Deterministic Robot-Network Localization is Hard

Abstract : This paper provides a complexity study of the deterministic localization problem in robot networks using local and relative observations only. This is an important issue in collective and cooperative robotics where global positioning systems (GPS) are not available, and the basic premise is the localization ability of the group. We prove that given a set of relative observations made by the robots, the unique unambiguous pose estimation of the robot network in a deterministic way is an NP-hard problem. This means that no polynomial-time algorithm can deterministically solve the unique pose estimation problem based on relative observations unless P=NP. The consequence is that no guarantee can be provided, in a polynomial time, that the possibly estimated poses of the robots will correspond to the effective (actual) ones. The proof is based on complexity theory where we build appropriate polynomial-time reductions interrelating the multirobot localization problem to a well-known NP-complete problem (the partition problem). This NP -hardness result opens questions and perspectives for research into approximations to overcome its intractability.
Document type :
Journal articles
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01197395
Contributor : Lip6 Publications <>
Submitted on : Friday, September 11, 2015 - 3:59:52 PM
Last modification on : Friday, April 19, 2019 - 1:50:11 AM

Identifiers

Citation

Yoann Dieudonné, Ouiddad Labbani-Igbida, Franck Petit. Deterministic Robot-Network Localization is Hard. IEEE Transactions on Robotics, IEEE, 2010, 26 (2), pp.331-339. ⟨10.1109/tro.2010.2042753⟩. ⟨hal-01197395⟩

Share

Metrics

Record views

158