Behavioral Diversity Generation in Autonomous Exploration through Reuse of Past Experience

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(1)Behavioral Diversity Generation in Autonomous Exploration through Reuse of Past Experience Fabien Benureau, Pierre-Yves Oudeyer. To cite this version: Fabien Benureau, Pierre-Yves Oudeyer. Behavioral Diversity Generation in Autonomous Exploration through Reuse of Past Experience. Frontiers in Robotics and AI, Frontiers Media S.A., 2016, 3 (8), �10.3389/frobt.2016.00008�. �hal-01404329�. HAL Id: hal-01404329 https://hal.inria.fr/hal-01404329 Submitted on 28 Nov 2016. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.. Distributed under a Creative Commons Attribution| 4.0 International License.

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YU ← 1FSUVSCE YOO. *OWFSTF .PEFM. ◃ ZOO JT UIF OFBSFTU OFJHICPS PG H ◃ 1FSUVSCJOH UIF NPUPS DPNNBOE PG UIF OFBSFTU FGGFDU. "-(03*5). ] */7&34&-#'(4#-8-3 HU ) . "O JOWFSTF NPEFM JT VTFE XIFOFWFS HPBM CBCCMJOH JT DIPTFO BT BO FYQMPSBUJPO TUSBUFHZ JO UIF &ŅĽĹļĿĲ BMHPSJUIN -FU VT SFNBSL UIBU PVS PCKFDUJWF IFSF JT OPU UP BDRVJSF B GPSXBSE PS JOWFSTF NPEFM PG UIF FOWJSPONFOU 5IF MFBSOJOH BMHPSJUINT BSF GVODUJPOBM FOUJUJFT PG UIF FYQMPSBUJPO QSPDFTT BOE UIF NPEFMT UIFZ QSPEVDF BSF OPU FWBMVBUFE *O QBSUJDVMBS UIFZ NBZ NBLF BTTVNQUJPOT UIBU QSFDMVEF UIFN GSPN DSFBUJOH BDDVSBUF NPEFMT PG UIF FOWJSPONFOU o XF XJMM EJTDVTT TVDI B DBTF JO 4FDUJPO *O UIJT BSUJDMF XF XJMM CF VTJOH UXP EJGGFSFOU JOWFSTF NPEFMT B TJNQMF QFSUVSCBUJPOCBTFE POF BOE BOPUIFS CBTFE PO BO PQUJNJ[FE SFHSFTTJPO NFUIPE. *OQVU HU ∈ 4 *OQVU ) = \ YK ZK ^≤K < U− ∈ . × 4 U− 0VUQVU YU ∈ . YOO ZOO ← BSHNJOYK ,ZK ∈) ]]HU −ZK ]]. *OJUJBMJ[F -#'(4# PQUJNJ[BUJPO XJUI YOO YU ← .JOJNJ[F-#'(4#Y ∈. ]]HU o 1SFEJDU-8-3 Y ) ]]. ◃ ZOO JT UIF OFBSFTU OFJHICPS PG HU . 5IJT QFSUVSCBUJPOCBTFE JOWFSTF BMHPSJUIN JT TJNQMF BOE FGGFD UJWF *UT DPNQMFYJUZ JT MJOFBS JO CPUI E. 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B QFSUVSCBUJPO PG Y JT EFGJOFE CZ 1&3563#E (Y) = {3"/%0.(NBY(BJ , YJ − E(CJ − BJ )),. NJO(YJ + E(CJ − BJ ), CJ ))}≤J<E.. & XJUI . = ≤J<E. [BJ , CJ ] BT B IZQFSSFDUBOHMF PG RE. BOE XJUI UIF GVODUJPO 3ĮĻıļĺ B C ESBXJOH B SBOEPN WBMVF JO UIF JOUFSWBM <B C> BDDPSEJOH UP B VOJGPSN EJTUSJCVUJPO E JT UIF QFSUVSCBUJPO QBSBNFUFS BOE CFMPOHT UP < > JU JT UIF POMZ QBSBNFUFS PG UIF JOWFSTF NPEFM UIBU XF DBO OPX FYQSFTT JO "MHPSJUIN . 'SPOUJFST JO 3PCPUJDT BOE "* ] XXXGSPOUJFSTJOPSH. ◃ " HPBM ◃ $VSSFOU IJTUPSZ QBTU Uo PCTFSWBUJPOT ◃ $BOEJEBUF NPUPS DPNNBOE. 0QUJNJ[FE 3FHSFTTJPO *OWFSTF .PEFM 8F BMTP VTF BO PQUJNJ[FE SFHSFTTJPO JOWFSTF NPEFM JO TPNF FYQFSJNFOUT CBTFE PO BO PQUJNJ[BUJPO SPVUJOF -#'(4# . .BSDI ] 7PMVNF ] "SUJDMF .

