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Navigation Method for VTOL Type UAV using a Limit-cycle Navigation Method and Fuzzy Logic Control. Byung-Cheol Min Kyung Hee University (Thesis Advisor : Prof. Donghan Kim). Contents. Introduction Path Planning Algorithm UAV (Unmanned Aerial Vehicle) Path Tracking Method Conclusion. - PowerPoint PPT Presentation
Citation preview
Background Problem Statement Proposed Solution Simulation Conclusion
Automatic Control Lab.
Navigation Method for VTOL Type UAV using a Limit-cycle Navigation Method and Fuzzy Logic Control
Byung-Cheol MinKyung Hee University
(Thesis Advisor : Prof. Donghan Kim)
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method ConclusionIntroduction
1. Introduction 2. Path Planning Algorithm3. UAV (Unmanned Aerial Vehicle)4. Path Tracking Method5. Conclusion
Contents
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
NavigationPath Planning Path Tracking
- What is a navigation method?
(c) Commercial Airplanes(a) Unmanned Aerial Vehicles (b) Unmanned Ground Vehicles
1. Introduction
Introduction
- Applications
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Classic Path Planning Approach
- Potential Field Method
- Limit-cycle Navigation Method
(d) Simulation on the Limit-Cycle navigation method
)1()1(22
21212
22
21121
xxxxxxxxxx
(b) r = 50 (c) r = 70 (a) r = 30
1. Introduction
Introduction
)( y
)(
222
222
yxryxdd
yxrxyddx
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
The Basic Concept of Limit-cycle method in three dimensions (3D)
22 dydxDh
)arctan(Dhdz
tan22 yxh
zhz
dz
dx dy
Dh
dx = current x position – obstacle x positiondy = current y position – obstacle y positiondz = current z position – center of the obstacle z position
center of the obstacle
current position
yyy
xxx
ΔhΔyΔx
Dh is a tangent line between the current position and the tangent point of an obstacle circle.
With this obtained angle, the input of the z-value can be calculated as
Δx and Δy values are obtained by the original limit-cycle navigation method.
Path Planning Algorithm
2. Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
(a) unsuitable path (b) possible paths
(c) unsuitable path (d) suitable path
Although the proposed method verified a variety of merits in 3D, it also showed several drawbacks.
1. The method usually draws the path with setting previous along the center of obstacle’s height, depicted in (a).
2. The method generates the path only by avoiding to the side of the obstacle, depicted in (c).
Problem Statement
Initial Position
Destination
Initial Position
Destination
Initial Position
Destination
Initial Position
Destination
2. Path Planning Algorithm
Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Put the initial point for Pi and the destination point for Pd
Render the obstacle
Draw a line P(t) between Pi and Pd
START
Ray Tracing
Path Planning
Ray tracing is an algorithm that shoots beams of light to determine the accurate location and the size of the objects. In this paper, however, the method is used for the aircraft to find the shortest path to reach the destination while avoiding the obstacle.
Path Planning Based on the Methods of Ray Tracing and Limit-Cycle
2. Path Planning Algorithm
Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Put the initial point for Pi and the destination point for Pd
Render the obstacle
Draw a line P(t) between Pi and Pd
Does two Intersections exist?
Generate a straight path
START
Ray Tracing
Path Planning
Yes
No
END
0
))()()((2))()()((
2222
2222
rzyx
tzzzyyyxxxtzzyyxx
iii
idiidiidi
ididid
02 cbtat
0))()()((2
)()()(
2222
222
rzyxczzzyyyxxxb
zzyyxxa
iii
idiidiidi
ididid
Eq. (1) can be expressed as
The coefficients a, b, and c in Eq. (2) can be expressed as follows.
By solving the discriminant, we can know whether the line P(t) intersects the sphere or not.
abd 42
(1)
(2)
(3)
Path Planning Based on the Methods of Ray Tracing and Limit-Cycle
2. Path Planning Algorithm
Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Put the initial point for Pi and the destination point for Pd
Render the obstacle
Draw a line P(t) between Pi and Pd
Does two Intersections exist?
