewed, the consensusability issue was addressed for directed graph and some other anti-stable discrete-time agents with an undirected graph. i think by considering this issue i must try to build a control protocol that can contain the consensus problem.
I'll check you references as well. Thanks again
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