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(9) #FOVSFBV BOE 0VEFZFS. #FIBWJPSBM %JWFSTJUZ (FOFSBUJPO UISPVHI 3FVTF. A SOURCE TASK selected effects. selected motor commands. reuse exploration (400 steps). reuse exploration (5000 steps). no reuse exploration (400 steps). no reuse exploration (5000 steps). B TARGET TASK, REUSE ALGORITHM reused motor commands. C TARGET TASK, EXPLORE ALGORITHM random motor commands. '*(63& ] *MMVTUSBUJPO PG UIF 3&64& BMHPSJUIN "GUFS UIF FOE PG UIF FYQMPSBUJPO PG UIF TPVSDF BSN " B × HSJE QBSUJUJPOT UIF FGGFDU TQBDF BOE BT NBOZ UJNFT BT OFDFTTBSZ UJNFT IFSF B SBOEPN DFMM JT DIPTFO BT XFMM BT B SBOEPN FGGFDU JOTJEF JU EPUT IJHIMJHIUFE JO SFE 5IF NPUPS DPNNBOET UIBU QSPEVDFE UIF DIPTFO FGGFDUT BSF UIFO SFFYFDVUFE PO UIF UBSHFU BSN # 5IJT SFQMBDFT UIF JOJUJBM NPUPS CBCCMJOH TUFQT PG UIF &91-03& BMHPSJUIN $ *O CPUI DBTFT UIF FGGFDUT QSPEVDFE CZ SBOEPN NPUPS CBCCMJOH PS B SFVTFE NPUPS DPNNBOE IBWF CFFO IJHIMJHIUFE JO SFE 8IJMF SBOEPN NPUPS CBCCMJOH QSPEVDFT DPOWPMVUFE BSN QPTUVSFT XIPTF FGGFDUT BSF DMVTUFSFE BSPVOE UIF DFOUFS UIF SFVTFE NPUPS DPNNBOET QSPEVDF FGGFDUT TQSFBE PVU PWFS UIF SFBDIBCMF TQBDF BOE GFBUVSF TUSBJHIUFS QPTUVSFT 5IJT EJGGFSFODF JO CPPUTUSBQQJOH IBT B IVHF JNQBDU PO UIF DPWFSBHF BU U = BOE B MFTTFS CVU TUJMM QSFTFOU POF BGUFS TUFQT. CFUUFS UIBO UIF CFTUDBTF TDFOBSJP PG UIF &ŅĽĹļĿĲ TUSBUFHZ 5IF VTBHF PG 3ĲłŀĲ BDDFMFSBUFT UIF FYQMPSBUJPO PG UIF SFBDIBCMF TQBDF. 'SPOUJFST JO 3PCPUJDT BOE "* ] XXXGSPOUJFSTJOPSH. )PXFWFS BO JOUFSFTUJOH QIFOPNFOPO JT QSFTFOU 5IF XPSTU DBTF PG UIF 3ĲłŀĲ TUSBUFHZ BT TIPXO CZ UIF EPUUFE MJOFT QFSGPSNT XPSTF UIBO UIF XPSTU DBTF PG UIF &ŅĽĹļĿĲ TUSBUFHZ. . .BSDI ] 7PMVNF ] "SUJDMF .

(10) #FOVSFBV BOE 0VEFZFS. coverage area (in m2). #FIBWJPSBM %JWFSTJUZ (FOFSBUJPO UISPVHI 3FVTF. UFOEFODZ UP IBWF FJUIFS MPPQT OFBS UIF UJQ PG UIF BSN PS OP MPPQT BU BMM 5IF POMZ XBZ GPS QPTUVSFT XJUI DPTUMZ MPPQT OFBS UIF CBTF PG UIF BSN UP CF TFMFDUFE PO UIF UBSHFU BSN JT GPS UIFN UP IBWF UIF SFTU PG UIF BSN SBUIFS TUSBJHIU BOE JO B GBTIJPO EJTQSPQPSUJPOBUF XJUI UIF PUIFS BSN QPTUVSFT UIFZ DPNQFUF XJUI 5IJT JT FYBDUMZ UIF TDFOBSJP UIBU IBQQFOT JO UIF XPSTU DBTF PG 3ĲłŀĲ BMM UIF SFVTFE BSN QPTUVSFT XIFSF UIF UJQ JT GBS GSPN UIF DFOUFS IBWF MPPQT OFBS UIF CBTF PG UIF BSN BT 'JHVSF JMMVTUSBUFT 5IJT JT OPU B QSPCMFN GPS UIF TPVSDF BSN CVU GPS UIF UBSHFU BSN JU MJNJUT UIF BDIJFWBCMF TQBO NVDI NPSF UIBO JG UIF MPPQT XFSF OFBS UIF UJQ PG UIF BSN 5IJT FYQMBJOT UIF EJGGFSFODF JO DPWFSBHF CFUXFFO UIF XPSTU DBTF PG UIF 3ĲłŀĲ BOE &ŅĽĹļĿĲ BMHPSJUIN PO UIF UBSHFU BSN BOE TFSWFT UP JMMVTUSBUF B EBOHFS PG UIF 3ĲłŀĲ BMHPSJUIN