4 Experimental Results
4.1 Image Capture
       
    The Experiment conducted, consisted of taking stereo images at certain intervals, and then tracks the robot’s movements. The robot was instructed to move forward 100 cms. each time. Measurements were taken (see Table 1), and the robot’s odometry readings noted (see Table 2).

    Table 1. Robot’s location experimentally measured in the laboratory.

       
      Location
      Location (x,y,z)
      dx
      dz
      0
      257.5
      0
      0
      		    
      1
      257.5
      0
      100
      0.0
      100
      2
      264.0
      0
      199
      6.5
      99
      3
      269.5
      0
      298
      5.5
      99
      4
      275.5
      0
      400
      6.0
      102

     

    Table 2. Robot’s location obtained by its own odometry.

       
      Location
      		 q (degrees) x (cms.) z (cms.) dx dz Distance to front wall
      0
      0.00
      0
      0.1
      		    
      721.5
      1
      359.47
      7
      98.5
      7
      98.4
      623.1
      2
      359.16
      18
      196.8
      11
      98.3
      524.8
      3
      358.80
      34
      295.0
      16
      98.2
      426.6
      4
      358.48
      59
      398.4
      25
      103.4
      323.2

     

    To begin, the images captured are chromatic, but don’t need this much information, so only the blue component con the images is stored. The images are also reduced to one quarter to improve speed in detecting features. The resulting images are achromatic (grey scale) and occupy 384´ 288 pixels, see Figure 7.

    Figure 7. Stereo images captured at initial position.

    4.2 Feature Detection

       
    Once the images were stored we attempt to find 25 features in each image. The KLT filter to find features is constrained by the following parameters:
     
     
       
      Parameter
      Value
      mindist
      20
      window_size 
      7
      min_eigenvalue 
      1
      min_determinant
      0.01
      min_displacement
      0.1
      max_iterations
      10
      max_residue
      10
      grad_sigma
      1
      smooth_sigma_fact
      0.1
      pyramid_sigma_fact
      0.9
      sequentialMode
      FALSE
      smoothBeforeSelecting
      TRUE
      writeInternalImages
      FALSE
      search_range
      15
      nSkippedPixels
      0

     

    Two images are saved Lfeat0.ppm and Rfeat0.ppm showing all the features detected in each image.
     
     

    Figure 8. Lfeat0.ppm and Rfeat0.ppm showing the features detected by the KLT algorithm.
     
     

    Next the features coordinates xL,yL and xR,yR are converted to camera pixels
     
     

    u = xscale ´ x

    v = yscale ´ y
     
     

    where xscale and yscale are the ratios of the images height and width respectively.
     
     

    xscale = 752 ¸ 384

    = 1.9583

    yscale = 582 ¸ 288

    = 2.0208

       
    4.3 Stereo Match


    Then for each feature an epipolar line in the right image is calculated and the nearest features searched in a range given by mindisp=20 and closest to a predicted disparity given by:
     
     

    where Z was the approximate distance of the features and B the inter-ocular separation of the head, 25.2 cms. (see Figure 4).

    After all the matches have been found, a search is done to remove any duplicates, i.e. if two left features are matched to the same right feature.

    Now we can calculate the matched features 3D position using the following head parameters:
     
     

    Fku = 1939.53;

    Fkv = 2009.64;

    U0 = 752/2;

    V0 = 582/2;

    Pp = 25.2/2; /* Horizontal offset between pan and elevation axes */

    Cc = 4.0; /* Offset between elevation axis and optic axes */

    Nn = 7.5; /* Offset along optic axis between vergence axes and optic

    centres of cameras */

    Ii = 25.2; /* Inter-ocular separation */

    Hh =79; /* Height of head centre above the ground */
     
     

    And the coordinates, changed to the Fixed World Coordinate Frame. With this the position of the robot can be estimated and then the appropriate files are saved (see Figure 9). In file LMatches0.txt the coordinates of each feature are shown as well as the number of the corresponding feature in the right image. Features with no match found are given a value of –1. RMatches0.txt contains the features found in the right image. A value of 1 represents that it has been matched with a left feature, while –1 represents that no match was found.

    File RealWorld0.txt contains the 3D coordinates of the matched features, as seen in Figure 11.
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     

(a)
(b)

 
     
     

    (a) (b)

    Figure 9. (a) Contents of file LMatches0.txt . (b) Contents of file RMatches0.txt.
     
     

    The matched features are also placed on the images and saved in PPM format. Two files are generated; LMatch0.ppm and RMatch0.ppm, see Figure 10. Comparing the image pair in Figure 8 and Figure 10, we see not all features detected were stereo matched.
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     

    Figure 10. Lmatch0.ppm and Rmatch0.ppm showing matched features in each image.
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     

    Figure 11. Contents of file RealWordl0.txt

    4.4 Feature Tracking

       
    At this moments we proceed to track the features from the previous left image to the new left image taken at the new location. If some features are not tracked to the next image, the algorithm attempts to find new features to replace them. Then 25 features are searched in the new right image, and the process repeats itself.