Decide the path between a horizontal direction and a vertical direction
START
Ray Tracing
Path Planning
Yes
No
END (b) x-y plane, z=0 (c) x-z plane, y=0
(a) line P(t) from Pi to Pd
Generate a straight path
When the horizontal direction is chosen, limit cycle is generated on the x-y plane.
When the vertical direction is chosen, limit cycle is generated on the x-z plane.
Path Planning Based on the Methods of Ray Tracing and Limit-Cycle
Pd
Pi
P(t)
2. Path Planning Algorithm
Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Only slight difference occurs between the hypothetical limit cycle in 3D and the proposed limit cycle in 2D.
The huge gap occurs if the radius of limit cycle is calculated based on the center of the obstacle.
Put the initial point for Pi and the destination point for Pd
Render the obstacle
Draw a line P(t) between Pi and Pd
Does two Intersections exist?
Decide the path between a horizontal direction and a vertical direction
Calculate a radius of the limit cycle based on the line
Generate a path by limit cycle
START
Ray Tracing
Path Planning
Yes
No
END
Generate a straight path
)()(22
21
2212
22
21
2121
xxrxxxxxrxxx
Path Planning Based on the Methods of Ray Tracing and Limit-Cycle
2. Path Planning Algorithm
Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Two suitable paths were generated among nu-merous paths that can be planned by limit cycle method.And then, the shortest path was decided by comparing two distances depicted as a solid line.
82.43 m89.1 m
Simulation Result 1
(a)
020
4060
80100
0
20
40
60
80
1000
20
40
60
80
100
X [m]Y [m]
Z [m
]
Initial Position
Destination
P(t)
2. Path Planning Algorithm
Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Simulation Result 2
(a) (b)
020
4060
80100
020
4060
801000
20
40
60
80
100
X [m]Y [m]
Z [m
]
Destination
Initial Position 2
Initial Position 1 Initial Position 3
Way Point
0204060801000
20
40
60
80
100
Y [m]
Z [m
]
Destination
Initial Position 1
Initial Position 3
Initial Position 2
2. Path Planning Algorithm
- The three paths from different initial points is successfully generated.
- There are no gaps between the sphere and three paths. Thus, each of paths is smooth enough for UAVs to fly because of limit cycle characteristics.
Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Path Planning for Dynamic Obstacle Avoidance: collision detection method
(a)
2. Path Planning Algorithm
diO
diPOOVPPV
Oi
PitVOtOtVPtP
)()(
(1) Velocity vector (2) Position of moving objectVP
VO
Pd
OiOd
Pi
rO
rP
22
22
22 )()(
tBAdtVOtVPd
tOtPd
OiPi
OP
iiVVBOPA
)()(2)( 22 AABAttBBd
2
2222 )()()(B
dABBABAt
(3) Calculate the time t whenthe distance d between P(t) and O(t) equals to rP + rO
- An algorithm to generate a path to avoid dynamic obstacles is mainly comprised of a collision detection method and standard rules of airplane traffic.
Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
2. Path Planning Algorithm
“If both airplanes approach from opposite sides, they are supposed to give way by turning right away from each other to avoid a collision, and if flying airplanes come into conflicting paths side by side, the left airplane turns right to yield.”
Path Planning for Dynamic Obstacle Avoidance: standard rules of airplane traffic
- “Right of way” of Federal Aviation Regulation (FAR) 91.113 to collision avoidance- “Rules of the air” of the International Civil Aviation Organization (ICAO) annex 2
In case there are more than two UAVs in the same operation area, standard rules to control their traffic are necessary.
Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Collision Detection Method
(b)
Pd
OiOd
Pi
2. Path Planning Algorithm
Similarly, we set up the standard rules of airplane traffic as follows:
- If two UAVs approach from opposite sides (i,e., more than 90 degrees), the UAV is supposed to give way by turning right away from the moving obstacle to avoid a collision.
Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Standard Rules of Airplane Traffic
(c)
Oi
Od
2 Sec
1 Sec
4 Sec
5 Sec
8 Sec
9 Sec
Pi
3~5 Sec
1 Sec
2 Sec
Wait for 2 Sec
3 Sec
6 Sec
2. Path Planning Algorithm
- If the dynamic obstacle comes into conflicting the UAV's path within less than 90 degrees, the UAV waits for a while to yield.
Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Simulation Result 3
(a)0 10 20 30 40 50 60 70 80 90 100
0
10
20
30
40
50
60
70
80
90
100
X [cm]
Y [c
m]
Moving obstacle avoidance
Pi Pd
OiOd
Position of a Collision Virtual Obstacle
2. Path Planning Algorithm
- the angle between the moving direction of the UAV and the obstacle was set for bigger than 90 degrees.
- The path was generated at the predicted position of a collision (42, 52) with the supposition that an obstacle exists at that position.
Path Planning Algorithm
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Common UAV Configurations
Fixed-wing Type
Vertical Take-Off and Landing Type(VTOL Type)
Configuration Picture Application Advantages & Drawbacks
fixed-wing(Predator)
-military reconnais-sance -combat
- high endurance flights-silent
-no hovering
single(Fire Scout)
-meteorology research-reconnaissance
-good controllability and maneuverability
- complex mechanics- large rotor
coaxial rotors(Airscooter)
-research-surveillance
- compactness-simple mechanics
-complex aerodynamics
quad rotors(DraganFlyer)
-research-surveillance
- good maneuverability-Increased payload
- high energy consumption- large size
UAV
3. UAV(Unmanned Aerial Vehicle)
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
(a) Hovering configuration
(b) Pitching & rolling configuration
(c) Yawing configurationF1(0) + F2 (0) + F3 (0) + F4(0) = mg
For a hovering flight, the four driven forces are
Basic Principles of the Quad-rotor UAV
3. UAV(Unmanned Aerial Vehicle)
UAV
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
CCCS S
CSSSCCCSSSSCSS CSC SCCSSCC
RRRR
EB
1) The rotational transformation matrix between the earth-frame {E} and the body frame {B}
2) Equations of the translational motion in the earth frame are derived by the Newton’s laws
mgyKFyKFxKF
mgzyx
KK
K
FFF
zyx
mfzzE
fyyE
fxxE
fz
fy
fx
zE
yE
xE
00
0 0 0 0 0 0
(a) The coordinate system with an earth frame {E} and a body frame {B}
The Dynamic Modeling of the Quad-rotor UAV
3) Resultant equations of motion as follows
42314
133
242
43211
FFFFuFFuFFu
FFFFu
4) Control inputs of the model
z
d
y
l
x
l
fz
fy
fx
IKuI
KulI
Kul
gm
zKuz
myKu
ym
xKux
)(
)(
)(
)cos(cos
)cossinsinsin(cos
)sinsincossin(cos
4
3
2
1
1
1
3. UAV(Unmanned Aerial Vehicle)
UAV
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
(b) The path tracking scheme(a) Typical Fuzzy Logic Control (FLC)
Fuzzy Logic Control
Path Tracking Method
Fuzzifier InferenceEngine Defuzzifier Output
Scaling
ControlRule Base
Fuzzy Logic Controller
Input Scaling
epx= dpx - cpx
Destination
Current Positioncpx, cpy, cpz
dpx, dpy, dpz
epy= dpy - cpy
epz= dpz - cpz
Way Point 2Way Point 3
Way Point 4
Way Point …
Desired Position (Way Point 1)
4. Path Tracking Method
- To control thrust and attitude of the VTOL Type UAV, which mostly affect its position, fuzzy logic control (FLC) is proposed.
- The FLC, which is activated after generating the path, will be in charge of controlling the overall system of the quad-rotor UAV so that it can move to any desired position effectively.
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Nine Fuzzy Logic Controllers (FLCs) were used to handle nonlinear system.