QSPWJEJOH HPPE TPMVUJPOT USBQQFE JO MPDBM NJOJNB FBSMZ JO FYQMPSBUJPO DBO QSFWFOU UIF EJTDPWFSZ PG CFUUFS TPMVUJPOT NPSF BEBQUFE UP UIF UBSHFU UBTL -FU VT SFNBSL IFSF UIBU BMM UIF NPUPS CBCCMJOH TUFQT PG UIF &ŅĽĹļĿĲ BMHPSJUIN XFSF SFQMBDFE CZ SFVTF TUFQT JO UIF 3ĲłŀĲ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ĲłŀĲ TIPVME CF BWPJEFE 8IJMF JU IBT UIF QPUFOUJBM UP JOEVDF QFSGPSNBODFIJOEFSJOH MPDBM NJO JNB JU BMTP IBT UIF QPUFOUJBM UP QSPQPTF HPPE TPMVUJPOT FBSMZ JO FYQMPSBUJPO %VSJOH UIF GJSTU TUFQT UIF XPSTU DBTF TDFOBSJP PG UIF 3ĲłŀĲ BMHPSJUIN JT BDUVBMMZ CFUUFS UIBO UIF CFTUDBTF TDFOBSJP PG UIF &ŅĽĹļĿĲ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ĲłŀĲ NFUIPE JT FGGFDUJWF "T QPJOUFE PVU CFGPSF UIF UXP BSNT IBWF EJGGFSFOU JOWFSTF NPE FMT BOE UIF SFMBUJPOTIJQ CFUXFFO UIFN JT OPOUSJWJBM #Z SFVTJOH NPUPS DPNNBOET UIBU QSPEVDF B EJWFSTJUZ PG FGGFDUT XF NBLF UIF BTTVNQUJPO UIBU UIF EJWFSTJUZ NBQQJOH JT TJNQMFS CFUXFFO UIF UXP UBTLT B TFU PG NPUPS DPNNBOET HFOFSBUJOH B DFSUBJO BNPVOU PG EJWFSTJUZ PO UIF TPVSDF BSN XJMM HFOFSBUF B TJNJMBS BNPVOU PO UIF UBSHFU BSN 5IJT JT TPNFUIJOH XF DBO WFSJGZ FYQFSJNFOUBMMZ. maximum coverage. with reuse. without reuse. timesteps. '*(63& ] 5IF FYQMPSBUJPO XJUI 3FVTF PO UIF TFDPOE BSN DPWFST TJHOJGJDBOUMZ NPSF PG UIF SFBDIBCMF TQBDF FBSMZ PO UIBO UIF POF XJUIPVU 5IF HSBQI TIPXT UIF τ DPWFSBHF XJUI τ = PG UIF TFDPOE BSN FYQMPSFE XJUI UIF 3&64& BOE &91-03& BMHPSJUIN SFTQFDUJWFMZ PWFS SFQFUJUJPOT PG FBDI FYQFSJNFOU 5IF NFEJBO DBTF JT EJTQMBZFE TVSSPVOEFE CZ B NBSHJO HPJOH GSPN UIF UI UP UIF UI QFSDFOUJMFT *O EBTIFE MJOFT UIF XPSTU BOE UIF CFTU DPWFSBHFT BSF BMTP QJDUVSFE. 5P VOEFSTUBOE XIZ JU JT JOUFSFTUJOH UP MPPL BU HPBM CBCCMJOH BT BO FWPMVUJPOBSZ BMHPSJUIN 'SPN BO FWPMVUJPOBSZ SPCPUJDT QFS TQFDUJWF UIF NPUPS DPNNBOET BSF UIF HFOFUJD FODPEJOH UIF BSN QPTUVSF UIF QIFOPUZQF BOE UIF FGGFDU o UIF QPTJUJPO PG UIF FOE FGGFDUPS o JT UIF CFIBWJPS PG UIF BSN "U FBDI UJNFTUFQ PG HPBM CBC CMJOH B SBOEPN HPBM JT DIPTFO 5IF EJTUBODF UP UIJT HPBM EFGJOFT B GJUOFTT GVODUJPO BOE UIF IJHIFTUQFSGPSNJOH QBTU PCTFSWBUJPO XIPTF FGGFDU JT UIF OFBSFTU OFJHICPS PG UIF HPBM JT DIPTFO UP SFQSPEVDF UISPVHI NVUBUJPO UIJT JT IPX PVS QFSUVSCBUJPOCBTFE JOWFSTF NPEFM XPSLT 5IFSFGPSF BGUFS UIF CPPUTUSBQQJOH QIBTF BSN QPTUVSFT BSF DIP TFO GPS SFQSPEVDUJPO JO QSPQPSUJPO PG IPX DMPTF UIFJS FGGFDUT BSF UP UIF DIPTFO HPBMT 8IFO VTJOH SBOEPN NPUPS CBCCMJOH NPTU QPT UVSFT QSPEVDF FGGFDUT OFBS UIF DFOUFS #FDBVTF HPBMT BSF SBOEPNMZ DIPTFO JO UIF <− > × <− > TRVBSF NPTU HPBMT BSF GBSUIFS GSPN UIF DFOUFS UIBO NPTU PCTFSWFE FGGFDUT *U NFBOT UIBU QPTUVSFT QSPEVDJOH