Introduction to Mobile Robotics Mapping with Known Poses

Transcription

1 Iroducio o Mobile Roboics Mappig wih Kow Poses Wolfra Burgard Cyrill Sachiss Mare Beewi Kai Arras

2 Why Mappig? Learig aps is oe of he fudaeal probles i obile roboics Maps allow robos o efficiely carry ou heir asks allow localiaio Successful robo syses rely o aps for localiaio pah plaig aciviy plaig ec. 2

3 The Geeral Proble of Mappig Wha does he eviroe look like? 3

4 The Geeral Proble of Mappig Forally appig ivolves give he sesor daa d { u u 2 2 u } o calculae he os likely ap * arg ax P d 4

5 Mappig as a Chicke ad Egg Proble So far we leared how o esiae he pose of he vehicle give he daa ad he ap. Mappig however ivolves o siulaeously esiae he pose of he vehicle ad he ap. The geeral proble is herefore deoed as he siulaeous localiaio ad appig proble SLAM. Throughou his secio we will describe how o calculae a ap give we kow he pose of he vehicle. 5

6 Types of SLAM-Probles Grid aps or scas [Lu & Milios 97; Gua 98: Thru 98; Burgard 99; Koolige & Gua 00; Thru 00; Arras 99; Haehel 0; ] Ladark-based [Leoard e al. 98; Caselaos e al. 99: Dissaayake e al. 200; Moeerlo e al. 2002; 6

7 Probles i Mappig Sesor ierpreaio How do we exrac releva iforaio fro raw sesor daa? How do we represe ad iegrae his iforaio over ie? Robo locaios have o be esiaed How ca we ideify ha we are a a previously visied place? This proble is he so-called daa associaio proble. 7

8 Occupacy Grid Maps Iroduced by Moravec ad Elfes i 985 Represe eviroe by a grid. Esiae he probabiliy ha a locaio is occupied by a obsacle. Key assupios Occupacy of idividual cells [xy] is idepede Bel P u 2 u x y Robo posiios are kow! Bel [ xy ] 8

9 Updaig Occupacy Grid Maps Idea: Updae each idividual cell usig a biary Bayes filer. Bel [ xy] η p [ xy] p [ xy] [ xy] u Bel [ xy] d [ xy] Addiioal assupio: Map is saic. Bel η p Bel [ xy ] [ xy ] [ xy ] 9

10 Updaig Occupacy Grid Maps Updae he ap cells usig he iverse sesor odel Bel [ xy ] [ xy ] P u + [ xy ] P u [ xy ] P [ xy ] Or use he log-odds represeaio [ xy ] [ ] xy P Bel Bel [ xy ] [ xy ] [ xy ] [ xy ] B log odds u B : logodds [ xy logodds ] P x odds x : [ xy ] P x + B 0

11 Typical Sesor Model for Occupacy Grid Maps Cobiaio of a liear fucio ad a Gaussia:

12 Key Paraeers of he Model 2

13 Occupacy Value Depedig o he Measured Disace +d +d 2 +d 3 -d 3

14 Deviaio fro he Prior Belief he sphere of ifluece of he sesors 4

15 Calculaig he Occupacy Probabiliy Based o Sigle Observaios 5

16 Icreeal Updaig of Occupacy Grids Exaple 6

17 Resulig Map Obaied wih Ulrasoud Sesors 7

18 Resulig Occupacy ad Maxiu Likelihood Map The axiu likelihood ap is obaied by clippig he occupacy grid ap a a hreshold of 0.5 8

19 Occupacy Grids: Fro scas o aps 9

20 Tech Museu Sa Jose CAD ap occupacy grid ap 20

21 Aleraive: Siple Couig For every cell cou hisxy: uber of cases where a bea eded a <xy> issesxy: uber of cases where a bea passed hrough <xy> Bel [ xy ] his x his x y y + isses x y Value of ieres: Preflecsxy 2

22 22 The Measuree Model if if k k x f x f k k x f x p ς ς ς. pose a ie : 2. bea of sca : 3. axiu rage readig: 4. bea refleced by a obec: 0 ς x 0 x f

23 23 Copuig he Mos Likely Map Copue values for ha axiie Assuig a uifor prior probabiliy for p his is equivale o axiiig applic. of Bayes rule ax arg * x x P T T x P x P x x P * l arg ax arg ax ax arg

24 24 Copuig he Mos Likely Map + 0 * l l arg ax k J T N k x f I x f I ς Suppose T N x f I ς α T N k k x f I 0 β

25 Meaig of α ad β α T N I f x ς correspods o he uber of ies a bea ha is o a axiu rage bea eded i cell his β T N k 0 I f x k correspods o he uber of ies a bea ierceped cell wihou edig i i isses. 25

26 Copuig he Mos Likely Map We assue ha all cells are idepede: * J arg ax α l If we se α β 0 + β l we obai α α + β Copuig he os likely ap aous o couig how ofe a cell has refleced a easuree ad how ofe i was ierceped. 26

27 Differece bewee Occupacy Grid Maps ad Couig The couig odel deeries how ofe a cell reflecs a bea. The occupacy odel represes wheher or o a cell is occupied by a obec. Alhough a cell igh be occupied by a obec he reflecio probabiliy of his obec igh be very sall. 27

28 Exaple Occupacy Map 28

29 Exaple Reflecio Map glass paes 29

30 Exaple Ou of 000 beas oly 60% are refleced fro a cell ad 40% iercep i wihou edig i i. Accordigly he reflecio probabiliy will be 0.6. Suppose pocc 0.55 whe a bea eds i a cell ad pocc 0.45 whe a cell is ierceped by a bea ha does o ed i i. Accordigly afer easurees we will have *0.6 * *0.4 9 *0.6 * 9 *0.4 9 *0.2 Whereas he reflecio ap yields a value of 0.6 he occupacy grid value coverges o. 30

31 Suary Occupacy grid aps are a popular approach o represe he eviroe of a obile robo give kow poses. I his approach each cell is cosidered idepedely fro all ohers. I sores he poserior probabiliy ha he correspodig area i he eviroe is occupied. Occupacy grid aps ca be leared efficiely usig a probabilisic approach. Reflecio aps are a aleraive represeaio. They sore i each cell he probabiliy ha a bea is refleced by his cell. We provided a sesor odel for copuig he likelihood of easurees ad showed ha he couig procedure uderlyig reflecio aps yield he opial ap. 3