Fuzzy Logic Control
FLCmodule 1
epz u1
u3
u4
dpx, dpy ,dpz
dvz
dvy
dvx
daφ, da θ, daψ
Δepz
epy
Δepy
epx
Δepx
evz
Δevz
evy
Δevy
evx
Δevx
eaθ
Δeaθ
eaψ
Δea ψ
Desired Position
Position Control Velocity Control
Angle Control
Current Position Cpx, Cpy, Cpz
Current Velocity Cvx, Cvy, Cvz
Current Angle
eaφ
Δeaφu2Desired Velocity Desired Angle
FLCmodule 2
FLCmodule 3
FLCmodule 4
FLCmodule 5
FLCmodule 6
FLCmodule 7
FLCmodule 8
FLCmodule 9
epx= dpx - cpx
Destination
Current Positioncpx, cpy, cpz
dpx, dpy, dpz
epy= dpy - cpy
epz= dpz - cpz
Way Point 2Way Point 3
Way Point 4
Way Point …
Desired Position (Way Point 1)
4. Path Tracking Method
Path Tracking Method
e/Δe NB NM NS ZO PS PM PB
NB NB NB NB NB NM NS ZO
NM NB NB NB NM NS ZO PS
NS NB NB NM NS ZO PS PM
ZO NB NM NS ZO PS PM PB
PS NM NS ZO PS PM PB PB
PM NS ZO PS PM PB PB PB
PB ZO PS PM PB PB PB PB
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
(a) The traces of path tracking by the quad-rotor UAV while ascending using FLC.
(b) The each velocity ratio of x-y-z axes per time axis based while the quad-rotor UAV is ascending.
(c) The each position of x-y-z axes per time axis based while the quad-rotor UAV is ascending.
Simulation Result 1
-100
1020
3040
0
10
20
30
400
5
10
15
20
25
30
35
40
X [m]Y [m]
Z [m
]
Desired Position
Initial Position
0 10 20 300
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
t[s]
V[m
/s]
x Velocityy Velocityz Velocity
0 10 20 300
10
20
30
40
t[s]
x[m
]
Quad-rotor Pos x
0 10 20 300
10
20
30
40
t[s]
y[m
]
Quad-rotor Pos y
0 10 20 300
10
20
30
40
t[s]
z[m
]
Quad-rotor Pos z
4. Path Tracking Method
Path Tracking Method
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
(d) The traces of path tracking by the quad-rotor UAV while descending using FLC.
(e) The each velocity ratio of x-y-z axes per time axis based while the quad-rotor UAV is descending.
(f) The each position of x-y-z axes per time axis based while the quad-rotor UAV is descending.
Simulation Result 2
-100
1020
3040
0
10
20
30
400
5
10
15
20
25
30
35
40
X [m]Y [m]
Z [m
]
Initial Position
Desired Position
0 10 20 30-2
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
t[s]
V[m
/s]
x Velocityy Velocityz Velocity
0 10 20 300
10
20
30
40
t[s]
x[m
]
Quad-rotor Pos x
0 10 20 300
10
20
30
40
t[s]
y[m
]
Quad-rotor Pos y
0 10 20 300
10
20
30
40
t[s]
z[m
]
Quad-rotor Pos z
4. Path Tracking Method
Path Tracking Method
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
(a) The result of a simulation on the proposed navigation method: There are three different initial posi-tions and the same destination. ‘’ indicates way points from the initial position of the UAV to its des-tination.
Simulation Result 3
4. Path Tracking Method
Path Tracking Method
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
(b) An enlarged portion of the problem of path tracking.
Problem with Simulation Result 3
-100
-80
-60
-40
-20
0
20
40
60
80
100
-100
-80
-60
-40
-20
0
20
40
60
80
100
0
10
20
30
40
50
60
X [m]
Y [m]
Way Point
0 20 40 60 80 100 120 140 160 180 200-5.0
-4.0
-3.0
-2.0
-1.0
0
1.0
2.0
3.0
4.0
5.0
t[s]
V[m
/s]
x Velocityy Velocityz Velocity
(c) The each velocity ratio of x-y-z axes per time axis based while the quad-rotor UAV is flying toward the destination. There is a problem that the UAV repeats stop-and-go at regular inter-vals.
4. Path Tracking Method
Path Tracking Method
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Method to Solve the Problem with Simulation Result 3
1. Spheres centered at the way points are drawn in the form of ,where x, y, and z represent the position of the way point (desired position), and i means the order of way points, and r means a radius of sphere.