FGGFDUT PO UIF FEHF PG UIF JOJUJBM DMVTUFS BSF DIPTFO BOE NVUBUFE XJUI EJTQSPQPSUJPOBUF GSFRVFODZ 5ISPVHI SFQFBUFE TFMFDUJPO BOE NVUBUJPOT UIPTF QPTUVSFT BOE UIFJS EFTDFOEBOUT TUSBJHIUFS BOE TUSBJHIUFS QPTUVSFT BSF EJTDPWFSFE 4PNFUJNFT IPXFWFS UIPTF JOJUJBM BSN QPTUVSFT DPOUBJO MPPQT 5IPTF MPPQT SFQSFTFOU MPDBM NJOJNB UIBU BSF EJGGJDVMU UP FTDBQF 5IF NVUBUJPO BOE TFMFDUJPO QSPDFTT o PVS QFSUVSCBUJPOCBTFE JOWFSTF NPEFM o UFOET UP TUSBJHIUFO BSN QPTUVSFT UP SFBDI EJTUBOU UBSHFU *O UIF QSPDFTT MPPQT BSF UJHIUFOFE OPU SFNPWFE 5IFSFGPSF UIF NBYJNVN TQBO PG UIF BSN JT SFEVDFE BOE UIF FYQMPSBUJPO DPWFST POMZ B GSBDUJPO PG UIF SFBDIBCMF TQBDF BT TIPXO JO UIF HSBQIT PG 'JHVSF 0O UIF TPVSDF BSN CFDBVTF UIF MJOLT BSF BMM PG UIF TBNF MFOHUI MPPQT IBWF UIF TBNF DPTU JO TQBO SFHBSEMFTT PG XIFSF UIFZ BQQFBS #VU PO UIF UBSHFU BSN UIFZ BSF NPTU DPTUMZ OFBS UIF CBTF PG UIF BSN XIFSF MJOLT BSF MPOHFS 5IFSFGPSF BSN QPTUVSFT GFBUVSJOH MPPQT OFBS UIF CBTF PG UIF BSN UFOE UP CF TIPSUFS PO BWFSBHF UIBO QPTUVSFT XJUI MPPQT OFBS UIF UJQ FWFO JO B SBOEPN NPUPS CBCCMJOH TBNQMJOH *U NFBOT UIBU XIFO VTJOH UIF &ŅĽĹļĿĲ BMHPSJUIN NPTU PG UIF UJNF UIPTF QPTUVSFT EP OPU HFU TFMFDUFE GPS GBS HPBMT BGUFS UIF CPPUTUSBQQJOH QIBTF BT CFUUFS TPMVUJPOT FYJTU 5IFSFGPSF UIF QPTUVSFT UIBU FYQMPSF UIF FEHF PG UIF SFBDIBCMF TQBDF IBWF B. 'SPOUJFST JO 3PCPUJDT BOE "* ] XXXGSPOUJFSTJOPSH. . .BSDI ] 7PMVNF ] "SUJDMF .

(11) #FOVSFBV BOE 0VEFZFS. #FIBWJPSBM %JWFSTJUZ (FOFSBUJPO UISPVHI 3FVTF. A WORST CASE, REUSE ALGORITHM:. B. REUSED COMMANDS. SOURCE ARM. all 50 transferred motor commands (executed on the target arm) L1. L1. L2. L2. L1. L2 L1 L2. C WORST CASE, REUSE ALGORITHM:. D. TARGET ARM. WORST CASE, EXPLORE ALGORITHM: TARGET ARM. L2. L2. L2. L1. L2. smaller coverage. L1. L2. L2. '*(63& ] 6TJOH 3&64& DBO CF XPSTF UIBO OPU VTJOH JU 5IJT HSBQIT EFQJDUT UIF XPSTU DBTF o DPWFSBHFXJTF o PG UIF 3&64& BOE &91-03& BMHPSJUINT BNPOH UIF DBTFT VTFE UP DPNQVUF 'JHVSF GPS U = *O " $ % UIF BSN QPTUVSFT XJUI UIF MPOHFTU TQBO JO UIF DBSEJOBM BOE JOUFSDBSEJOBM EJSFDUJPOT BSF EJTQMBZFE *O UIF XPSTU DBTF PG 3&64& UIF TPVSDF FYQMPSBUJPO GFBUVSFT QPTUVSFT UIBU IBWF MPPQT OFBS UIF CBTF PG UIF BSN " 8F DBO FWFO EJTUJOHVJTI CFUXFFO UXP TQFDJFT PG QPTUVSFT 0OFT UIBU IBWF B MPPQ TUBSUJOH PO UIF GJSTU KPJOU - BOE POFT PO UIF TFDPOE KPJOU - 5IPTF QPTUVSFT BSF TFMFDUFE CZ UIF 3&64& BMHPSJUIN # BOE SFFYFDVUFE JO UIF UBSHFU UBTL $ SFTVMUJOH JO QPTUVSF XJUI MPPQT UIBU TFWFSFMZ MJNJUT UIF TQBO PG UIF BSN BT UIFZ BSF DPNQPTFE PG MPOH TFHNFOUT 5IF TQFDJFT EJTUSJCVUJPO -- JT SFNBSLBCMZ TJNJMBS CFUXFFO UIF TPVSDF BOE UIF UBSHFU UBTL 8IFO &91-03& JT