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Synthesising
Mr. Antony Gerdelan
Dr. Napoleon Reyes, Ph.D.
Computer Science, Massey University, Auckland, New Zealand
Using a
Fuzzy Logic, Neural Networks, Evolutionary Algorithms
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Motivation: Autonomous Navigation Challenges
Central Idea: Integrating Complementary Path-
Finding Systems
Defining Robot Behaviours:
Target Pursuit, Obstacle Avoidance & Opponent
Evasion
Integrating the two complementary systems:
A Novel Hybrid Fuzzy A* Navigation System
Results & Analysis: Robot Soccer Simulations
Conclusions & Future Works
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Simulations
3-D Hybrid Fuzzy A* Navigation System
Cascade of Fuzzy Systems
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Robot Soccer Set-up
Colour objects
Fluorescent lampsOverhead
Camera
Exploratory environment is indoor – room totally obstructed from sunlight
Multiple monochromatic light sources – fluorescent / fluoride lamps
Colour Object Recognition (Recognition speed: < 33ms)*
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We introduce a new algorithm that is
designed to handle the robot
navigation part of the robot soccer
system and incorporates several
behaviours
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• allot time for vision, team strategy, path-planning
Time Constraints
Finding an Optimal Path in Real-time
• calculate shortest path dynamically
Local minima Problem
• prevent robot from being trapped
Inaccuracy of Sensors
• position, robot orientation, distance from target,
etc. could be inaccurate
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• reactionary algorithm + optimal path planning
• allow for course correction dynamically
• simplify the path-planning algorithm to calculate
only a rough estimation of the route and let the
reactionary algorithm iron-out the complete path
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Path-Finding With the A* Algorithm
*
S
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Path-Finding With the A* Algorithm
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Path-Finding in a Static Environment
• Generally not used in a dynamic environment for
these reasons
• Used in computer games for decades
•‘Tile-based’ environments (fixed nodes)
• Pre-calculation of paths (does not account for
dynamic obstacles)
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Path-Finding With the A* Algorithm
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Calculating h* values for a
computerised map:
•Start Node at (1,S1)
•Goal is (13,S13)
•Optimal Path (not
considering obstacles) is
from highest point to
lowest point
Heuristic Map (h*)
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Path-Finding With the Modified A* Algorithm
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Evasion Incorporated in
path planning layer:
•Must specify perceived
level of threat to areas of
environment
•A second computerised
map is created. Each
where each cell is
awarded an undesirability
value.
•Function specific to
problem must be created
to award u values. In our
case a teardrop effect
around hostile robots.
Undesirability Map (u*)
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Path-Finding With the Modified A* Algorithm
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Undesirability Map (u*)
Undesirability across
environment can also be
represented as a 3D map.
•Z-axis represent
undesirability value of
each cell.
•Higher peaks = more
undesirable areas.
•Similar to potential fields
approach, but also pre-
empts movements and
direction of travel of hostile
agents.
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An Evasive Path-Finding Algorithm
*
The Modified A*. The Figure depicts the sum of (h* + u*)
Combining A* With
Undesirability Maps We
Inculcate an Evasive
Property into our path-
planning behaviour.
A new f* score:
f* = h* + u* + g*
•Balances undesirability u*
with heuristic h*
•Can be represented in 3D for
a hills-and-valleys effect
(pictured).
•Ranges of u* must be very
carefully balanced with h*
values
•g* components ensures
overall steepest downhill
(shortest) path
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Complementary Path Finding Systems
*
• Reactive
• Very refined robot movement thanks to C.O.G.
calculation
• Limited long-term path-planning ability
Fuzzy Logic:
A* algorithm:
f* = h* + g*
• Very fast calculation thanks to heuristic h*
• Optimal long-term planning (finds best path if one
exists)
• Paths are very rigid – movement produced is not
natural or refined
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Sensors
Environment Information
Nearest
Obstacle and
Final Target
Locations
Environment
Processor
The A* Algorithm
Path Planning Layer
Fuzzy Logic
Reactionary Layer
Map
Actuator Control
Module
Speed and Rotation
Motor Instructions
Next Waypoint
Actuators
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Path-Finding With the A* Algorithm
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Specially Modified A* for a Dynamic Environment
Demands of the Problem
• Environment not tile-basedA map (grid) must be created
• Obstacles move dynamically and so the path
can not be pre-calculatedPath must be continually recalculated to take into account moving
obstacles
Our Approach
• Entire path generated, but only the next path
point is passed down to the Fuzzy Logic layerNow, if a moving obstacle disrupts the planned path, it is re-
calculated on the fly
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Path-Finding With the A* Algorithm
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Specially Modified A* for a Dynamic Environment
Because we now only consider the next path
point:
The effective path can ‘cut corners’ in practice
For this reason, Dynamic A* Path Finding is
not effective alone as a navigation system.
Fuzzy Logic is required to smooth out the
effective path
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*
S
Complementary Path Finding Systems
The Hybrid Fuzzy A* Navigation Algorithm
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*
S
Disagreements between Layers
Real case scenarios
The A* Algorithm may
direct the robot to
take a straight path
between two close
obstacles, but the
Cascade of Fuzzy
Systems would
engage in obstacle
avoidance.
