Piecewise linear robot motion (with obstacles)
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The problem is best described with the image below. An robot (the diamond shape) is only allowed to move in a piecewise linear fashion, with each halt being a point of a curve (the red curve). The robot always attempts a linear motion toward the end (on the right), but the motion is not always possible (note the "X", indicating collision).
As you can see, even if the robot moves from position 0 to position 1, the linear motion to the end is still impossible. But the motion 0-1, followed by f-End is acceptable because there are no collisions.
The question is: do you know of any paper studying a similar problem? I am interested in a mathematically sound solution (possibly with certain bounds on, e.g., number of linear segments or an error measure). Another way to approach the problem is studying ways to piecewise linear approximation of an arbitrary curves; a suggestion on a related work is highly appreciated.
ps. A simple solution would be a recursive splitting the curve into two parts, an process which would eventually give one an acceptable sequence; however, bounds are hard to establish in this case.
Robot_motion
geometry approximation curves recursion
asked Nov 22 at 12:51
kevin811
62
add a comment |
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0
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The problem is best described with the image below. An robot (the diamond shape) is only allowed to move in a piecewise linear fashion, with each halt being a point of a curve (the red curve). The robot always attempts a linear motion toward the end (on the right), but the motion is not always possible (note the "X", indicating collision).
As you can see, even if the robot moves from position 0 to position 1, the linear motion to the end is still impossible. But the motion 0-1, followed by f-End is acceptable because there are no collisions.
The question is: do you know of any paper studying a similar problem? I am interested in a mathematically sound solution (possibly with certain bounds on, e.g., number of linear segments or an error measure). Another way to approach the problem is studying ways to piecewise linear approximation of an arbitrary curves; a suggestion on a related work is highly appreciated.
ps. A simple solution would be a recursive splitting the curve into two parts, an process which would eventually give one an acceptable sequence; however, bounds are hard to establish in this case.
Robot_motion
geometry approximation curves recursion
asked Nov 22 at 12:51
kevin811
62
You could get the book by Stephen La Valle, Planning Algorithms, available here.
– Fabio Somenzi
Nov 22 at 13:00
You should also be able to download Nikolaus Correl's Introduction to Autonomous Robots from the author's website. Another good book is Jean-Claude Latombe's Robot Motion Planning, published by Springer.
– Fabio Somenzi
Nov 22 at 13:04
@FabioSomenzi Thanks, Fabio! Leafing through the pages I see that the problem studied in the books is formulated differently. In my case, the points visited have to belong to the pre-specified curve; it is a question of sampling with some smart bounds
– kevin811
Nov 22 at 13:47
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
The problem is best described with the image below. An robot (the diamond shape) is only allowed to move in a piecewise linear fashion, with each halt being a point of a curve (the red curve). The robot always attempts a linear motion toward the end (on the right), but the motion is not always possible (note the "X", indicating collision).
As you can see, even if the robot moves from position 0 to position 1, the linear motion to the end is still impossible. But the motion 0-1, followed by f-End is acceptable because there are no collisions.
The question is: do you know of any paper studying a similar problem? I am interested in a mathematically sound solution (possibly with certain bounds on, e.g., number of linear segments or an error measure). Another way to approach the problem is studying ways to piecewise linear approximation of an arbitrary curves; a suggestion on a related work is highly appreciated.
ps. A simple solution would be a recursive splitting the curve into two parts, an process which would eventually give one an acceptable sequence; however, bounds are hard to establish in this case.
Robot_motion
geometry approximation curves recursion
asked Nov 22 at 12:51
kevin811
62
The problem is best described with the image below. An robot (the diamond shape) is only allowed to move in a piecewise linear fashion, with each halt being a point of a curve (the red curve). The robot always attempts a linear motion toward the end (on the right), but the motion is not always possible (note the "X", indicating collision).
As you can see, even if the robot moves from position 0 to position 1, the linear motion to the end is still impossible. But the motion 0-1, followed by f-End is acceptable because there are no collisions.
