1. Instructor Prof. Shih-Chung Kang 2008 Spring
Motion Planning (3/3)
Instructor
Prof. Shih-Chung Kang
2008 Spring

2. The motion planning problem
Goal
Obstacle R
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3. (I) Configuration Space

4. What is a Path? Goal obstacle obstacle obstacle 4 May 10, 2018
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5. How to simplify this problem?
What is a Path?
How to simplify this problem?
Use C-space
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6. Tool: Configuration Space (C-Space C)θ y
goal l
goal
C-obstacle
obstacle
start
start x
Cartesian (real-world) space
C-space θ
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7. Tool: Configuration Space(C-Space C)
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8. Configuration Space (C-space)qn
q=(q1,…,qn) q3 q1 q2
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9. Definition
A robot configuration is a specification of the positions of all robot points relative to a fixed coordinate system
Usually a configuration is expressed as a “vector” of position/orientation parameters
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10. Rigid Robot Example q y x workspace robot reference direction
reference point x
3-parameter representation: q = (x,y,q)
In a 3-D workspace q would be of the form (x,y,z,a,b,g)
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11. Articulated robot exampleq1 q2
q = (q1,q2,…,q10)
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12. Find the C-space of a tower crane
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13. Using C-space to simplify the motion planning of a tower crane
Tower crane in Cartesian space
Forward kinematics
Tower crane in C-space
Inverse kinematics
The geometrical information to describe a tower crane
Four parameters:
θ1, d2, d3, and θ4
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14. Using C-space to simplify the motion planning of a tower crane
Forward kinematics
Tower crane in Cartesian space
Tower crane in C-space
Inverse kinematics
Can be represented by a point in C-space
The attitude of the tower crane
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15. The benefit from using C-space (1/2)
In C-space, we are able to describe the crane geometry in space using the minimal set of parameters.
For example, the position in space (the attitude) of a tower crane in Cartesian space can be described by only four variables, θ1, d2, d3, and θ4.
Because C-space is constructed by the four space factors, a set of the four variables is a point in C-space.
A motion of a tower crane can be described by a series of these four variables, which can form a continuous line in C-space.
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16. The benefits from using C-space (2/2)
After the direct and inverse kinematics of manipulators are derived, we can transfer the crane model and obstacles from the Cartesian space to a C-space.
The problem of finding a collision-free erection path on a complex construction site can be simplified by finding a path that does not go into C-obstacle regions in the C-space.
Because this method does not need to deal with the full geometry and kinematics information of the whole crane in the Cartesian space, the computation and complexity of the path planning problem is significantly reduced.
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17. (II) Motion planning
PRM and RRTs method
A tower crane example 17

18. Probabilistic Roadmap (PRM)
local path
free space
milestone mb mg
[Kavraki, Svetska, Latombe,Overmars, 95]
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19. Rapidly-exploring Random Trees (RRTs)
free space mb mg
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20. Weaker Completeness Complete planner  Too slow
Heuristic planner  Too unreliable
Probabilistic completeness: If there is a solution path, the probability that the planner will find is a (fast growing) function that goes to 1 as running time increases.
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21. Issues Why random sampling? -convenient incremental scheme
Smart sampling strategies -sample the points which have higher probability to be chosen in the final path.
Final path smoothing
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22. How to find an erection path?
The path needs to be collision-free
Also needs to reachable by the crane
Target
Start
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23. How to find an erection path?
Using Probabilistic Roadmap approach (PRM) (Latombe, 1985)
Sample points within crane’s reachable area
Link the points to find a collision-free path
Target
Start Point
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24. Demo: PRM method
This video is the final project in course of Motion Planning taught by Prof. Jean-Claude Latombe. Mr. Xiaoshan Pan is another team member of the project 24

25. How to find an erection path?
1. QuickLink Mothod:Try linking two trees vertical to initial and goal point
Tgoal
target
Tinit
start
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26. Demo: The paths generated by QuickLink Method
A collision free path
Video
Demo: The paths generated by QuickLink Method 26

27. How to find an erection path?
2. QuickGuess Mothod: Add a random middle point between two trees and try to link them by passing a random middle point
Tgoal
Tinit
target
start
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28. Demo: Collision-free paths found by using QuickGuess method
A collision free path
Video
Demo: Collision-free paths found by using QuickGuess method 28

29. How to find an erection path?
3. Modified Random Method: Sample more points in the region with higher possibility to find a path
Tinit
Tgoal
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30. How to refine an erection path?
The process to refine a collision-free path
(a)
(b)
(c)
(d)
Collision-free path without any refining
Eliminate redundant nodes in the path
Smoothen the path reduce sharp angles
Replace the straight line by curves
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31. A collision free path after refining
Demo
Video
A collision free path after refining
Demo: Refined erection paths 31

32. Course website http://robot.caece.net
Question?
Course website