    At the end, a new file is saved containing the history of the features in the left image, see Figure 12.

    Figure 12. Feature Table showing the feature history in the left side.

    In Figure 12, we see that in frame0 (initial location), 16 features are stereo matched, denoted by their positive values. In frame 1, tracked features are given a value of zero. Only 5 features are tracked from the first image to the second. But since the algorithm searched new features to replace the untracked, in frame 2 we are able to track 8 features. Then only 2 features were tracked to frame 3, and finally only 1 features is tracked to frame 4.
     

    4.5 Experimental Environment

    The laboratory wall in front of the robot during this experiment is shown in Figure 13. The robot was placed approximately at 7 mts. from this wall and then moved toward the wall at 100 cms. intervals. The dimensions of this wall are shown in Figure 14. And Figure 15, shows the coordinates of the principal features. The origin for these coordinates was placed at the bottom-left hand corner of the wall. In Figure 16 the side- wall is shown with its dimensions.
     
     

    Figure 13. Laboratory wall which the robot faced during this experiment.

    Figure 14. Front wall with all dimensions shown in centimeters.
     


    Figure 15. Front Wall with principal feature coordinates shown.
    Figure 16. Partial view of the side-wall located to the right of the front wall shown in Figure 13.
     

    4.6 Results

    In Table 3 we see the 3D position of some features found at the starting position. The average error in the x direction is 0.3 cms. In the vertical direction the average error is 9 cms.

    Table 3. Experimental and Real coordinates of the features matched and found in Figure 15
     
    Experimental
    Real
    Feature
    x
    y
    z
    x
    y
    		 dx dy
    0
    210.1712
    124.4368
    733.8098
    210.9
    134.0
    -0.7
    -9.6
    2
    198.1255
    252.3184
    707.7735
    194.5
    259.0
    3.6
    -6.7
    3
    213.7301
    252.5516
    708.869
    214.5
    259.0
    -0.8
    -6.4
    4
    281.4418
    190.4332
    655.2688
    281.5
    212.0
    -0.1
    -21.6
    5
    277.3173
    142.9643
    724.0054
    277.3
    148.0
    0.0
    -5.0
    6
    245.7721
    169.7695
    739.1494
    244.0
    178.5
    1.8
    -8.7
    8
    277.4464
    126.1343
    720.4741
    277.3
    138.0
    0.1
    -11.9
    9
    264.5356
    167.4504
    719.7704
    264.9
    178.5
    -0.4
    -11.0
    11
    232.0163
    209.9571
    753.4997
    232.5
    217.0
    -0.5
    -7.0
    13
    277.4094
    185.1026
    730.7184
    275.3
    194.0
    2.1
    -8.8
    14
    205.1867
    238.3834
    710.5756
    204.5
    241.5
    0.7
    -3.1
    15
    354.0995
    208.4073
    747.6114
    356.0
    217.0
    -1.9
    -8.6

    In Figure 18, Figure 19, Figure 20, and Figure 21 the 3D position calculated for the matched features are shown for each stage. As can be seen the features appear shifted to the left as the robot progresses. This indicates that the robot has moved in the positive direction of the x-axis, agreeing with the robot’s odometry.

    Figure 17. Image sequence of left images captured during the experiment.

    Figure 18. Position of the features found and actual position of the features shown in Figure 15 at Location 0.

    Figure 19. Position of the features found and actual position of the features shown in Figure 15 at Location 1.

    Figure 20. Position of the features found and actual position of the features shown in Figure 15 at Location 2.

    Figure 21. Position of the features found and actual position of the features shown in Figure 15 at Location 3.

    Figure 22. Features detected and stereo matched at each location. The values used for Z are referenced to the robot’s coordinate frame.

    The results of robot localization are as follow:
     
     

    Location
    x
    -y
    z
    1
    12.8073
    -1.2278
    95.7116
    2
    3.0721
    -3.5914
    90.4321

     

    These values show the robot displacement calculated at the given location.
     
     

    Table 4. Statistics of Results

    Location Features

    Found and/or 

    Replaced

    		 Matched

    Features

    		 Tracked

    Features

    		 Features used 

    to Estimate

    Position
    0
    22,25
    16
    		    
    1
    25,23
    18
    5
    4
    2
    25,16
    12
    8
    5
    3
    25,08
    9
    2
    -
    4
    		  
    4
    1
    -


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Last update: 12/11/99

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Copyright © 1999 Manuel Noriega.