SVO EJSFDUMZ PO UIF UBSHFU BSN UIPTF MPPQT BSF FMJNJOBUFE CZ UIF DPNQFUJUJPO XJUI QPTUVSF XJUIPVU MPPQT PS XJUI MPPQT OFBS UIF UJQ PG UIF BSN PG GBS MFTT DPOTFRVFODF. *O 'JHVSF UIF DPWFSBHF PG TFUT PG SBOEPN NPUPS DPNNBOET PG EJWFSTF TJ[FT JT IJHIMZ DPSSFMBUFE CFUXFFO UIF UXP BSNT 5IJT DPSSFMBUJPO JO UIF QSPEVDUJPO PG EJWFSTJUZ JT UIFSFGPSF BO BTTVNQ UJPO JU TFFNT QPTTJCMF UP SFMZ PO BOE FYQMPJU FWFO JO TPNF DBTFT XIFO UIF TFOTPSZ NPEBMJUJFT PS UIF NPSQIPMPHZ PG UIF SPCPUT BSF EJGGFSFOU CFUXFFO UBTLT. 'SPOUJFST JO 3PCPUJDT BOE "* ] XXXGSPOUJFSTJOPSH. 0#+&$5 */5&3"$5*0/ 5"4,4 &YQFSJNFOUBM 4FUVQ. 8F DPOTJEFS BO FYQFSJNFOU XIFSF B SPCPUJD BSN JOUFSBDUT XJUI BO PCKFDU BOE PCTFSWFT JUT EJTQMBDFNFOU BU UIF FOE PG UIF JOUFSBDUJPO *O B EFWFMPQNFOUBM DPOUFYU BO JOUFSBDUJPO UBTL JT SFMFWBOU BT JU. . .BSDI ] 7PMVNF ] "SUJDMF .

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(15) #FOVSFBV BOE 0VEFZFS. A. #FIBWJPSBM %JWFSTJUZ (FOFSBUJPO UISPVHI 3FVTF. CUBE (SOURCE TASK), EXPLORE ALGORITHM random motor babbling until t = 200. t = 500. t = 1000. initial position of the cube. robot. REUSE B. BALL (TARGET TASK), REUSE ALGORITHM t = 200. t = 500. t = 1000. t = 500. t = 1000. diversity of effects over 200 steps. C BALL (NO REUSE), EXPLORE ALGORITHM. t = 200. initial position of the ball. three interactions over 200 steps '*(63& ] 5IF DPWFSBHF PG UIF 3&64& FYQMPSBUJPO CFOFGJUT GSPN B IJHI EJWFSTJUZ PG FGGFDUT EVSJOH UIF CPPUTUSBQQJOH QIBTF 5IF HSBQIT TIPX UIF EJTUSJCVUJPO PG FGGFDUT EVSJOH UIF TUFQ CPPUTUSBQQJOH QIBTF JO SFE BOE EVSJOH UIF TVCTFRVFOU HPBMCBCCMJOH QIBTF JO CMVF BOE UIF DPSSFTQPOEJOH τ DPWFSBHF JO HSFFO τ = NN BDSPTT UISFF FYQMPSBUJPOT 5IF TPVSDF UBTL " JT UIF DVCF UBTL *U JT VTFE CZ UIF 3&64& BMHPSJUIN GPS UIF UBSHFU UBTL UIF CBMM UBTL # 5P DPNQBSF UIF 3&64& BOE UIF &91-03& BMHPSJUIN UIF FYQMPSBUJPO PG UIF CBMM UBTL VOEFS UIF &91-03& BMHPSJUIN JT QSFTFOUFE JO $ *OUFSFTUJOHMZ XF DBO TFF UIBU EVSJOH UIF FYQMPSBUJPO PG UIF TPVSDF UBTL UIF SPCPU POMZ MFBSOFE UP QVTI UIF DVCF BXBZ 5IJT IBT B OPUBCMF JOGMVFODF PO UIF FYQMPSBUJPO PG UIF UBSHFU UBTL UIF SFVTFE NPUPS DPNNBOET QSPEVDF FGGFDUT UIBU BMTP MBSHFMZ QVTI UIF CBMM BXBZ &WFO BGUFS UIF FOE PG UIF HPBM CBCCMJOH QIBTF PO UIF TPVSDF UBTL UIF BSFB TVSSPVOEJOH UIF SPCPU GFBUVSFT GFXFS FGGFDUT UIBO UIF SFTU PG UIF FGGFDU TQBDF 5IJT JMMVTUSBUFT UIF TBNF TPSU PG JTTVF BT UIF POF EJTDVTTFE JO 4FDUJPO 4UJMM JO UIJT DBTF UIF &91-03& BMHPSJUIN EPFT XPSTF XJUI POMZ UISFF JOUFSBDUJPOT BGUFS TUFQT UIF FYQMPSBUJPO JT CJBTFE UPXBSE UIF MPXFSSJHIU DPSOFS. 'SPOUJFST JO 3PCPUJDT BOE "* ] XXXGSPOUJFSTJOPSH. . .BSDI ] 7PMVNF ] "SUJDMF .

