Optimal Path Planning for Mobile Robot-Trailer Systems

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Optimal Path Planning for Mobile Robot-Trailer
Systems

• Team 22 Siwei Wang
• Xin Yu
• Xi Li

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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.

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Task Description
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Basic Approach

• TSP( Travelling Salesman Problem)
• GA (Genetic Algorithm)
• Group the points
• Dubins Paths

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Travelling Salesman Problem

• Random Path

• Optimal Path

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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

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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)

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Simple Genetic Algorithm

• initialize population
• evaluate population
• while TerminationCriteriaNotSatisfied
• select parents for reproduction
• perform crossover and mutation
• evaluate population

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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

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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)

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Fitness Function

• Reciprocal of the total length L
• fitness 1 / L
• One individual is more fit than another one
  if fitness1 gt fitness2.

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Selection

• Elitism Selection
• Roulette Wheel Selection

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Crossover

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

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Crossover

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

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Crossover

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

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Crossover

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

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Crossover

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

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Mutation

• Reversion mutation
• Before (5 8 7 2 1 6 3 4)
• After (5 8 6 1 2 7 3 4)

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Mutation

• 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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Alternating Algorithm - an
established technique
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• Goal connecting the waypoints
• Details Connect points in the optimal order
• Odd-numbered edge - straight
  line
• Even-numbered edge -
  Dubins-path

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Example
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Example(con.)
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Without Group Waypoints
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Group Waypoints
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• 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

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Algorithm and Result
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Experiment

• Different algorithm under low waypoint density

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Experiment(con.)

• Different algorithm under high waypoint density

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Question?