Types of SLAM-Problems CSE-571 • Grid maps or scans Probabilistic Robotics [Lu & Milios, 97; Gutmann, 98: Thrun 98; Burgard, 99; Konolige & Gutmann, 00; Thrun, 00; Arras, 99; Haehnel, 01;…] Mapping • Landmark-based [Leonard et al., 98; Castelanos et al., 99: Dissanayake et al., 2001; Montemerlo et al., 2002;… Problems in Mapping Occupancy Grid Maps • Introduced by Moravec and Elfes in 1985 • Sensor interpretation • Represent environment by a grid. • How do we extract relevant information • Estimate the probability that a location is from raw sensor data? occupied by an obstacle. • How do we represent and integrate this information over time? • Key assumptions • Occupancy of individual cells is independent • Robot locations have to be known K Bel ( m ) P ( m | u , z , u , z ) = t t 1 2 t 1 t � • How can we estimate them during [ xy ] Bel ( m ) � = t mapping? x , y • Robot positions are known!
Typical Sensor Model Updating Occupancy Grid Maps for Occupancy Grid Maps • Idea: Update each individual cell Combination of a linear function and a using a binary Bayes filter. Gaussian: [ xy ] [ xy ] [ xy ] [ xy ] [ xy ] [ xy ] Bel ( m ) p ( z | m ) p ( m | m , u ) Bel ( m ) dm = � � t t t t t 1 t 1 t 1 t 1 � � � � • Additional assumption: Map is static. [ xy ] [ xy ] [ xy ] Bel ( m ) p ( z | m ) Bel ( m ) = � t t t t 1 � Updating Occupancy Grid Maps Alternative: Simple Counting • Updated using inverse sensor model and • For every cell count odds ratio • hits( x , y ): number of cases where a beam ended at < x , y> ( ) ( ) ( ) • misses( x , y ): number of cases where a beam P m [ xy ] | z , x 1 P m [ xy ] Bel m [ xy ] � � � ( ) [ xy ] t t t t t 1 Bel m 1 1 � = � � + � � � passed through <x,y> � ( ) ( ) ( ) � t [ xy ] [ xy ] [ xy ] 1 P m | z , x P m 1 Bel m � � � � t t t t t 1 � hits( x , y ) [ xy ] Bel ( m ) • or log-odds ratio = hits( x , y ) misses( x , y ) + ( ) ( ) ( ) ( ) • Assumption: P ( occupied ( x,y )) = P ( reflects ( x,y )) [ xy ] [ xy ] [ xy ] [ xy ] B m log odds m | z , x log odds m B m = � + t t t t t t 1 �
Incremental Updating Resulting Map Obtained with of Occupancy Grids (Example) Ultrasound Sensors Tech Museum, San Jose Occupancy Grids: From scans to maps CAD map occupancy grid map
Recommend
More recommend