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. Simulate the whole project with Visual Studio.

TASK DESCRIPTION

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

TRAVELLING SALESMAN PROBLEM Random Path Optimal Path

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

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)

SIMPLE GENETIC ALGORITHM { initialize population; evaluate population; while Termination. Criteria. Not. Satisfied { select parents for reproduction; perform crossover and mutation; evaluate population; } }

GA FORTRAVELING 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

ENCODING Permutation Encoding: An ordered list of waypoint numbers. Waypoint. List 1 Waypoint. List 2 (3 5 7 2 1 6 4 8) (2 5 7 6 8 1 3 4)

FITNESS FUNCTION Reciprocal of the total length L: fitness = 1 / L One individual is more fit than another one if fitness 1 > fitness 2.

SELECTION Elitism Selection Roulette Wheel Selection

CROSSOVER Heuristic Crossover Parent 1 (3 5 7 2 1 6 4 8) Parent 2 (2 5 7 6 8 1 3 4) Child (2 _ _ _ _)

CROSSOVER Heuristic Crossover Parent 2 5 7 1 6 4 8) (5 7 6 8 1 3 4 ) Child (2 5 _ _ _) Parent 1 (3

CROSSOVER • Heuristic Crossover Parent 1 Parent 2 (3 7 1 6 4 8) (7 6 8 1 3 4) Child (2 5 7 _ _ _)

CROSSOVER Heuristic Crossover Parent 1 (3 1 6 4 8) Parent 2 (6 8 1 3 4) Child (2 5 7 1 _ _). . .

CROSSOVER Heuristic Crossover Parent 1 Parent 2 Child (3) (2 5 7 1 6 8 4 3)

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

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

ALTERNATING ALGORITHM - AN ESTABLISHED TECHNIQUE

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

EXAMPLE:

EXAMPLE(CON. )

WITHOUT GROUP WAYPOINTS

GROUP WAYPOINTS

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

ALGORITHM AND RESULT

EXPERIMENT Different density algorithm under low waypoint

EXPERIMENT(CON. ) Different density algorithm under high waypoint

QUESTION?