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Agenda
▪ Motivation ▪ Fuzzy logic introduction ▪ Fuzzy logic-based navigation ▪ Conclusion ▪ Discussion
Anton Volkov 2 Fuzzy Logic for Robot Navigation
Fuzzy Logic for Robot Navigation Anton Volkov 05.11.2018 - - PowerPoint PPT Presentation
Fuzzy Logic for Robot Navigation Anton Volkov 05.11.2018 - - PowerPoint PPT Presentation
Fuzzy Logic for Robot Navigation Anton Volkov 05.11.2018 http://www.informatik.uni-hamburg.de/WTM/ Agenda Motivation Fuzzy logic introduction Fuzzy logic-based navigation Conclusion Discussion Anton Volkov Fuzzy Logic for
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Motivation
▪ Classical planning approaches are unable to cope with dynamic environment [1] ▪ Approach the problem of robot navigation in dynamic environment based on fuzzy logic ▪ Explore advantages and disadvantages of the given approach
Anton Volkov 3 Fuzzy Logic for Robot Navigation
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Fuzzy logic introduction
▪ Fuzzy logic
- Fuzzy set
- Membership function
- ...
▪ Fuzzy system design
- Fuzzification / Defuzzification
- Inference engine
- ...
Anton Volkov 4 Fuzzy Logic for Robot Navigation
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Fuzzy sets
Anton Volkov 5 Fuzzy Logic for Robot Navigation [http://cadia.ru.is]
(U, m) | m: U➝ [0, 1] U - universe of discourse m - membership function
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Fuzzy sets
Anton Volkov 6 Fuzzy Logic for Robot Navigation [http://cadia.ru.is]
(U, m) | m: U➝ [0, 1] U - universe of discourse m - membership function LOW(x) ≈ 0.6 MEDIUM(x) ≈ 0.25 HIGH(x) = 0
x
~0.25 ~0.6
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Fuzzy systems
Anton Volkov 7 Fuzzy Logic for Robot Navigation
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Fuzzifier
real-value inputs ↓ membership functions ↓ truth values
Anton Volkov 8 Fuzzy Logic for Robot Navigation
x ↓ LOW(x), MEDIUM(x), HIGH(x) ↓ 0.6, 0.25, 0
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Fuzzy Rule Base
Set of “if-then” rules that define system reaction to input
- 1. if x is LOW then y = 1
- 2. if x is MEDIUM then y = 2
- 3. if x is HIGH then y = 3
Anton Volkov 9 Fuzzy Logic for Robot Navigation
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Fuzzy Inference Engine
▪ Contains rules to define “logic” in fuzzy logic
- m(x∨y) = MAX(m(x), m(y))
- m(x∧y) = MIN(m(x), m(y))
- m(￢x) = 1 - m(x)
▪ Defines the relation between fuzzy input and fuzzy output
Anton Volkov 10 Fuzzy Logic for Robot Navigation
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Defuzzifier
Produces the output based on the most suitable rule
- 1. if x is LOW then y = 1
LOW(x) = 0.6
- 2. if x is MEDIUM then y = 2
MEDIUM(x) = 0.25
- 3. if x is HIGH then y = 3
HIGH(x) = 0
Anton Volkov 11 Fuzzy Logic for Robot Navigation
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Fuzzy system design for robot navigation
Anton Volkov 12 Fuzzy Logic for Robot Navigation
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Example fuzzy system - outline
Assumptions: ▪ 2 driving wheels on the same axis ▪ Goal position is known ▪ Obstacle positions are not known
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Navigation = goal tracking + obstacle avoidance
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Example fuzzy system - goal tracking
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Example fuzzy system - goal tracking
Anton Volkov 15 Fuzzy Logic for Robot Navigation [2] [2]
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Example fuzzy system - goal tracking
Anton Volkov 16 Fuzzy Logic for Robot Navigation [2]
VL , VR = {Z, F, M, B, VB}
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Example fuzzy system - goal tracking
Anton Volkov 17 Fuzzy Logic for Robot Navigation [2] [2]
Notes: ■
- utput is discrete
■ path is not optimal
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Example fuzzy system - obstacle avoidance
Anton Volkov 18 Fuzzy Logic for Robot Navigation [2]
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Example fuzzy system - obstacle avoidance
Anton Volkov 19 Fuzzy Logic for Robot Navigation [2]
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Example fuzzy system - obstacle avoidance
Anton Volkov 20 Fuzzy Logic for Robot Navigation
Rule base consists of 62 rules (Takagi-Sugeno fuzzy inference [3]) Example: ■ If (Distance is VS) and (Angle is NB) and (S1 is F) and (S2 is F) and (S3 is F) and (S4 is F) then (𝑊𝑆 is B) (𝑊𝑀 is Z) ■ If (Distance is VS) and (Angle is NM) and (S1 is F) and (S2 is F) and (S3 is F) and (S4 is F) then (𝑊𝑆 is M) (𝑊𝑀 is Z)
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Example fuzzy system - obstacle avoidance
Anton Volkov 21 Fuzzy Logic for Robot Navigation [2] [2]
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Conclusion
Anton Volkov 22 Fuzzy Logic for Robot Navigation
■ Pros
- Applicable for navigating in dynamic environments
- Computationally simple
■ Cons
- Outdated
- Without obstacles path is not optimal
- Relies on the set of predefined rules
- ...
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Reference
Anton Volkov 23 Fuzzy Logic for Robot Navigation
1. Ellips Masehian and Davoud Sedighizadeh, "Classic and Heuristic Approaches in Robot Motion Planning - A Chronological Review," Proceedings of World Academy of Science, Engineering and Technology,
- Vol. 23, pp. 101-106, August 2007