The document outlines a research project on developing edge detection methods and walking strategies for multi-legged robots. It discusses using morphological operations on hexagonal grid images to remove noise and detect edges for low resolution images in real-time applications with low computational power. It describes developing structuring elements of various sizes and directions, and comparing performance of hexagonal versus rectangular grid images. The document also explores using fuzzy morphology and discusses evaluating different methods to determine the optimal approach for edge detection to enable efficient walking strategies for robots with damaged legs.

1. Department of Mechanical & Electro-Mechanical Engineering
by Kazi Mostafa

2. Outline
Introduction and Background
Research Objectives
Related Research Work
Methodology
Conclusion
April 03, 2015 2

3. Outline
Introduction and Background
Research Objectives
Related Research Work
Methodology
Conclusion
April 03, 2015 3

4. Multi-legged Robot Walking Strategy
 For low computational power, low resolution images in real
time application; efficient edge detection method is crucial
 Edge detection method for multi legged robot to detect
standing zone edges, gap/obstacle
 Walking strategy for multi legged robot with damaged leg
 We focused small robot with low computation power
4April 03, 2015

5. Edge Detection
Edge detection effectiveness depends on quality of
input image
Images are processed in a rectangular grid
Increases cost & decreases performance
Numerous types of sampling systems are feasible
5April 03, 2015

6. Outline
Introduction
Background
Research Objectives
Related Research Work
Methodology
Conclusion
April 03, 2015 6

7. Mathematical Morphology
 Morphological erosions & dilations produce results identical to
the nonlinear minimum & maximum filters
7
Figural representation of Grayscale Morphology formula (Dilation)
Dilation
The value of the output pixel is the maximum value of all the
pixels in the input pixel's neighborhood
Structuring Element
Input Image Output Image

8. Classical Sets
8
Classical sets: either an element belongs to the set or it does
not
For example, for the set of integers, either an integer is even or
it is not (it is odd)
Another example is for black & white photographs, one cannot
say either a pixel is white or it is black
When we digitize a b/w figure, we turn all the b/w and gray
scales into 256 discrete tones
April 03, 2015

9. What is Fuzzy Set?
Fuzzy sets first introduced by Lotfi A. Zadeh[1] as an extension of the
classical set theory
In crisp set a pixel is either black or white. For edge detection, its an
edge or a no-edge. But the edges are not always precisely defined.
Fuzzy images are characterized by the degree to which each pixel
belongs to a particular region
9
Crisp set and fuzzy set for grayscale image
[1] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.
Crisp set
“dark gray-levels”
fuzzy set
“dark gray-levels”
April 03, 2015

10. Fuzzy Morphology
The word “fuzzy” means “vague”. Fuzziness occurs when the
border of information is not clear-cut
It can handle the idea of partial truth & false
Fuzzy set theory allows the gradual calculation
FM uses the concepts of fuzzy set theory
FM is the extension of mathematical morphology to fuzzy sets
10April 03, 2015

11. Outline
Introduction
Background
Research Objectives
Related Research Work
Methodology
Conclusion
11April 03, 2015

12. Research Objectives
The purpose of this study is to
Develop structuring elements (morphological gradients)
for low resolution images
Apply proposed method for noise removal and edge
detection
Derive efficient walking strategies by using image based
method and with damaged leg
12April 03, 2015

13. Outline
Introduction
Background
Research Objectives
Related Research Work
Methodology
Conclusion
13April 03, 2015

14. Mathematical Morphology
14April 03, 2015
Serra (1986)
Z. Yu-qian
(2006)
Y. Zhang
(2010)
X. Bai
(2010)
Zhang
(2015)
A good review of morphological operator
Detect the edge of lungs CT image with salt-and-
pepper noise
Comparison between Morphological edge detection
and traditional edge operator
Multiscale top-hat transformations based on SE’S has
been constructed
The Application of Mathematical Morphology & Sobel
Operator in Infrared Image Edge Detection

15. Fuzzy Morphology
15
Publications about Fuzzy Morphology in Image Processing over the last 30 Years
Tree of fuzzy morphology
 The most renowned concept of fuzzy
morphology is the alpha-morphology
 It’s founded on the level sets of fuzzy
membership degree function and first
introduced by Bloch et al

