An Image Based Method of Finding Better Walking Strategies for Hexapod on Discontinuous Terrains

1. An Image Based Method of Finding Better WalkingAn Image Based Method of Finding Better Walking
Strategies for Hexapod on DiscontinuousTerrainsStrategies for Hexapod on DiscontinuousTerrains
Kazi MostafaKazi Mostafa
kazimostafa@gmail.com
Professor Innchyn HerProfessor Innchyn Her
her@mail.nsysu.edu.tw
Kung-Ting WeiKung-Ting Wei
weikt321@gmail.com
Department of Mechanical & Electro-Mechanical EngineeringDepartment of Mechanical & Electro-Mechanical Engineering
National Sun Yat-sen University, TaiwanNational Sun Yat-sen University, Taiwan

2. IntroductionIntroduction
◦ Previous Research WorkPrevious Research Work
◦ ObjectivesObjectives
MethodsMethods
◦ Simulate Terrain EnvironmentSimulate Terrain Environment
◦ Proposed Hexapod ModelProposed Hexapod Model
◦ Walking StrategyWalking Strategy
ResultsResults
ConclusionConclusion
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3. Wheeled vs.Wheeled vs. LeggedLegged locomotion.locomotion.
OnOn discontinuous terrainsdiscontinuous terrains..
Multi legged animals have excellentMulti legged animals have excellent adaptabilityadaptability
to traverse overto traverse over rugged terrainrugged terrain..
Multi-leggedMulti-legged robots that imitate crawling insects.robots that imitate crawling insects.
HexapodHexapod configuration is mostconfiguration is most efficient &efficient &
statically stablestatically stable..
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4. 4

5. Vision systemVision system to recognize surroundingto recognize surrounding
terrainterrain
Image based methodImage based method of finding walkingof finding walking
strategiesstrategies
To simulateTo simulate a completea complete hexapod walkinghexapod walking
modelmodel
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6. Proposed research divided into 3 major steps:Proposed research divided into 3 major steps:
A.A.Establishment of Terrain EnvironmentEstablishment of Terrain Environment
B.B.The Hexapod Gait ModelThe Hexapod Gait Model
- A simplified forward gait- A simplified forward gait
- Rotation- Rotation
- Intelligent gait control- Intelligent gait control
A.A.Hexapod’s Walking StrategyHexapod’s Walking Strategy
-- Gait selection methodGait selection method
- Walking Strategy- Walking Strategy
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7. Proposed research divided into 3 major steps:Proposed research divided into 3 major steps:
A.A.Establishment of Terrain EnvironmentEstablishment of Terrain Environment
B.B.The Hexapod Gait ModelThe Hexapod Gait Model
- A simplified forward gait- A simplified forward gait
- Rotation- Rotation
- Intelligent gait control- Intelligent gait control
A.A.Hexapod’s Walking StrategyHexapod’s Walking Strategy
-- Gait selection methodGait selection method
- Walking Strategy- Walking Strategy
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8. DefinedDefined sizesize of the terrain & entered 250 circles.of the terrain & entered 250 circles.
ComputerComputer displayeddisplayed a topographic vector map bya topographic vector map by
using those circles.using those circles.
AppliedApplied Grayscale erosionGrayscale erosion to find the boundaryto find the boundary
of Circles.of Circles.
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9. The white regions areThe white regions are standingstanding areas, black regions areareas, black regions are
forbiddenforbidden areas & the yellow region is being eroded.areas & the yellow region is being eroded.
TheThe edgesedges of the terrain changes into a forbidden area.of the terrain changes into a forbidden area.
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Foothold Zone
Forbidden Zone
Forbidden Zone

10. Proposed research divided into 3 major steps:Proposed research divided into 3 major steps:
A.A.Establishment of Terrain EnvironmentEstablishment of Terrain Environment
B.B.The Hexapod Gait ModelThe Hexapod Gait Model
- A simplified forward gait- A simplified forward gait
- Rotation- Rotation
- Intelligent gait control- Intelligent gait control
A.A.Hexapod’s Walking StrategyHexapod’s Walking Strategy
-- Gait selection methodGait selection method
- Walking Strategy- Walking Strategy
10