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Complementary Path Finding Systems
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Resolving disagreements between systems
The Fuzzy Logic layer must be able to navigate the
robot between any two path points generated by the A*
Planning Layer
Tweaking of Fuzzy Set Membership values to solve
some tricky navigation
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*
S
Strength of the Hybrid Fuzzy A* Algorithm
Real case scenarios
The A* Algorithm
may direct the robot
to take a straight
path crossing the
obstacle, but the
Cascade of Fuzzy
Systems allow for
course corrections.
Obstacles may not be
perfectly sitting on just
one block (or cell). It
may be overlapping
several blocks at any
one time.
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Cascade of Fuzzy Systems
Adjusted Speed
Adjusted Angle
Next Waypoint
N
Y
Adjusted Speed
Adjusted Angle
Fuzzy System 1: Target Pursuit
Fuzzy System 2: Speed Control for Target Pursuit
Fuzzy System 3: Obstacle Avoidance
Fuzzy System 4: Speed Control for Obstacle
Avoidance
ObstacleDistance <
MaxDistanceTolerance
and closer than Target
Actuators
Path planning Layer:
The A* Algorithm
Multiple Fuzzy Systems employ the various robot behaviours
Fuzzy System 1
Fuzzy System 2
Fuzzy System 3
Fuzzy System 4
Path Planning Layer
Central
Control
Target
Pursuit
Obstacle
Avoidance
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Fuzzy Sets
Angles
Sub ranges for Small, Medium and Large Angles overlap
SMALL
MEDIUM
LARGE
*
Small Medium Large
Deg
ree
of
me
mb
ers
hip
Angle in degrees
Membership Functions
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Taking advantage of Angle Symmetry
Fuzzy Sets for Angles
The approach developed takes advantage of the
Angle symmetry, and is equivalent to having 6 Fuzzy
Sets for the Angles.
*
SMALL
MEDIUM
LARGE
SMALL
MEDIUM
LARGE
Left Right
A simplified
approach that
reduces the
computational cost
without sacrificing
accuracy.
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Fuzzy Sets
Distances
Sub ranges for Near, Far and Very Far Fuzzy Sets for Distances overlap*
De
gre
e o
f m
em
be
rsh
ip
Distances in cm.
Membership Functions
Near Far Very Far
NEAR
FAR
VERY FAR
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Fuzzy Systems for Target Pursuit
NEAR FAR VERY FAR
SMALL Mild Turn Mild Turn Zero Turn
MEDIUM Med Turn Mild Turn Mild Turn
LARGE Sharp Turn Med Turn Med Turn
Next Waypoint
The A* Algorithm
NEAR FAR VERY FAR
SMALL Med Speed Fast Speed Very Fast
MEDIUM Slow Speed Med Speed Fast Speed
LARGE Very Slow Slow Speed Slow Speed
e.g. If the Distance from the Target is NEAR and
the Angle from the Target is SMALL
Then the robot should make a Mild Turn.
Fuzzy System 1 (Steering)
Fuzzy System 2 (Speed Adjustment)
e.g. If the Distance from the Target is NEAR and
the Angle from the Target is SMALL
Then the robot should move at a Medium Speed.
Angle
Speed
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Fuzzy Systems for Obstacle Avoidance
NEAR FAR VERY FAR
SMALL Very Sharp Sharp Turn Med Turn
MEDIUM Sharp Turn Med Turn Mild Turn
LARGE Med Turn Mild Turn Zero Turn
Nearest Obstacle (Distance and Angle)
NEAR FAR VERY FAR
SMALL Very Slow Slow Speed Fast Fast
MEDIUM Slow Speed Fast Speed Very Fast
LARGE Fast Speed Very Fast Top Speed
e.g. If the Distance from the Obstacle is NEAR and
the Angle from the Obstacle is SMALL
Then turn Very Sharp.
Fuzzy System 3 (Steering)
Fuzzy System 4 (Speed Adjustment)
e.g. If the Distance from the Obstacle is NEAR and
the Angle from the Obstacle is SMALL
Then move Very Slowly.
Vision System
Angle
Speed
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ADVANTAGES
*
In the robot soccer game, there are 11 robots to
control at the most.
SPEED
We are able to demonstrate that our algorithm can
control more than 30 robots at twice the required
speed of calculation.
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*
The system is able to take advantage of A*’s
optimized path finding, as well as Fuzzy
Logic’s reactionary feature, allowing for a
significant improvement in speed and
adaptability to a harsh dynamic environment.
We have successfully developed a Hybrid
Fuzzy A* navigation system that inculcates
three adaptive robot behaviours:
• Target Pursuit
• Obstacle Avoidance
• Opponent Evasion
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The algorithm developed is able to combine
the strengths of the two intelligent techniques,
as well as eliminate their weaknesses in one
Hybrid Fuzzy A* architecture
New Predictive quality behaviour has been
inculcated into the system with the addition of
a new parameter in the A* formula.
*
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By tweaking the range of values assigned to
the undesirability feature we can vary the
degree of aggressiveness of the robots.
Ball Carrier – most evasive (high u* values)
Other Attackers – less evasive (low u* values)
Defender –not evasive (zero u* values)
*