16. Multi Legged Robot
Considerable research[1,2] done on robot vision and has been primarily
based on the rule of forbidden walking regions
Inagaki[3] investigated the leg failure situations in hexapod robots of
which one leg was damaged.
More recently, Yang[4] mentioned that it is helpful to lock the joint
associated with a damaged motor.
However, locking mechanism always cannot provide support. When
collapse occurs at 2nd or 3rd joint in a leg
16
[1] R. Ponticelli and P. G. de Santos, "Obtaining terrain maps and obstacle contours for terrain-recognition tasks," Mechatronics, vol. 20, 2010.
[2] J. Estremera, et. al. "Continuous free-crab gaits for hexapod robots on a natural terrain with forbidden zones: An application to humanitarian demining,” Robotics & Autonomous Systems, 2010.
[3] K. Inagaki, "Gait study for hexapod walking with disabled leg," in Intelligent Robots and Systems, IROS'97.
[4] J.-M. Yang, "Gait synthesis for hexapod robots with a locked joint failure," Robotica, vol. 23, 2005.

17. Outline
Introduction
Background
Research Objectives
Related Research Work
Methodology
Conclusion
17April 03, 2015

18. Binary Morphology
18April 03, 2015

19. Binary Morphology
19
Simulated Hexagonal Grid
d=3d=2d=1
Many square grids combine together to create a pixel block.
For example, d= 7;
Combines 120 rectangular grids.
Resolution = (Summation of 120 pixels gray values)/120
d=4
Image Resampling
April 03, 2015

20. Image Resampling
20
Different values for simulated hexagonal grid
Image conversion from rectangular to simulated hexagonal grid:
(a) hexagonal image(D=2) (b) hexagonal image (D=7)April 03, 2015

21. Simulated Hexagonal Image
21April 03, 2015

22. Structuring elements with various sizes
& directions
22April 03, 2015

23. Noise Removal
The proposed noise removal method: (a) Noisy image (a) Noise-free image
 The proposed method applied opening followed by closing with various combinations of
SEs
 The better combination to remove noise was defined by horizontal, 60°, 120°, and three-by-
three structuring element
23

24. Edge Detection
Edge detection achieved by applying
various directional three-by-three SEs
on the hexagonal grid
24
The performances of the three-by-three
hexagonal SEs were superior to those of
their five-by-five
The smaller circular-shape hexagonal
SEs achieved superior performance in
identifying curved edges
By contrast, larger SEs introduced
unwanted thickness & discontinuities
April 03, 2015

25. Edge Detection
Edge detection achieved by applying
various directional three-by-three SEs
on the rectangular grid
 Numerous unwanted discontinuities
in the rectangular images
April 03, 2015 25

26. Performance evaluation
26
Combination of
Structuring Elements
The Face Test Image
MSE Ratio of edge pixels
to image size (%)
Hexagonal
Image
Horizontal, 60° and 120° SE
Horizontal, Vertical and 120° SE
Horizontal, Vertical and 60° SE
Vertical, 60° and 120° SE
0.97
1.47
3.02
5.05
15.78
15.02
14.79
14.23
Rectangular
Image
Horizontal, 60° and 120° SE
Horizontal, Vertical and 120° SE
Horizontal, Vertical and 60° SE
10.56
11.36
12.02
13.07
12.93
12.71

27. 27
Rectangular Grid
Image
Hexagonal Image
Image
Fuzzification
Hexagonal
Fuzzy SE
Fuzzy
Morphology
Hexagonal
Multi scale SE
Grayscale
morphology
Noise Removal
& Edge
detection
Evaluate both
method
Find the
optimum one
Top Hat
Transformation
to enhance
edges
Resampling
(Rectangular
to hexagonal
Grid)
Grayscale & Fuzzy Morphology
April 03, 2015

28. Grayscale Morphology
28
D=2 D=4 D=7
April 03, 2015

29. Grayscale Morphology
Hexagonal Structuring Elements (3x3, 5x5, 7x7)
Hexagonal Grayscale Morphological Operator
29
(c)(b)(a)
(a) Hexagonal image
(b) Structuring element
(c) After Dilation
April 03, 2015

