Mobile Robots Mapping

Transcription

1 Mobile Robos Mapping 1

2 Roboics is Easy conrol behavior percepion modelling domain model environmen model informaion exracion raw daa planning ask cogniion reasoning pah planning navigaion pah execuion acuaor commands sensing acing environmen/world 2

3 Agenda Moivaion Basic Definiions Mapping wih Occupancy Grids 3

4 Moivaion problem of he acquisiion of a represenaion of he environmen generaion of maps is a cenral piece of navigaion maps are commonly used for localizaion basis for decision making probably enriched by semanic informaion 4

5 Mapping is (sill) a ho Topic 5

6 Plabusch Tunnel 6

7 The General Problem of Mapping formally, mapping involves, given he sensor daa, d { u, z, u, z 1 2 2,, u, z n 1 n } o calculae he mos likely map m * arg max m P( m d) u conrol inpu, z sensor measuremens 7

8 Wha is SLAM? we mainly alk abou Simulaneous Localizaion and Mapping (SLAM) is a chicken-and egg problem making a map is easy if we know he pose localizaion is easy if we have a map, we have o inerleave localizaion and mapping 8

9 Why is SLAM hard? he hypohesis space of all possible maps is huge (easily more han 10 5 variables) noise in percepion and acing - commands and observaions are uncerain percepional ambiguiies, differen places and landmarks may look similar cycles in he environmen, places reappear 9

10 The SLAM Problem a robo is exploring an unknown, saic environmen Given: he robo s conrols observaions of nearby feaures Esimae: map of feaures pah of he robo 10

11 Maps wih Landmarks map comprises (disinguishable) landmarks and heir posiion landmarks can be very differen rees special geomeric shapes RFID ags visual ags visual feaures robo need appropriae sensors 11

12 Maps as Occupancy Grids represen he environmen as grid map grid cells are eiher free or occupied may represen some uncerainy can be in 2d 2.5d 3d 12

13 Mapping wih Known Pose we make he problem less hard we assume an oracle ha ells us he robo s pose, e.g. odomery occupancy grids addresses he generaion of consisen maps from noisy observaions occupancy grids are a recangular arrangemen of random variables resembles a represenaion of probabiliy of maps 13

14 poserior The Basis likelihood prior P( x y) P( y x) P( x) P( y) Bayes Rule evidence 14

15 Bayes Condiioned P y x, z P(x z) P x y, z = P(y z) adding a addiional condiional random variable 15

16 Occupancy Grid Maps inroduced by Moravec and Elfes in 1985 represen environmen by a grid esimae he probabiliy ha a locaion m i is occupied by an obsacle key assumpions occupancy of individual cells (m[x, y]) is independen Bel ( m Bel ( m robo posiions are known! ) P( m i u1, z2, u [ i] ) 1, z ) 16

17 Updae Occupancy Grid rea single cells as binary random variable p(m i = 1) represens he probabiliy m i is occupied use log odds raio avoids problems wih probabiliies close o 0 or 1 rounding errors sauraion allows summaion insead of muliplicaion l( x) : log p( x) p( x) p( x) log 1 p( x) 17

18 Updae Occupancy Grid occupancy_grid_updae({l -1,i },x,z ) for all cells m i do if m i in percepual field of z hen l, i =l -1, i +inverse_sensor_model(m i,x,z )-l 0 else l, i =l -1, I endfor reurn {l,i } l 0 represens he iniial probabiliy in cells 18

19 Inverse Sensor Model represens he probabiliy of a cell being occupied given a posiion and sensor readings inverse_sensor_model(m i, x, z ) = log p(m i z, x ) 1 p(m_i z, x ) reflecs also he uncerainy of he sensor reading 19

20 Simple Inverse Sensor Model 20

21 Incremenal Updaing of Occupancy Grids 21

22 Compuing he Mos Likely Map 22

23 23 Compuing he Mos Likely Map compue values for m ha maximize assuming a uniform prior probabiliy for p(m), his is equivalen o maximizing (applicaion of Bayes rule) ),,,,, ( max arg 1 1 * m x x z z m P m T m T m m x m z P x m z P x x m z z P m * ), ( log arg max ), ( arg max ),,,,, ( max arg

24 Mos Likely Map Algorihm map_occupancy_grip_mapping(x 1:, z 1: ) se m = 0 repea unil convergence for all cells m i do reurn m endfor endrepea m i = argmax k=1,0 log p z x, m i = k 24

25 Compuing he Mos Likely Map [Thrun e.al] 25

26 Sensor wih Muliple Measuremens laser scanner repor a se of k measuremens a we assume he individual measuremens independen p z x, m = p(z k x, m) i=1..k 26

27 Thank you! 27