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O PTIMAL P ATH P LANNING FOR M OBILE R OBOT -T RAILER S YSTEMS Team 22: Siwei Wang Xin Yu Xi Li

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O UTLINE OF P ROJECT Introduction of project (mainly on task description, approach) Explain on GA & Dubins Path. Explain how to group the waypoints, analysis on the experiment. Simulate the whole project with Visual Studio.

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T ASK D ESCRIPTION

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B ASIC A PPROACH TSP( Travelling Salesman Problem) GA (Genetic Algorithm) Group the points Dubins Paths

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T RAVELLING S ALESMAN P ROBLEM Random Path Optimal Path

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T HE G ENETIC A LGORITHM Global searching method that mimics the natural evolution process to optimize the searching problem. Provide efficient, effective techniques for optimization and machine learning applications Widely-used today in scientific and engineering fields

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C OMPONENTS OF A GA A problem to solve, and... Encoding technique ( gene, chromosome ) Initialization (creation) Fitness function (environment) Selection of parents (reproduction) Genetic operators (crossover, mutation) Parameter settings (practice and art)

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S IMPLE G ENETIC A LGORITHM { initialize population; evaluate population; while TerminationCriteriaNotSatisfied { select parents for reproduction; perform crossover and mutation; evaluate population; }

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GA FOR T RAVELING S ALESMAN P ROBLEM The Traveling Salesman Problem: Find a tour of a given set of waypoints so that each waypoint is visited only once the total distance traveled is minimized

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E NCODING Permutation Encoding: An ordered list of waypoint numbers. WaypointList1(3 5 7 2 1 6 4 8) WaypointList2(2 5 7 6 8 1 3 4)

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F ITNESS F UNCTION Reciprocal of the total length L: fitness = 1 / L One individual is more fit than another one if fitness1 > fitness2.

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S ELECTION Elitism Selection Roulette Wheel Selection

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Heuristic Crossover Parent1 (3 5 7 2 1 6 4 8) Parent2 (2 5 7 6 8 1 3 4) Child (2 _ _ _ _ _ _ _) C ROSSOVER

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Heuristic Crossover Parent1 ( 3 5 7 1 6 4 8 ) Parent2 ( 5 7 6 8 1 3 4 ) Child (2 5 _ _ _ _ _ _) C ROSSOVER

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Heuristic Crossover Parent1 (3 7 1 6 4 8) Parent2 (7 6 8 1 3 4) Child (2 5 7 _ _ _ _ _)

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Heuristic Crossover Parent1 (3 1 6 4 8) Parent2 (6 8 1 3 4) Child (2 5 7 1 _ _ _ _)....... C ROSSOVER

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Heuristic Crossover Parent1 (3) Parent2 (3) Child (2 5 7 1 6 8 4 3) C ROSSOVER

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Reversion mutation Before: ( 5 8 7 2 1 6 3 4) After: (5 8 6 1 2 7 3 4) M UTATION

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Reciprocal exchange mutation Before: (5 8 7 2 1 6 3 4) After: (5 8 6 2 1 7 3 4)

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A LTERNATING A LGORITHM - AN ESTABLISHED TECHNIQUE

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Goal: connecting the waypoints Details: C onnect points in the optimal order ; O dd-numbered edge - straight line; E ven-numbered edge - Dubins-path;

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E XAMPLE :

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E XAMPLE ( CON.)

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W ITHOUT G ROUP W AYPOINTS

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G ROUP W AYPOINTS

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Goal: Cover all points ( with suitable circle) Details: E ach circle is independent; A standard circle C r. (according to the trailer) T est whether the current point belong to the last circle

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A LGORITHM AND R ESULT

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E XPERIMENT Different algorithm under low waypoint density

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E XPERIMENT ( CON.) Different algorithm under high waypoint density

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Q UESTION ?

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