30. Grayscale Morphology (Multiscale)
 Multi scale morphological analysis seems to be more favorable than single-scale
analysis
where B is the SE and n is the number of operations
 Multiscale Dilation = A⊕nB, and Multiscale Erosion = AΘnB,
where A is the input image, B is the SE, and n is the number of operations
 Multiscale Gradient = (A⊕nB) – (AΘnB)
 Multiscale Gradient = (A●nB) – (AonB)
30
,
1
   
timesn
BBBBBnB


April 03, 2015

31. Edge Detection (Morphological Gradient)
Multi-scale Gradient = (A⊕nB) – (AΘnB)
31
Edge image by using hexagonal morphological gradient operator (a) 3x3(b) 5x5
Multiscale hexagonal morphological gradient 3x3 SE (a) n=1(b) n=2(c) n=3
April 03, 2015

32. Edge Enhancement (Top hat transformation)
White top-hat transformation:
𝑾𝑻𝑯 𝒙, 𝒚 = 𝒇 𝒙, 𝒚 − 𝒎𝒊𝒏 𝒇 ⊖ 𝑩 ⊕ 𝑩, 𝒇 𝒙, 𝒚
Black top-hat transformation:
𝑩𝑻𝑯 𝒙, 𝒚 = 𝒎𝒂𝒙((𝒇 ⊕ 𝑩) ⊖ 𝑩, 𝒇 𝒙, 𝒚 ) − 𝒇 𝒙, 𝒚
32
MW = max (WTH1, WTH2, …); MB = max (BTH1, BTH2, …)
Enhanced Edges = (Original Image x W1) + (MW x W2) – (M B x W3)
April 03, 2015

33. Edge Enhancement
 Enhanced edges after applying top-hat transform (3x3 SE)
33April 03, 2015

34. PerformanceEvaluation
SE Lena Pepper Barbara
MSE Linear Index
of fuzziness
MSE Linear Index
of fuzziness
MSE Linear Index of
fuzziness
3x3 52.98 0.064 57.47 0.062 38.56 0.116
5x5 46.47 0.137 48.77 0.137 31.28 0.203
7x7 41.24 0.201 42.36 0.205 26.65 0.283
9x9 37.16 0.255 37.37 0.265 23.35 0.353
34
Comparison of different HSE Edge detection using morphological gradient
SE Lena Pepper Barbara
MSE Linear Index
of fuzziness
MSE Linear Index
of fuzziness
MSE Linear Index
of fuzziness
3x3 56.21 0.054 59.23 0.055 43.41 0.101
5x5 53.91 0.126 56.36 0.105 42.56 0.155
7x7 51.09 0.153 53.01 0.133 40.55 0.189
9x9 46.81 0.181 48.25 0.175 36.41 0.229
Comparison of different HSE enhanced Edge detection
April 03, 2015

35. Fuzzy Morphology
35
Rectangular
grid Gray scale
Image
Image
Resampling
(Rectangular to
Hexagonal Grid)
Image
Fuzzification
(S-membership
function)
Fuzzy
Morphology
(Noise removal &
Edge detection)
Defuzzification
Performance
Evaluation
System diagram for performing fuzzy image processing on hexagonally sampled grid
April 03, 2015

36. Steps of Fuzzy Image Processing
36April 03, 2015

37. Image Fuzzification
S-membership function as given below:
μ(x) = 0 x<a,
= 2 [(x -a)/(c - a)]2 a < x < b
= 1 – 2 [(x - c)/(c - a)]2 b < x < c,
= 1 x > c,
where, b is any value between a and c. For a = Xmin, c = Xmax
37
Membershipdegree
Pixels
April 03, 2015

38. Image Fuzzification
38
Image fuzzification (a) test image pepper, and (b) fuzzified image pepper
April 03, 2015

39. Fuzzy Structuring Elements
39April 03, 2015

40. Noise Removal
40
The proposed noise removal method: (a) noisy image (10.13 dB),
(b) Rectangular grid (19.97 dB), (c) hexagonal grid (27.09 dB)
April 03, 2015

41. Edge Detection
Edge detection by applying different directional 3 by 3 fuzzy SE on hexagonal grid41

42. Performance evaluation
Mean Square Error (MSE),
Signal to Noise Ratio (SNR) and
The ratio of edge pixels to image size 42
Standard test image & it’s Ground Truth prepared manually for evaluation
April 03, 2015