11.  Semi-circular shaped areas are Hexapod gait range of motionSemi-circular shaped areas are Hexapod gait range of motion
 Maximum range RMaximum range Rmaxmax = 60 (pixels), minimum range R= 60 (pixels), minimum range Rminmin = 20= 20
(pixels), length between two successive gaits B = 100(pixels), length between two successive gaits B = 100
(pixels), width W = 50 (pixels), and the offset value D = 50(pixels), width W = 50 (pixels), and the offset value D = 50
(pixels).(pixels).
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12.  Measured ranges of movement (Measured ranges of movement (KKmm) for various angle &) for various angle &
stored in the matrix.stored in the matrix.
 The largest value defined asThe largest value defined as 255255 (white), lowest as(white), lowest as 00 (black).(black).
 This study chooseThis study choose 8 forward gait angle8 forward gait angle matrix databasematrix database
[0 °, 15 °, 30 °, 45 °, 60 °, -15 °, -30 °, -45 °][0 °, 15 °, 30 °, 45 °, 60 °, -15 °, -30 °, -45 °]
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13.  Parameters of forward gait:Parameters of forward gait: forward angle , strideαforward angle , strideα
length S, and Slength S, and SXX, S, SYY are the S in X direction and Y direction.are the S in X direction and Y direction.
Various parameters of forward gait
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α -15° -30° -45° 0° 15° 30° 45° 60°
S 111.6 101.2 83.4 112 111.6 101.2 83.4 67.2
SX -28 -50 -59 0 28 50 59 58
SY 108 88 59 112 108 88 59 34

14.  Measurement of gait rotation can be divided into twoMeasurement of gait rotation can be divided into two
steps;steps; FirstFirst, we calculated the distance between each point, we calculated the distance between each point
of motion range and C.G.of motion range and C.G.
 SecondSecond, used same size of matrix to store the range of, used same size of matrix to store the range of
movement .movement .
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Rotation Angle
θ2
θ3
θ6

15.  When the hexapod robot rotates clockwise, theWhen the hexapod robot rotates clockwise, the center ofcenter of
rotationrotation move to right direction.move to right direction.
 The value of θThe value of θ33 decreases & θdecreases & θ22,θ,θ66 increases gradually.increases gradually.
 When θWhen θ22, θ, θ33, θ, θ66 turnedturned equalequal, hexapod could get, hexapod could get maximummaximum
rotation anglerotation angle..
 The location of OThe location of OTT isis 6262 units right from CGunits right from CG
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62 Units

16. The rotation around CG hasThe rotation around CG has nono forward movement.forward movement.
But, for the maximum rotation angle of 37.7° gait, theBut, for the maximum rotation angle of 37.7° gait, the
robot can move forward ofrobot can move forward of 40.2 units40.2 units, which includes, which includes
13 units in X direction, 38 units Y direction.13 units in X direction, 38 units Y direction.
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θ S SX SY R
Rotation around C.G. 30.03° 0 0 0 0
Max. angle of rotation 37.67° 40.1640.16 1313 3838 6262

17. This method assumes that the target point is in frontThis method assumes that the target point is in front
of the robot & center of rotation is in the right rear.of the robot & center of rotation is in the right rear.
In each step robot can rotate degree depends onθIn each step robot can rotate degree depends onθ
the condition and distance of movement.the condition and distance of movement.
After finished movement, hexapod’s center ofAfter finished movement, hexapod’s center of
rotation can be measured.rotation can be measured.
Then, by using previously mentioned method,Then, by using previously mentioned method,
measured the radius of rotation and parameters formeasured the radius of rotation and parameters for
5° and 10° of rotation.5° and 10° of rotation.
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18.  Stride length S for 5° is 101.9 unit and for 10° is 93 unit.Stride length S for 5° is 101.9 unit and for 10° is 93 unit.
 For10°, the hexapod moved less distance in the Y direction,For10°, the hexapod moved less distance in the Y direction,
but it added value in rotation.but it added value in rotation.
 If Hexapod needs to move & want to rotate simultaneously,If Hexapod needs to move & want to rotate simultaneously,
it should choose 5° of rotational gait.it should choose 5° of rotational gait.
 If the greater rotation is needed, hexapod might be choosingIf the greater rotation is needed, hexapod might be choosing
10°.10°.
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θ S SX SY R
5° 101.92 28 98 1162.3
10° 93.01 27 89 527.68

