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Motion Planning

Motion Planning. Majd Srour. Definition. Motion planning refers to the computational process of moving from one place to another in the presence of obstacles. Work space. The physical space in which the robot of finite-size. – Real world. Configuration Space (Only translation).

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Motion Planning

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  1. Motion Planning MajdSrour

  2. Definition • Motion planning refers to the computational process of moving from one place to another in the presence of obstacles.

  3. Work space • The physical space in which the robot of finite-size. – Real world

  4. Configuration Space (Only translation) • The configuration space is a transformation from the physical space in which the robot is of finite-size into another space in which the robot is treated as a point. • The configuration space is obtained by shrinking the robot to a point, while growing the obstacles by the size of the robot.

  5. Work space vs Configuration space

  6. Free Space • The free space of a configuration space simply consists of the areas not occupied by obstacles.  Any configuration within this space is called a free configuration.

  7. Free Path • The free path between an initial configuration and a goal configuration is the path which lies completely in free space and does not come into contact with any obstacles.

  8. Motion Planning • Problems (from easy to hard) : • Completely knownstatic Obstacles • Completely known dynamic Obstacles • Partially Known static Obstacles • Partially Known dynamic Obstacles

  9. Roadmap Approach • Visibility Graph • Voronoi method • Cell Decomposition

  10. Visibility Graph • A visibility graph is a graph of intervisible locations, typically for a set of points and obstacles in the Euclidean plane

  11. Visibility Graph • Given a set S of disjoint (open) polygons..

  12. Visibility Graph • Let V(S) be the vertex of S

  13. Visibility Graph • Let V(S) be the vertex of S • Letbe the visibility graph of S.

  14. Visibility Graph • Let V(S) be the vertex of S • Letbe the visibility graph of S. • Where:

  15. Visibility Graph • Let V(S) be the vertex of S • Letbe the visibility graph of S. • Where:

  16. Visibility Graph • Let V(S) be the vertex of S • Letbe the visibility graph of S. • Where:

  17. Visibility Graph • Let V(S) be the vertex of S • Letbe the visibility graph of S. • Where:

  18. Visibility Graph • Let V(S) be the vertex of S • Letbe the visibility graph of S. • Where:

  19. Visibility Graph • Let V(S) be the vertex of S • Letbe the visibility graph of S. • Where:

  20. Visibility Graph • Let V(S) be the vertex of S • Letbe the visibility graph of S. • Where:

  21. Visibility Graph • Let V(S) be the vertex of S • Letbe the visibility graph of S. • Where:

  22. Visibility Graph • Let V(S) be the vertex of S • Letbe the visibility graph of S. • Where:

  23. Visibility Graph • Let V(S) be the vertex of S • Letbe the visibility graph of S. • Where:

  24. Visibility Graph • Corollary: The shortest path between P_start and P_goal corresponds to a shortest path in

  25. Finding the shortest path • We’ll use Dijkstra algorithm in order to find the shortest path in G • For each • return

  26. Dijkstra • Assign to every node a distance value of infinity, and to the first node 0 • Mark all nodes as unvisited, set initial node as current • For current node, consider all of its unvisited neighbors and calculate their tentative distances • When we are done considering all of the neighbors of the current node, mark the current node as visited and remove it from the unvisited set. A visited node will never be checked again; its distance recorded now is final and minimal. • If the destination node has been marked visited then stop. • Set the unvisited node marked with the smallest tentative distance as the next "current node" and go back to step 3.

  27. Example • Find shortest path from a to z • http://www.youtube.com/watch?v=UG7VmPWkJmA

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