A robot is moving in a 2D planar world coordinate plane. Starting from the initial point, the robot has reached point (4,5) with a heading angle of 30° relative to the x-axis. The robot's body frame is oriented in such a way that its x-aris aligns with the direction of the robot's heading angle, and the y-axis is to the left of the robot. At that point, a sonar sensor, which is placed at (2, 1) w.r.t. body coordinate with an orientation 45° from the robot heading, has detected a point object 2 i.e. (2,0) meters directly in front of the itself. A robotic arm is also placed on the robot. The end-effector of this arm is located at (3,−1) w.r.t. robot body frame and aligning its y-axis with x-axis of body frame i.e. rotated 90° clockwise direction. b) A map is generated in the world coordinate frame by the information coming from the robot. Where should this object be located in the map?

A robot is moving in a 2D planar world coordinate plane. Starting from the initial point, the robot has reached point (4,5) with a heading angle of 30° relative to the x-axis. The robot's body frame is oriented in such a way that its x-aris aligns with the direction of the robot's heading angle, and the y-axis is to the left of the robot. At that point, a sonar sensor, which is placed at (2, 1) w.r.t. body coordinate with an orientation 45° from the robot heading, has detected a point object 2 i.e. (2,0) meters directly in front of the itself. A robotic arm is also placed on the robot. The end-effector of this arm is located at (3,−1) w.r.t. robot body frame and aligning its y-axis with x-axis of body frame i.e. rotated 90° clockwise direction. b) A map is generated in the world coordinate frame by the information coming from the robot. Where should this object be located in the map?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Engineering Drawing

Technical drawing has been around since ancient times. As in the ancient Renaissance, complicated drawings were created, including Leonardo da Vinci's drawing. Modern engineering drawing, including its specific orthographic projection with scale conventions, began in Europe (France) during the early stages of Industrialization. L.T. C. Rolt also made some of Marc's drawings for its block-making machinery (in 1799) that also may have contributed significantly to British engineering technology. Since he learned the art of presenting three-dimensional(3D) items in a two-dimensional(2D) plane, as we now term mechanical drawing. 

Question

I would be very happy if you solve it quickly and clearly.

1. A robot is moving in a 2D planar world coordinate plane. Starting from the initial
point, the robot has reached point (4,5) with a heading angle of 30° relative to the
x-axis. The robot's body frame is oriented in such a way that its x-aris aligns with
the direction of the robot's heading angle, and the y-axis is to the left of the robot.
At that point, a sonar sensor, which is placed at (2, 1) w.r.t. body coordinate with
an orientation 45° from the robot heading, has detected a point object 2 i.e. (2,0)
meters directly in front of the itself. A robotic arm is also placed on the robot. The
end-effector of this arm is located at (3,-1) w.r.t. robot body frame and aligning its
y-axis with x-axis of body frame i.e. rotated 90° clockwise direction.
b) A map is generated in the world coordinate frame by the information coming
from the robot. Where should this object be located in the map?

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