19.  First, take snapshot & pre-calculated the next foothold point.First, take snapshot & pre-calculated the next foothold point.
 Based on the terrain's ranges overlap with the gait ranges ofBased on the terrain's ranges overlap with the gait ranges of
motion, themotion, the 33rdrd
gaitgait is beyond the region.is beyond the region.
 So the robot chooses 1-4-5 gait sequence for foothold. AndSo the robot chooses 1-4-5 gait sequence for foothold. And
select the maximum number of points (gray region).select the maximum number of points (gray region).
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Terrain’s Foothold Zone
Gait Ranges of Motion
OverlappedNo Foothold
1
4
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20.  Started with tripod gait. Difficulties in transformation between 1-4-5 andStarted with tripod gait. Difficulties in transformation between 1-4-5 and
2-3-6 gait. Gait number 2 had no foothold.2-3-6 gait. Gait number 2 had no foothold.
 Hexapod using symmetrical gait (1-3-4-6) for foothold and move.Hexapod using symmetrical gait (1-3-4-6) for foothold and move.
 Hexapod again converted back in to tripod gait (2-3-6). Thus, if hexapodHexapod again converted back in to tripod gait (2-3-6). Thus, if hexapod
stuck again it will transformed 1-4-5 gait sequence to continue walk.stuck again it will transformed 1-4-5 gait sequence to continue walk.
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Current Km
Residual Km
1
3 4
6
No Foothold

21. 211-4-5 Gait Sequence 2-3-6 Gait Sequence Symmetrical Gait Target

22. Proposed research divided into 3 major steps:Proposed research divided into 3 major steps:
A.A.Establishment of Terrain EnvironmentEstablishment of Terrain Environment
B.B.The Hexapod Gait ModelThe Hexapod Gait Model
- A simplified forward gait- A simplified forward gait
- Rotation- Rotation
- Intelligent gait control- Intelligent gait control
A.A.Hexapod’s Walking StrategyHexapod’s Walking Strategy
-- Gait selection methodGait selection method
- Walking Strategy- Walking Strategy
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23.  Proposed hexapod has 8 different angles of forward gait. InProposed hexapod has 8 different angles of forward gait. In
total 64 combinations of gaits. But, 0° forward gait is a firsttotal 64 combinations of gaits. But, 0° forward gait is a first
choice.choice.
 Categorized these 64 combination of gait into 3 groups.Categorized these 64 combination of gait into 3 groups.
 The combination of smaller angle gait is the most preferredThe combination of smaller angle gait is the most preferred
one.one.
 In every step, hexapod compared stride length with TableIn every step, hexapod compared stride length with Table 11. If. If
stride length is at least 80% of tablestride length is at least 80% of table 11, hexapod walk by 0°, hexapod walk by 0°
forward gait.forward gait.
 If it is less, hexapod will choose other optimum gait angle.If it is less, hexapod will choose other optimum gait angle.
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α -15° -30° -45° 0° 15° 30° 45° 60°
S 111.6 101.2 83.4 112 111.6 101.2 83.4 67.2
SX -28 -50 -59 0 28 50 59 58
SY 108 88 59 112 108 88 59 34
Table 1