43. Performance evaluation
Method
Pepper Test Image
MSE SNR Ratio of edge pixels to
image size
Hexagonal
Image
Combination of Horizontal, 60° and 120° SE 0.74 21.97 17.8%
Combination of Horizontal, Vertical and 120° SE 1.92 19.85 17.01%
Combination of Horizontal, Vertical and 60° SE 4.02 17.67 16.61%
Combination of Vertical, 60° and 120° SE 7.05 15.22 16.01%
Combination of 60° and 120° SE 7.31 15.06 15.85%
Rectangular
Image
Combination of Horizontal, 60° and 120° SE 10.56 12.56 14.06%
Combination of Horizontal, Vertical and 120° SE 11.36 12.43 14.01%
Combination of Horizontal, Vertical and 60° SE 12.02 12.09 13.81%
Combination of 60° and 120° SE 13.06 11.06 13.61%
43
Quantitative measure obtained by edge detectors in hexagonal grid and rectangular
grid by using fuzzy hexagonal morphology for real test images Pepper

44. Better Walking Strategies for Multi-legged Robots
Multi legged robots present various limitations, such as traveling
on discontinuous terrain and navigation systems
Moreover, there are several kinds of damages can be happen in
multi legged robot legs
Thus, we proposed image-based walking strategy
44April 03, 2015

45. Better Walking Strategies for Multi-legged Robots
An Image-based Walking Strategy
45
Geometric model of the
proposed hexapod robot A uniformly distributed random terrain Terrain edges (black lines)
April 03, 2015

46. 46
Discontinuous terrain consisting of the
standing zone (white), forbidden zone
(black), and edges (yellow)
7 by 7 structuring element
An Image-based Walking Strategy

47. Hexapod Parameters
47
The 2-3-6 gait support pattern of the hexapodHexapod parameters
Rmax = 60 Pixels
Rmin = 20 Pixels
B = 100 Pixels
W = 50 Pixels
D = 50 Pixels
April 03, 2015

48. Grayscale Image of a Simplified Forward Gait
48
 Each step of the simplified forward gait’s ranges of movement (Km) was
measured and stored in a matrix
 Brighter zones represent higher Km values, and vice versa. White denotes wide
ranges of movement & black represents shortest ranges of movement.
April 03, 2015

49. Gait Selection for Forward Walking
49
α -15° -30° -45° 0°
S 111.57 101.21 83.43 112
SX -28 -50 -59 0
SY 108 88 59 112
The parameter values of robot’s forward gait
α 15° 30° 45° 60°
S 111.57 101.21 83.43 67.23
SX 28 50 59 58
SY 108 88 59 34
 Forward angle α; Stride length S;
 SX, SY (S in X and Y directions)
 This study create an adaptive forward gait list by selecting from
eight simplified forward gait angles, namely 0°, 15°, 30°, 45°, 60°,
-15°, -30°, and -45°.
April 03, 2015

50. Rotational Gait (Around the CG)
 The distance between every point of motion range and the CG was measured
Then applied the aforementioned ranges of movement matrix for the hexapod’s
movement. A gray value of 255 was defined for the maximal angle of rotation
50April 03, 2015

51. Maximal Angle of Rotation
51
θ S SX SY R x y
Rotation around the CG 30.03° 0 0 0 0 0 0
Max. angle of rotation 37.67° 40.16 13 38 62 62 0
The comparison of rotational gait
Rotation around the point OT and after rotation
θ3 as 58.85°
θ2 as 30.03°
θ6 as 30.39°
Rotated clockwise with 2-3-6 gait
The hexapod reached
the maximal angle of
rotation when θ2, θ3,
and θ6 were equivalent.

52. Rotation around Any Point
52
For 5 ° angle of rotation For 10° angle of rotation
θ S SX SY R X Y
5° 101.90 28 98 1162 1130 272
10° 93 27 89 527.68 515 115
The Parameters for rotation of 5° and 10°
Hexapod’s destination
target point was in front and
the CG was on the right
side of the rear position
In each step, the hexapod
could rotate θ degrees
However, the rotation of the
hexapod depended on the
condition of the forbidden
edges, zones, and target
distance
After each movement, the
hexapod’s CG and stability
margin were measured and
updated

53. The Algorithm for Gait Selection
53
Changes in the gait sequence
( 1-4-5 gaits, 2-3-6 gaits,  symmetrical gaits)
The gray regions indicate the
overlapping ranges of motion
April 03, 2015