2. When the UAV passes the ith sphere, the current desired position (xi, yi, zi) is changed to the following desired position (xi+1, yi+1, zi+1).
-100-80
-60-40
-200
2040
6080
100
-100
-80
-60
-40
-20
0
20
40
60
80
100
0
20
40
60
80
100
120
140
160
180
200
X [m]
Y [m]
ith Way Point (xi, yi, zi)
ith Sphere
i+1th Sphere
i+2th Sphere
i+3th Sphere
Initial Position
i+1th Way Point (xi+1, yi+1, zi+1)
4. Path Tracking Method
2222 rzyx iii
Path Tracking Method
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
(a) The result of a simulation on the new path tracking solving the problem that the UAV repeats stop-and go around the way points
Simulation Result 4
4. Path Tracking Method
Path Tracking Method
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
(b) An enlarged portion of the simulation result
Simulation Result 5
(c) The each velocity ratio of x-y-z axes per time axis based while the quad-rotor UAV is flying toward the destination
-100
-80
-60
-40
-20
0
20
40
60
80
100
-100
-80
-60
-40
-20
0
20
40
60
80
100
0
10
20
30
40
50
60
X [m]
Y [m]
Way Point
0 20 40 60 80 100 120 140 160 180 200-5.0
-4.0
-3.0
-2.0
-1.0
0
1.0
2.0
3.0
4.0
5.0
t[s]
V[m
/s]
x Velocityy Velocityz Velocity
4. Path Tracking Method
Path Tracking Method
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
(a) The result of dynamic obstacle avoidance in a case where the obtacle comes into a conflicting the UAV's path within less than 90 degree
Simulation on Dynamic Obstacle Avoidance: the Second Standard Rule of Airplane Traffic
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
100
X [m]
Y [m
]
Moving Obstacle Avoidance
Pi
Pd
Oi
Od
Position of a Collision
Oi
Od
2 Sec
1 Sec
4 Sec
5 Sec
8 Sec
9 Sec
Pi
3~5 Sec
1 Sec
2 Sec
Wait for 2 Sec
3 Sec
6 Sec
(b) Dynamic Obstacle Avoidance: the Second Standard Rule of Airplane Traffic
4. Path Tracking Method
Path Tracking Method
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
Simulation on Dynamic Obstacle Avoidance: the Second Standard Rule of Airplane Traffic
0 10 20 30 40 50 60 70 80 90 100-5.0
-4.0
-3.0
-2.0
-1.0
0
1.0
2.0
3.0
4.0
5.0
t[s]
V[m
/s]
x Velocityy Velocityz Velocity
0 10 20 30 40 50 60 70 80 90 100-5.0
-4.0
-3.0
-2.0
-1.0
0
1.0
2.0
3.0
4.0
5.0
t[s]
V[m
/s]
x Velocityy Velocityz Velocity
0 10 20 30 40 50 60 70 80 90 1000
50
100
t[s]
x[m
]
Obstacle Pos xUAV Pos x
0 10 20 30 40 50 60 70 80 90 1000
50
100
t[s]
y[m
]
Obstacle Pos yUAV Pos y
0 10 20 30 40 50 60 70 80 90 1000
50
100
t[s]
z[m
]
Obstacle Pos zUAV Pos z
area A
(a) Obstacle
(b) UAV
(c) The each position of the UAV
4. Path Tracking Method
Path Tracking Method
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
- Extension of the original limit-cycle navigation method of three dimensional spaces
- New path planning algorithm based on the methods of ray tracing and the extended limit-cycle navigation method
- Algorithm comprised of a collision detection method and standard rules of airplane traffic that generates a path to avoid collisions with dynamic obstacles
- Fuzzy logic control method in order for the UAV to converge quickly on the desired position
- Solving the problem that the UAV repeats stop-and go around the way points, using virtual spheres
Conclusion
5. Conclusion
Automatic Control Lab.