The question is: do you know of any paper studying a similar problem? I am interested in a mathematically sound solution (possibly with certain bounds on, e.g., number of linear segments or an error measure). Another way to approach the problem is studying ways to piecewise linear approximation of an arbitrary curves; a suggestion on a related work is highly appreciated.
ps. A simple solution would be a recursive splitting the curve into two parts, an process which would eventually give one an acceptable sequence; however, bounds are hard to establish in this case.
Robot_motion
geometry approximation curves recursion
geometry approximation curves recursion
asked Nov 22 at 12:51
kevin811
62
asked Nov 22 at 12:51
kevin811
62
asked Nov 22 at 12:51
kevin811
62
asked Nov 22 at 12:51
kevin811
62
asked Nov 22 at 12:51
kevin811
62
62
You could get the book by Stephen La Valle, Planning Algorithms, available here.
– Fabio Somenzi
Nov 22 at 13:00
You should also be able to download Nikolaus Correl's Introduction to Autonomous Robots from the author's website. Another good book is Jean-Claude Latombe's Robot Motion Planning, published by Springer.
– Fabio Somenzi
Nov 22 at 13:04
@FabioSomenzi Thanks, Fabio! Leafing through the pages I see that the problem studied in the books is formulated differently. In my case, the points visited have to belong to the pre-specified curve; it is a question of sampling with some smart bounds
– kevin811
Nov 22 at 13:47
add a comment |
You could get the book by Stephen La Valle, Planning Algorithms, available here.
– Fabio Somenzi
Nov 22 at 13:00
You should also be able to download Nikolaus Correl's Introduction to Autonomous Robots from the author's website. Another good book is Jean-Claude Latombe's Robot Motion Planning, published by Springer.
– Fabio Somenzi
Nov 22 at 13:04
@FabioSomenzi Thanks, Fabio! Leafing through the pages I see that the problem studied in the books is formulated differently. In my case, the points visited have to belong to the pre-specified curve; it is a question of sampling with some smart bounds
– kevin811
Nov 22 at 13:47
You could get the book by Stephen La Valle, Planning Algorithms, available here.
– Fabio Somenzi
Nov 22 at 13:00
You could get the book by Stephen La Valle, Planning Algorithms, available here.
– Fabio Somenzi
Nov 22 at 13:00
You should also be able to download Nikolaus Correl's Introduction to Autonomous Robots from the author's website. Another good book is Jean-Claude Latombe's Robot Motion Planning, published by Springer.
– Fabio Somenzi
Nov 22 at 13:04
You should also be able to download Nikolaus Correl's Introduction to Autonomous Robots from the author's website. Another good book is Jean-Claude Latombe's Robot Motion Planning, published by Springer.
– Fabio Somenzi
Nov 22 at 13:04
@FabioSomenzi Thanks, Fabio! Leafing through the pages I see that the problem studied in the books is formulated differently. In my case, the points visited have to belong to the pre-specified curve; it is a question of sampling with some smart bounds
– kevin811
Nov 22 at 13:47
@FabioSomenzi Thanks, Fabio! Leafing through the pages I see that the problem studied in the books is formulated differently. In my case, the points visited have to belong to the pre-specified curve; it is a question of sampling with some smart bounds
– kevin811
Nov 22 at 13:47
add a comment |
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You could get the book by Stephen La Valle, Planning Algorithms, available here.
– Fabio Somenzi
Nov 22 at 13:00
You should also be able to download Nikolaus Correl's Introduction to Autonomous Robots from the author's website. Another good book is Jean-Claude Latombe's Robot Motion Planning, published by Springer.
– Fabio Somenzi
Nov 22 at 13:04
@FabioSomenzi Thanks, Fabio! Leafing through the pages I see that the problem studied in the books is formulated differently. In my case, the points visited have to belong to the pre-specified curve; it is a question of sampling with some smart bounds
– kevin811
Nov 22 at 13:47