(16) #FOVSFBV BOE 0VEFZFS. #FIBWJPSBM %JWFSTJUZ (FOFSBUJPO UISPVHI 3FVTF. ball. coverage (in m 2). ball. cube. coverage (in m 2). 0.36. ball. 0.36. maximum coverage. maximum coverage. with reuse. 0.20. 0.20. without reuse. 0.10. 0.10. 0. 0 0. 200. 400. 600. 800. 1000. 0. 200. 400. 600. 800. timesteps. cube. coverage (in m 2). cube. 0.36. 1000. timesteps. ball. coverage (in m 2). cube. 0.36. maximum coverage. 0.20. 0.20. 0.10. 0.10. 0. maximum coverage. 0 0. 200. 400. 600. 800. 1000. 0. 200. 400. 600. 800. timesteps. 1000. timesteps. '*(63& ] 8IFUIFS SFVTJOH UIF DVCF PO UIF CBMM UBTL PS UIF CBMM PO UIF DVCF UBTL 3&64& CSJOHT BO JNQPSUBOU DPWFSBHF CPPTU FBSMZ JO FYQMPSBUJPO 5IF GJHVSF QSFTFOUT UIF NFEJBO PG UIF DPWFSBHF GPS UIF 3&64& BOE &91-03& DBTFT JO UIF GPVS QPTTJCMF DPNCJOBUJPOT PG UIF DVCF BOE CBMM UBTLT 5IF TIBEFE BSFB JT EFMJNJUFE CZ UIF UI BOE UI QFSDFOUJMFT PG SFQFUJUJPOT PG FBDI FYQFSJNFOU BOE UIF CFTU BOE XPSTU DBTF JT TIPXO CZ EBTIFE MJOFT 5IF FGGFDU PG 3&64& JT JODSFBTFE XIFO SFVTJOH GSPN UIF TBNF UBTL BOE UIF CBMM UBTL JT BCMF UP FYQMPJU UIF DVCF UBTL CFUUFS UIBO UIF SFWFSTF. random cube. coverage (in m 2). ball. 0.36. random ball. coverage (in m 2). cube. 0.36. maximum coverage. maximum coverage. with reuse. 0.20. 0.20. reuse ceiling. 0.10. 0.10. without reuse 0. 0 0. 200. 400. 600. 800. 1000. 0. timesteps. 200. 400. 600. 800. 1000. timesteps. '*(63& ] 5IF 3&64& NFUIPE JT BCMF UP FYQMPJU PCTFSWBUJPOT HFOFSBUFE CZ SBOEPN NPUPS CBCCMJOH 5IF TPVSDF UBTL JO UIFTF HSBQIT XBT FYQMPSFE VTJOH B QVSF SBOEPN NPUPS CBCCMJOH TUSBUFHZ 3FQFBUFE UJNFT. DPNNBOET GSPN UIF TPVSDF UBTL UIF 3ĲłŀĲ NFUIPE XPVME CF FRVJWBMFOU UP UIF SBOEPN NPUPS CBCCMJOH TUSBUFHZ XIFO SFVTJOH B SBOEPN NPUPS CBCCMJOH TPVSDF SBOEPNMZ TFMFDUJOH TBNQMFT GSPN B SBOEPN TPVSDF JT FRVJWBMFOU UP EJSFDUMZ TBNQMJOH UIF SBOEPN TPVSDF 5IF JNQSPWFNFOU JO DPWFSBHF IFSF DBO POMZ CF BUUSJCVUFE UIFO UP UIF TFMFDUJPO PG NPUPS DPNNBOET UISPVHI EJWFSTJUZ. QSJNJUJWFT FYQSFTTFE JO BO PCKFDUDFOUFSFE SFGFSFODF GSBNF o UIFZ BSF OPU UIF GPDVT PG UIJT BSUJDMF )PXFWFS BO JNQPSUBOU DPOTJEFSBUJPO JT UP FYBNJOF JG UIF 3ĲłŀĲ BMHPSJUIN DBO EFDSFBTF UIF QFSGPSNBODF PG UIF FYQMPSBUJPO 5IF SFTQPOTF JT PG DPVSTF QPTJUJWF 0OF DBO DPOTUSVDU B TPVSDF BOE B UBSHFU UBTL TP UIBU XBTUJOH IBMG PG UIF SBOEPN NPUPS CBCCMJOH QIBTF PO SFVTJOH NPUPS DPNNBOET HVBSBOUFFE OPU UP QSPEVDF BOZ JOUFSFTUJOH FGGFDUT DPVME OFHBUJWFMZ JNQBDU UIF FYQMPSBUJPO QFSGPSNBODF )FSF XF TIPX UIBU UIF 3ĲłŀĲ BMHPSJUIN JT SFBTPO BCMZ SPCVTU UP B DIBOHF JO UIF QPTJUJPO PG UIF PCKFDU JO UIF CBMM FOWJSPONFOU TPNF CVU OPU NVDI PG UIF QFSGPSNBODF JT MPTU *O UIF CBMM UBTL UIF CBMM JT MPDBUFE KVTU VOEFS UIF SPCPU 5IF EJTQMBDFE UBTL JT JO FWFSZ XBZ JEFOUJDBM UP UIF CBMM UBTL FYDFQU. 