IntJSocRobot(2012)4:15–27 DOI10.1007/s12369-011-0102-2 ORIGINALPAPER Regression Analysis of Multi-Rendezvous Recharging Route in Multi-Robot Environment Soheil Keshmiri · Shahram Payandeh Accepted:24July2011/Publishedonline:8September2011 ©SpringerScience&BusinessMediaBV2011 Abstract Oneofthecrucialissueinthefieldofautonomous mobileroboticsisthevitalityofenergyefficiencyofrobots and the entire system they form. By efficiency here we re- fertoabilityofrobots(orthesysteminwhichtheyarede- ployed) to maintain their survival throughout the course of theoperationsoastoprovidethemselveswiththeopportu- nityofattainingenergyonceneeded.Inthispaper,issueof rechargingofagroupofautonomousworkerrobotsintheir workingenvironmenthasbeenaddressed.Todelivertheob- jective, a tanker robot’s planner, capable of determining an energysupplyroutebasedonregressionanalysistechniques, has been implemented. Specifically we have examined the practicality of ordinary and weighted least squares (OLS and WLS respectively) as well as orthogonal least abso- lutevalues(ORLAV)regressionsforrechargingroutecom- putation (hence the terms Least Square Recharging Route (LSRR) and Orthogonal Recharging Route (ORR)). Stud- ies were conducted (while examining OLS and WLS tech- niques) to analyze the effect of various uncertainties which mayexistinlocationinformationoftherobotswithregards to the recharging route. It has been proven that ORLAV based planner may result to a recharging route that mini- mizesthecumulativesumofworkerrobotsdistancetraver- sal during the recharging process, irrespective of tanker lo- cation. Simulations in both, environment with and without obstacles, have been conducted to examine the practicality ofthetechniquesincontrastwithfixedchargingstationsce- S.Keshmiri( ) · S.Payandeh ExperimentalRoboticsLaboratory,SchoolofEngineering Science,SimonFraserUniversity,8888UniversityDrive, Burnaby,BC,CanadaV5A1S6 e-mail: ska61@sfu.ca S.Payandeh e-mail: shahram@cs.sfu.ca nario.Appropriategraphs,diagramsandtables,representing theresultsobtainedinsimulationsareprovidedforillustra- tivecomparisonsamongdifferenttechniques. Keywords Multi-robotsystems · Motionplanning · Least squareregression · Orthogonalregression · Recharging route 1 Introduction Every mechanism, whether biological or otherwise, which is capable of interacting with its environment, requires to maintain its energy for survival. Issue of equipping robots with the capability of maintaining their energy (au- tonomously or with the aid of other party such as recharg- ingstation,etc.)hasbeentopicofseveralongoingresearch projects. Depending on nature of one such recharging sta- tion,differentstrategieshavebeenadapted.Initsearlierat- tempt, the problem was addressed via introduction of fixed chargingstationinrobots’environment,therebyinstructing robotstomovebetweentheircurrentworkinglocationsand the charging station [1–3]. Such approach, however, will leave the system with the short-come of expending power for being recharged instead of performing their designated task(s). It may also suffer the limitation of determining the energy threshold for individuals as robots start spreading overtheworkingenvironmentsincetheincreaseofdistance between the robot and fixed charging station increases the amount of energy to be expended by robots to reach the recharginglocation. Providing robots with opportunity of being recharged in their deployment units (i.e. displaceable charging station) would not only increase the energy preservation of the en- tiresystem,butwouldalsosavethecomputationalresources