54. Gait Selection for
Forward Walking
54April 03, 2015

55. Walking strategy
for the proposed
multi-legged robot
55April 03, 2015

56. Parameters for hexapod movement
56
Steps Position Gait Foothold Position Angle
1 (641,1642) 30 2-3-6 (742,1512) (540,1584) (742,1712) 0
2 (691,1554) Turn5° 1-4-5 (640,1396) (764,1525) (608,1687) 0
3 (693,1544) -15 2-3-6 (744,1484) (547,1520) (748,1586) 0.49
4 (688,1522) -15 1-4-5 (604,1380) (789,1542) (601,1577) 0.49
5 (677,1481) Turn10° 2-3-6 (739,1340) (565,1523) (753,1528) 0.49
6 (680,1467) Turn10° 1-4-5 (630,1309) (786,1495) (615,1511) 1.94
7 (690,1428) 60 2-3-6 (780,1285) (590,1402) (799,1519) 6.25
8 (729,1405) Turn5° 1-4-5 (653,1280) (865,1358) (664,1477) 6.25
9 (744,1346) Turn10° 2-3-6 (831,1222) (638,1288) (795,1482) 9.22
10 (750,1320) Turn5° 1-4-5 (671,1174) (866,1273) (690,1363) 12.08
11 (768,1252) 30 2-3-6 (869,1222) (667,1194) (869,1322) 15.55
12 (818,1164) 60 1-4-5 (768,1084) (977,1155) (768,1222) 15.55
13 (859,1141) Turn10° 2-3-6 (935,1039) (759,1183) (922,1257) 15.55
14 (862,1126) 15 1-4-5 (803,984) (997,1084) (804,1168) 17.13
15 (887,1033) 30 2-3-6 (988,903) (787,990) (988,1103) 17.13
16 (933,952) 30 1-4-5 (882,794) (1084,922) (878,1009) 17.13
17 (977,875) 30 2-3-6 (1076,751) (876,817) (1078,945) 17.13
18 (1025,791) 15 1-4-5 (966,633) (1158,746) (968,835) 17.13
19 (1054,683) 45 2-3-6 (1136,581) (954,625) (1154,751) 17.13
20 (1085,652) 0 1-4-5 (1021,567) (1186,689) (1026,770) 17.13
21 (1085,629) 0 2-3-6 (1136,570) (963,593) (1163,691) 17.13
22 (1085,610) -45 1-4-5 (1024,560) (1237,583) (1028,763) 17.13
23 (1083,608) 0 2-3-6 (1134,562) (963,593) (1159,693) 17.13
24 (1083,602) -45 1-4-5 (1025,520) (1237,582) (979,680) 17.13
25 (1079,598) 0 2-3-6 (1130,554) (959,594) (1155,695) 17.13
26 (1079,594) 15 1-4-5 (1023,436) (1236,577) (993,648) 17.13
27 (1096,531)

57. 57April 03, 2015

58. 58

59. Walking Strategy with Damaged Leg
The use of removable sliding legs
59
Fixed Position Adjustment
Step 01: Damaged leg removed
Step 02: Middle leg slide into the removed leg
When the position of the leg started to move
& remaining leg may not provide stable
support
However as any of these legs lifts above the
ground, the remaining legs fail to provide a
usable support polygon
Thus, firstly let R1 swing backward a distance
S, & secondly make R2 also move in the
same direction an amount of S, then swing R1
back to original stances. Repeat these steps
April 03, 2015

60. Axial stability for an adjusted gait
60
 Maximum stride length is 2S; SL+ & SL‐ are the
front and rear axial stability limit respectively
 The standard stride length is 2S. The maximum
swing for both the front & the rear leg is assumed
to be S
 Most insects can walk with the tripod gait, which is
a fast and statically balanced gait (SBG) for
Hexapods.
 However, when one or more legs are missing,
regular tripod gait is no longer possible. To get
around this, a “common leg” needs to be shared in
two tripod groups.
April 03, 2015
Multi-legged Robot Schematics

61. Alternative Gait
Configuration
The 6‐1‐R2 case
Common Leg R3
 A hexapod robot which has no R2 leg
 In (a), hollow arrow indicates half step &
solid arrow indicates full step (2S)
 Dash lines are indicate the support
polygon
 In each interval the robot travels a
distance S
Robot schematics
Enhanced Gait Chart (EGC)April 03, 2015 61
L1
L2
L3
R1
R3

