Toward a Possibilistic Swarm Multi-robot Task Allocation: Theoretical and Experimental Results
- 338 Downloads
Selecting the best task to execute (task allocation problem) is one of the main problems in multi-robot systems. Typical ways to address this problem are based on swarm intelligence and very especially using the so-called response threshold method. In the aforementioned method a robot has a certain probability of executing a task which depends on a task threshold response and a task stimulus. Nevertheless, response threshold method cannot be extended in a natural way to allocate more than two tasks when the theoretical basis is provided by probability theory. Motivated by this fact, this paper leaves the probabilistic approach to the problem and provides a first theoretical framework towards a possibilistic approach. Thus, task allocation problem is addressed using fuzzy Markov chains instead of probabilistic processes. This paper demonstrates that fuzzy Markov chains associated to a task allocation problem can converge to a stationary stage in a finite number of steps. In contrast, the probabilistic processes only can converge asymptotically, i.e. the number of steps is not bounded in general. Moreover, fuzzy Markov chains predicts in a better way the future behavior of the system in the presence of vagueness when measuring distances. The simulations performed confirm the theoretical results and show how the number of steps needed to get a stable state with fuzzy Markov chains is reduced more than 10 times and the system’s behavior prediction can be improved more than a 60% compared to probabilistic approaches.
KeywordsMulti-robot Possibility theory Swarm intelligence Task allocation
This research was funded by the Spanish Ministry of Economy and Competitiveness under Grants DPI2014-57746-C03-2-R, TIN2014-53772-R, TIN2014-56381-REDT (LODISCO), TIN2016-81731-REDT (LODISCO II) and AEI/FEDER, UE funds.
- 1.Agassounon W, Martinoli A (2002) Efficiency and robustness of threshold-based distributed allocation algorithms in multi-agent systems. In: 1st international joint conference on autonomous agents and multi-agents systems, Bolonia, Italy, July 2002, pp 1090–1097Google Scholar
- 3.Bonabeau E, Sobkowski A, Theraulaz G, Deneubourg J-L (1997) Adaptive task allocation inspired by a model of division of labor in social insects. In: Lundh D, Olsson B, Narayanan A (eds) Bio computation and emergent computing. World Scientific, Singapore, pp 36–45Google Scholar
- 7.Dubois D, Prade H, Sandri S (1993) On possibility/probability transformations. In: Lowen R, Roubens M (eds) Fuzzy logic. Theory and decision library, vol 12. Springer, Netherlands, pp 103–112Google Scholar
- 8.Gerkey BP (2003) On multi-robot task allocation. PhD thesis, Center of robotics and embedded systems, University of Southern California, Los Angeles, USA, August 2003Google Scholar
- 13.Kalra N, Martinoli A (2006) A comparative study of market-based and threshold-based task allocation. In: 8th international symposium on distributed autonomous robotic systems, Minneapolis, USA, July 2006, pp 91–102Google Scholar
- 18.Navarro I, Matía F (2013) An introduction to swarm robotics. ISRN Robot 2013:1–10Google Scholar
- 19.Ranjbar-Sahraei B, Weiss G, Tuyls K (2013) A macroscopic model for multi-robot stigmergic coverage. In: Proceedings of the 12th international conference on autonomous agents and multiagent systems (AAMAS 2013), pp 1233–1234Google Scholar
- 21.Vajargah BF, Gharehdaghi M (2014) Ergodicity of fuzzy Markov chains based on simulation using sequences. Int J Appl Math Comput Sci 11(2):159–165Google Scholar
- 23.Yang Y, Zhou C, Tin Y (2009) Swarm robots task allocation based on response threshold model. In: 4th international conference on autonomous robots and agents, Willengton, New Zeland, February 2009, pp 171–176Google Scholar