3PCVTUOFTT UP %JTTJNJMBSJUZ *O UIF QSFWJPVT FYQFSJNFOUT UIF DVCF BOE UIF CBMM TIBSF UIF TBNF MPDBUJPO SFMBUJWF UP UIF SPCPU 5IJT JT PG DPVSTF BO JNQPSUBOU SFBTPO GPS UIF FGGFDUJWFOFTT PG UIF 3ĲłŀĲ BMHPSJUIN 8IJMF UIFSF NBZ CF XBZT GPS UIF SPCPU UP BEBQU UP TVDI DIBOHF BOE TUJMM CF BCMF UP UBLF BEWBOUBHF PG 3ĲłŀĲ o GPS JOTUBODF CZ IBWJOH IJHIMFWFM NPUPS. 'SPOUJFST JO 3PCPUJDT BOE "* ] XXXGSPOUJFSTJOPSH. . .BSDI ] 7PMVNF ] "SUJDMF .

(17) #FOVSFBV BOE 0VEFZFS. coverage (in m 2). #FIBWJPSBM %JWFSTJUZ (FOFSBUJPO UISPVHI 3FVTF. random cube. ball [short reuse]. 0.36. coverage (in m 2). random ball. cube [short reuse]. 0.36. maximum coverage. maximum coverage. with reuse. 0.20. 0.20. 50 reuse steps 0.10. 0.10. without reuse. 0. 0 0. 200. 400. 600. 800. 1000. 0. 200. 400. 600. 800. timesteps. 1000. timesteps. '*(63& ] 3&64& BMMPXT UP TIPSUFO UIF CPPUTUSBQQJOH QIBTF 5IF , CPPU QBSBNFUFS JT FRVBM UP TUFQT JO GPS UIF 3&64& BMHPSJUIN IFSF 5IF TPVSDF UBTL JT FYQMPSFE XJUI SBOEPN NPUPS CBCCMJOH 3FQFBUFE UJNFT. ball. coverage (in m 2). displaced ball. 0.36. displaced ball. coverage (in m 2). ball. 0.36. maximum coverage. maximum coverage. displaced ball task 0.20. 0.20. entile. 0.10. 10th. 10th perc tile percen. 0.10. worst cases 0. 0 0. 200. 400. 600. 800. 1000. 0. 200. 400. 600. timesteps. 800. 1000. timesteps. '*(63& ] 3FVTJOH GSPN B EJTTJNJMBS CBMM UBTL IBT OP TJHOJGJDBOU JNQBDU PO QFSGPSNBODF *O UIF EJTQMBDFE UBTL UIF CBMM IBT CFFO NPWFE UP UIF TJEF PG UIF SPCPU SFOEFSJOH NPTU NPUPS DPNNBOET VTFGVM GPS JOUFSBDUJOH XJUI UIF CBMM PO POF UBTL VTFMFTT JO UIF PUIFS 3FQFBUFE UJNFT. UIBU UIF CBMM IBT CFFO NPWFE PO UIF SJHIU TJEF PG UIF SPCPU .PTU NPWFNFOUT HFOFSBUJOH BO JOUFSBDUJPO XJUI B CBMM XJMM OPU HFOFSBUF POF XJUI UIF PUIFS CBMM .PSFPWFS UIJT CBMM JT IBSEFS UP IJU XJUI SBOEPN NPWFNFOUT XJUI BO JOUFSBDUJPO QSPCBCJMJUZ PG WFSTVT CFGPSF 5IJT JT JNQPSUBOU CFDBVTF JU NFBOT UIBU JG NPWFNFOUT BSF XBTUFE PO SFFYFDVUJOH NPUPS DPNNBOET UIBU XJMM OPU IJU UIF CBMM UIF QSPCBCJMJUZ PG JOUFSBDUJOH XJUI UIF CBMM HPFT