24. Group 01Group 01
0°0° 0°, 15°, -15°0°, 15°, -15°
15°15° 30°, 0°30°, 0°
-15°-15° 30°, 0°30°, 0°
Measure StrideMeasure Stride
LengthLength
StrideStride
length islength is
80% of max80% of max
stridestride
KeepKeep
MovingMoving
Group 02Group 02
0°0° 30°, -30°30°, -30°
15°15° 45°, -15°45°, -15°
-15°-15° -45°, 15°-45°, 15°
30°30° 0°, 15°, 45°0°, 15°, 45°
-30°-30° 0°,-15°,-45°0°,-15°,-45°
Measure StrideMeasure Stride
LengthLength
StrideStride
length islength is
80% of max80% of max
stridestride
KeepKeep
MovingMoving
YesYes
NoNo
…
NoNoYesYes

25. The walking strategy database contains 8 kinds of linearThe walking strategy database contains 8 kinds of linear
motion, 4 rotational movements, and the tripod gait andmotion, 4 rotational movements, and the tripod gait and
the symmetrical gait.the symmetrical gait.
The hexapod’s first choice is 0 ° forward gait for largestThe hexapod’s first choice is 0 ° forward gait for largest
stride length and ± 10 ° is second.stride length and ± 10 ° is second.
If the angle between the robot and the target is greaterIf the angle between the robot and the target is greater
than 45°, then hexapod choose the rotation gait.than 45°, then hexapod choose the rotation gait.
If the angle between the robot and the target is less thanIf the angle between the robot and the target is less than
45 °, then 5 ° or 10 ° of rotation gait can be used.45 °, then 5 ° or 10 ° of rotation gait can be used.
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26. 26
Angle (α)
of Target
Less than 5°
0° Straight
Forward Gait
Next step
foothold
Yes
Hexapod
moving to target
Reaches
Target
Point
Yes
Complete
No
Greater
than 5°
Angle (α)
of Target
Greater
than 45° Max angle of
rotation
Less than 45°
Rotation around
any point
Angle (α)
of Target
Greater
than
5°Less than 5°
Transform to
symmetrical gait
No
Next step
foothold
Yes

27. IntroductionIntroduction
◦ Previous Research WorkPrevious Research Work
◦ ObjectivesObjectives
MethodsMethods
◦ Simulate Terrain EnvironmentSimulate Terrain Environment
◦ Hexapod ModelHexapod Model
◦ Walking StrategyWalking Strategy
ResultsResults
ConclusionConclusion
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28. In proposed simulated terrain, there are 250 circlesIn proposed simulated terrain, there are 250 circles
with radius 15, 30, 45, 60, 75 where hexapod canwith radius 15, 30, 45, 60, 75 where hexapod can
stand. The average radius of these circles is 29.7.stand. The average radius of these circles is 29.7.
The significant advantage of proposed hexapod isThe significant advantage of proposed hexapod is
use of databases with image processing technique.use of databases with image processing technique.
Hexapod can use database to reduce computationHexapod can use database to reduce computation
time.time.
Proposed design is based on KProposed design is based on Kmm to select gait andto select gait and
foothold.foothold.
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29. 29

30. IntroductionIntroduction
◦ Previous Research WorkPrevious Research Work
◦ ObjectivesObjectives
MethodsMethods
◦ Simulate Terrain EnvironmentSimulate Terrain Environment
◦ Hexapod ModelHexapod Model
◦ Walking StrategyWalking Strategy
ResultsResults
ConclusionConclusion
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31. This study showed the use of image processingThis study showed the use of image processing
based technique to design an adaptive gait.based technique to design an adaptive gait.
Matrix database combined with image processingMatrix database combined with image processing
method made the hexapod’s walking strategy easymethod made the hexapod’s walking strategy easy
to determine.to determine.
Thus, the robot can simulate routes in advance, andThus, the robot can simulate routes in advance, and
achieve the artificial intelligence capabilities.achieve the artificial intelligence capabilities.
Finally, we hope that the proposed research methodFinally, we hope that the proposed research method
and strategy can provide a reference for futureand strategy can provide a reference for future
research to scholars.research to scholars.
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32. As part of our continuing research, we areAs part of our continuing research, we are
developing a physical model by using proposeddeveloping a physical model by using proposed
computer simulation results and improvingcomputer simulation results and improving
efficiency for real-time control application toefficiency for real-time control application to
proof the optimality of the design.proof the optimality of the design.
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