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Optimal Path Planning for Mobile Robot-Trailer Systems

Optimal Path Planning for Mobile Robot-Trailer Systems. Team 22: Siwei Wang Xin Yu Xi Li. Outline of Project. Introduction of project (mainly on task description, approach) Explain on GA & Dubins Path. Explain how to group the waypoints, analysis on the experiment.

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Optimal Path Planning for Mobile Robot-Trailer Systems

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  1. Optimal Path Planning for Mobile Robot-Trailer Systems Team 22: Siwei Wang Xin Yu Xi Li

  2. Outline of Project • 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.

  3. Task Description

  4. Basic Approach • TSP( Travelling Salesman Problem) • GA (Genetic Algorithm) • Group the points • Dubins Paths

  5. Travelling Salesman Problem Random Path Optimal Path

  6. The Genetic Algorithm • 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

  7. Components 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)

  8. Simple Genetic Algorithm { initialize population; evaluate population; while TerminationCriteriaNotSatisfied { select parents for reproduction; perform crossover and mutation; evaluate population; } }

  9. GA for Traveling Salesman Problem 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

  10. Encoding • 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)

  11. Fitness Function • Reciprocal of the total length L: fitness = 1 / L One individual is more fit than another one if fitness1 > fitness2.

  12. Selection • Elitism Selection • Roulette Wheel Selection

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

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

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

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

  17. Crossover • Heuristic Crossover Parent1 (3) Parent2 (3) Child (2 5 7 1 6 8 4 3)

  18. Mutation • Reversion mutation Before: (5 8 7 2 1 6 3 4) After: (5 8 6 1 2 7 3 4)

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

  20. Alternating Algorithm- an established technique

  21. Goal: connecting the waypoints • Details: Connect points in the optimal order ; Odd-numbered edge - straight line; Even-numbered edge - Dubins-path;

  22. Example:

  23. Example(con.)

  24. Without Group Waypoints

  25. Group Waypoints

  26. Goal: Cover all points ( with suitable circle) • Details: Each circle is independent; A standard circle Cr. (according to the trailer) Test whether the current point belong to the last circle

  27. Algorithm and Result

  28. Experiment • Different algorithm under low waypoint density

  29. Experiment(con.) • Different algorithm under high waypoint density

  30. Question?

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