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## PowerPoint Slideshow about ' Motion Planning' - chaela

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### Motion Planning

MajdSrour

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)

- 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.

Work space vs Configuration space

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.

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.

Motion Planning

- Problems (from easy to hard) :
- Completely knownstatic Obstacles
- Completely known dynamic Obstacles
- Partially Known static Obstacles
- Partially Known dynamic Obstacles

Roadmap Approach

- Visibility Graph
- Voronoi method
- Cell Decomposition

Visibility Graph

- A visibility graph is a graph of intervisible locations, typically for a set of points and obstacles in the Euclidean plane

Visibility Graph

- Given a set S of disjoint (open) polygons..

Visibility Graph

- Let V(S) be the vertex of S

Visibility Graph

- Let V(S) be the vertex of S
- Letbe the visibility graph of S.

Visibility Graph

- Let V(S) be the vertex of S
- Letbe the visibility graph of S.
- Where:

Visibility Graph

- Let V(S) be the vertex of S
- Letbe the visibility graph of S.
- Where:

Visibility Graph

- Let V(S) be the vertex of S
- Letbe the visibility graph of S.
- Where:

Visibility Graph

- Let V(S) be the vertex of S
- Letbe the visibility graph of S.
- Where:

Visibility Graph

- Let V(S) be the vertex of S
- Letbe the visibility graph of S.
- Where:

Visibility Graph

- Let V(S) be the vertex of S
- Letbe the visibility graph of S.
- Where:

Visibility Graph

- Let V(S) be the vertex of S
- Letbe the visibility graph of S.
- Where:

Visibility Graph

- Let V(S) be the vertex of S
- Letbe the visibility graph of S.
- Where:

Visibility Graph

- Let V(S) be the vertex of S
- Letbe the visibility graph of S.
- Where:

Visibility Graph

- Let V(S) be the vertex of S
- Letbe the visibility graph of S.
- Where:

Visibility Graph

- Corollary: The shortest path between P_start and P_goal corresponds to a shortest path in

Finding the shortest path

- We’ll use Dijkstra algorithm in order to find the shortest path in G
- For each
- return

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.

Example

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

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