essentially results in the avoidance of the entire line segment. Consider the Figure 3. Show th (a, – a,) (a, – a,)* +(b, -b,)* |(b, – b,) (a, - a,)° +(b, –b,) 2=(x-a,)c+(y-b )d where e=- and d = Hint:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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In robotics, a scheme, known as the Minimum Distance Technique (MDT) is used to avoid line obstacles. The
MDT involves the calculation of the minimum distance from the robot to the line segment and the avoidance
of the resultant point on the line segment. Avoidance of the closest point on the line at any time t20
essentially results in the avoidance of the entire line segment. Consider the Figure 3. Show that
(a, - a,)
(a, - a,) +(b, -b,)
(b, - h)
(a, -a,) +(b, - b,)
a=(x-a,)c+(y-b,)d where c=-
and d =
Hint:
1. Detemine the parametric equations of the line.
2. Find the Euclidean distance from the robot to the line segment.
3. Optimize the distance.
Page |3
JR.
2-0
(a,.b.)
(a,,b.)
(x., y)
Mobile robot
Figure 3: Schematic representation of a robot avoiding a line segment.
Transcribed Image Text:In robotics, a scheme, known as the Minimum Distance Technique (MDT) is used to avoid line obstacles. The MDT involves the calculation of the minimum distance from the robot to the line segment and the avoidance of the resultant point on the line segment. Avoidance of the closest point on the line at any time t20 essentially results in the avoidance of the entire line segment. Consider the Figure 3. Show that (a, - a,) (a, - a,) +(b, -b,) (b, - h) (a, -a,) +(b, - b,) a=(x-a,)c+(y-b,)d where c=- and d = Hint: 1. Detemine the parametric equations of the line. 2. Find the Euclidean distance from the robot to the line segment. 3. Optimize the distance. Page |3 JR. 2-0 (a,.b.) (a,,b.) (x., y) Mobile robot Figure 3: Schematic representation of a robot avoiding a line segment.
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