62. Comparison of Alternative Gait
62
Fault type
(Severed Legs)
d min Stride length PE
1st Tripod 2nd Tripod
6-1-R2 0 1 1 0.5
0.5 0.5 1 0.429
0.8 0.2 0.2 0.5
6-1-R3 0 2 1 0.429
0.5 1 0.5
8-3-L1L4R2 0 2 2 0.5
0.25 1.5 1.5
0.5 0.5 0.5
1 0.2 0.2
8-3-L1L4R1 0 1 2 0.429
0.25 0.5 1.5 0.4
8-3-L2L3R2 0 1 1 0.5
0.5 0.5 1.5 0.4April 03, 2015

63. Comparison of
Alternative Gait
Fault type
(Severed Legs)
Axial stability
PE
[SL+]min [SL-]min
6-2
6-2-L3R3 3.75 0 0
6-2-L1R2 2 3.75 <0.2
6-2-L2R2 3.75 3.75 0.333
8-2
8-2-L2R3
1.52
1.52
1
8-2-L4R2
1.25
8-2-L4R1 1.25
8-2-L4R3
2.64 08-2-L4R4
8-2-L2L4
8-2-L2L3 0 0
8-2-L2R2 1.52 2.64
8-2-L1L4 1.25 1.25
8-3
8-3-L1L4R1
0
1.25
0.5
8-3-L2L3R2 2.64
8-3-L2L4R1, L4R1R2 1.25
8-3-L2L4R3, L3L4R2
1.52
0
8-3-L2L3R1, L2L4R4 <0.2
8-3-L3L4R3 2.64
0
8-3-L4R3R4 - -
8-3-L1L4R2
1.52 1.25 0.5
8-3-L2L4R2
8-4
8-4-L2L3R1R2
1.52
3.75
0
8-4-L2L4R1R2
2.64
8-4-L1L4R1R2 0
8-4-L2L4R3R4 3.75 0
8-4-L1L4R2R3
2.64
2.64
<0.2
8-4-L1L4R2R4 1.25
8-4-L2L3R1R3
3.75
8-4-L2L4R2R3
3.75
8-4-L2L4R2R4 1.25
8-4-L3L4R3R4 - - 0
8-4-L2L3R2R3 3.75 3.75 0.333
April 03, 2015 63

64. Non Fixed Position Adjustment (NFP)
64
Best Combination for [3|3] type gait sequence
(a) 8-2-L2 R3 type as an example
(b) Before adjustment, L3 R1 R4 constitute
support polygon
(c) SL + = 1.52 S, SL- = 2.64 S, d min = 0.53 S
(d) Six legged standard form by using step
less transportation.
(e) Now, SL + and SL- become equal (both
2.08 S), and d min = 1.08S and the whole
system become more stable
April 03, 2015
Support Polygon (L3 R1 R4 )
L3
R4
R1

65. Non Fixed Position Adjustment (NFP)
65
Best combination for [2|4] type
 The R3 leg in (L3, R1, R3) support polygon
is first moved downward by 0.5S, making
(SL+) increase from 1.25S to 1.5S
 Then L3 is move downward by 0.03S to
equalize the two SL values to 1.51S.
 Since the other group (L2, R2, R4) is of
opposite shape, so it is adjusted reversely
 The minimal SL value (dmin) is thus increased
from 1.25S to 1.51S.
 This is now the better configuration for [2|4]
category
Support Polygon
(L3 R1 R3 )
R3L3
R1
L2 R2
L4

66. Procedure to resume its task after leg failure
66April 03, 2015

67. Outline
Introduction
Background
Research Objectives
Related Research Work
Methodology
Conclusion
67April 03, 2015

68. Contributions
Developed various membership functions for image
fuzzification and find out the better one
Moreover, this study provided an application of edge
detection and noise removal technique for low resolution
image
Developed multi legged robots walking strategies by
applying mathematical morphology image processing
based method
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69. Contributions
Developed multi legged robots with damaged leg walking
strategy
This study developed “Severed Leg” & “Sliding Leg”
approach to maintaining the efficiency & stability of robot
69April 03, 2015

70. Future Work
Although this study has accomplished a small step toward edge
detection & multi legged robot walking strategies, the quest for a
better edge detection and walking strategy system will continue to
persist.
There are some research topics worth continued study. For
instance, fuzzy fusion concepts to extend fuzzy morphology to
color data (Color Fuzzy Morphology).
In addition, the recognition of low-resolution images needs to be
extended to a more general geometric transformation as well.
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71. 71