GSPN UP 5IJT JT SFGMFDUFE JO UIF SFTVMUT 'JHVSF 8IJMF UIF MPTT JO DPWFSBHF BU UIF NFEJBO JT TNBMM UIF EJGGFSFODF JT BQQBSFOU BU UIF UI QFSDFOUJMF JO CPUI DBTFT "OE UIF XIFO UIF EJTQMBDFE UBTL JT UIF UBSHFU UBTL UIF QFSGPSNBODF CFMPX UIF UI QFSDFOUJMF JT NVDI XPSTF GPS 3ĲłŀĲ UIBO GPS &ŅĽĹļĿĲ 8IJMF UIFZ BSF OPU FYQMPSFE IFSF UIFSF BSF TFWFSBM XBZT UP QSFWFOU OFHBUJWF USBOTGFS 0OF JT UP EFDSFBTF QSFVTF BT JU EFDSFBTFT UIF IPX UIF 3ĲłŀĲ BMHPSJUIN NPEJGJFT UIF PSJHJOBM &ŅĽĹļĿĲ BMHP SJUIN 8IFO QSFVTF JT FRVBM UP [FSP CPUI BMHPSJUINT BSF FRVJWBMFOU "OPUIFS QPTTJCJMJUZ JT UP EZOBNJDBMMZ BEKVTU QSFVTF CBTFE PO UIF SFMBUJWF QFSGPSNBODF PG UIF UXP CPPUTUSBQQJOH TUSBUFHJFT SBOEPN NPUPS CBCCMJOH PS SFVTFE NPUPS DPNNBOET 8F IBWF QSPQPTFE BO BMHPSJUINJD GSBNFXPSL UP EP QSFDJTFMZ UIBU JO #FOVSFBV BOE 0VEFZFS 6MUJNBUFMZ UIF EFDJTJPO UP VTF 3ĲłŀĲ PS OPU TPNFUJNFT DBOOPU CF NBEF JOTJEF UIF QSPCMFN XF EFGJOFE JU NVTU DPNF GSPN BO FYUFSOBM NFDIBOJTN XIJDI OFFET POMZ UP QPJOU PVU UIF FYJTUFODF PG B SFMBUJPOTIJQ CFUXFFO UBTLT XJUIPVU TQFDJGZJOH. 'SPOUJFST JO 3PCPUJDT BOE "* ] XXXGSPOUJFSTJOPSH. JU 8F JOWFTUJHBUF BO FYBNQMF XIFSF B DBSFHJWFS DPVME GJMM UIBU SPMF JO UIF OFYU TFDUJPO. 4DBGGPMEJOH %JWFSTJUZ 5IF 1PPM &YQFSJNFOU. 4P GBS UIF 3ĲłŀĲ BMHPSJUIN IBT CSPVHIU RVBOUJUBUJWF JNQSPWF NFOUT JO DPWFSBHF NPTU PG UIF UJNF JO UIF FBSMZ QIBTF PG UIF FYQMP SBUJPO 8F OPX JOUSPEVDF BO FYQFSJNFOU UIBU TIPX UIBU 3ĲłŀĲ DBO SBEJDBMMZ BGGFDU IPX FYQMPSBUJPO IBQQFOT OBNFMZ UIBU DBO BMMPX UP FYQMPSF BO FOWJSPONFOU UIBU JT EJGGJDVMU UP FYQMPSF EJSFDUMZ 8F DPOTJEFS UIF QPPM UBTL XIFSF UXP CBMMT BSF QSFTFOU JO UIF BSFOB XJUI POF PVU PG SFBDI 5IF SPCPU NVTU TUSJLF UIF GJSTU CBMM BOE NBLF JU DPMMJEF XJUI UIF TFDPOE CBMM UP JOUFSBDU XJUI JU 'JHVSF " 5IF TFDPOE PVUPGSFBDI CBMM JT UIF POMZ POF UIBU JT QFSDFJWFE UISPVHI UIF TFOTPSZ QSJNJUJWF 5IFSFGPSF JO SFTQPOTF UP UIF FYFDVUJPO PG B NPUPS DPNNBOE UIF FYQMPSBUJPO BMHPSJUIN SFDFJWFT UIF EJTQMBDFNFOU PG UIF TFDPOE CBMM POMZ 5IF FYQMPSBUJPO BMHPSJUIN JT UIFSFGPSF VOBXBSF PG BOZ JOUFSBDUJPO XJUI UIF GJSTU CBMM &YQMPSJOH TVDI B UBTL XJUI UIF &ŅĽĹļĿĲ BMHPSJUIN JT JOFGGJ DJFOU 5IF QSPCBCJMJUZ PG JOUFSBDUJOH XJUI UIF GJSTU CBMM EVSJOH UIF SBOEPN NPUPS CBCCMJOH QIBTF JT MPX 5IF QSPCBCJMJUZ PG JOUFSBDUJOH XJUI UIF GJSTU CBMM JO TVDI B XBZ UIBU JU DPMMJEFT XJUI UIF TFDPOE CBMM JT WFSZ MPX &WFO CZ TFUUJOH , CPPU UP . . .BSDI ] 7PMVNF ] "SUJDMF .