Introduction Path Planning Algorithm UAV Path Tracking Method Conclusion
function [x, y, z] = limtcycle(Pos_x, Pos_y, Pos_z, ObPosx , ObPosy, ObPosz, r, direct) dx = (Pos_x -ObPosx); dy = (Pos_y -ObPosy); dz = (ObPosz - Pos_z); Dh = sqrt(dx^2 + dy^2); if(direct == -1) ddx = -dy*r^2 + dx * (r^2 - dx^2 - dy^2); ddy = dx*r^2 + dy * (r^2 - dx^2 - dy^2); else ddx = dy*r^2 + dx * (r^2 - dx^2 - dy^2); ddy = -dx*r^2 + dy * (r^2 - dx^2 - dy^2); end theta_xy = atan2(ddy,ddx); Theta_z = atan2(dz,Dh); Del = 5; Del_x = Del*cos(theta_xy); Del_y = Del*sin(theta_xy); Del_h = Del*tan(Theta_z); x = Del_x + Pos_x; y = Del_y + Pos_y; z = Del_h + Pos_z;end
Limit-cycle Matlab Source
Background Problem Statement Proposed Solution Simulation Conclusion
Automatic Control Lab.
Publications - 5 Journal Publications, 5 Conference & Symposium Proceedings
- Journal Publications1) B.C. Min, and D.H. Kim, “A Navigation Method for VTOL type UAV Using Limit-cycle Navigation Method and Fuzzy Logic
Control," IEEE Transactions on Systems, Man, and Cybernetics, 2010. (in preparation)2)B.C. Min, M. Kim, and D. Kim, "Fuzzy Logic Path Planner and Motion Controller by Evolutionary Programming for Mobile Robots," International Journal of Fuzzy Systems, Vol. 11, No. 3, September 2009.3)B.C. Min, D. Kim, Y.H. Kim, K.Y. Kim, and C. Park, "Development of Violin Self-Training Algorithm Using Fuzzy Logic," Journal of Korean Institute of Intelligent Systems, Vol. 19, No. 4, August 2009. (in Korean)4)B.C. Min, C.H. Cho, K.M. Choi, and D. H. Kim, "Development of a Micro Quad-Rotor UAV for Monitoring an Indoor Environment,", Lecture Notes in Computer Science (LNCS), FIRA CIRAS 2009, Vol. 5744, pp. 262-271, August 2009.5)C.H. Cho, B.C. Min, and D. H. Kim, "A Gait Generation for an Unlocked Joint Failure of the Quadruped Robot with Bal-ance Weight," Lecture Notes in Computer Science (LNCS), FIRA CIRAS 2009, Vol. 5744, pp. 251-261, August 2009.
- Conference & Symposium Proceedings6)B.C. Min, H.Y. Kwon, and D.H. Kim, "Path Planning Algorithm for VTOL Type UAVs Based on the Methods of Ray Tracing and Limit Cycle," IEEE International Symposium on Computational Intelligence in Robotics and Automation (CIRA 2009), Decem-ber 2009.7)B.C. Min, E.J. Lee, S.H. Kang, and D.H. Kim, "Limit-cycle Navigation Method for a Quad-rotor Type UAV," Industrial Elec-tronics, 2009. ISIE 2009, IEEE International Symposium on, pp. 1352-1357, July 2009.8)S.H. Kang, B.C. Min, C.H. Cho, S.Y. Nam, and D.H. Kim, "The Position Control for Three Wheel Omni-directional Mobile Robot Using FLC," IEEK Summer Conference 2009, Vol. 32, No. 1, pp. 691-692, July 2009. (in Korean)9)Y.W. Lim, B.C. Min, J.W. Kim, S.Y. Nam, and D.H. Kim, “Local-Path Planning Using the Limit-cycle Navigation Method Applied to the Edge of an Obstacle with the Edge Detection Method”, International Conference On Electronics, Information, & Communication (ICEIC 2010), April 2010.10)Y.H. Kim, J.W. Kim, B.C. Min, and D.H. Kim, “Dynamic Obstacle Avoidance Using Vector Function Algorithm”, International Conference On Electronics, Information, & Communication (ICEIC 2010), April 2010.