Page 70 - Toucpad robotics C11

Polar Coordinate System
The polar coordinate system is a two-dimensional system that defines a point by its distance from a central point and
its angle from a reference direction.

Description
A point is defined by two coordinates:
u
r (radius): The radial distance from the origin (the central point).
l
(theta): The angle measured from a fixed reference direction (the polar axis).
l
A point is written as (r, ).
u
2
3 2 3
3
4 4
5 5, 3
6 6
r

0.2
1 2 3 4 5 6

7 11
6 6
5 7
4 4
4 5
3 3 3
2

Application in Robotics

Robotic Arms with Revolute Joints: The base joint of a robotic arm often rotates around a central point, making it
u
natural to describe its motion in polar coordinates. The robot’s arm can extend or retract (changing the radius ‘r’)
and rotate around its base (changing the angle ‘ ’).
Circular Movement: When a robot needs to move in a circle around a central object, or sweep a sensor (like a LIDAR)
u
in a circular motion, the polar coordinate system is the most natural and efficient way to program it.
Range-Finding Sensors: Sensors that measure distance and angle (like some ultrasonic or infrared sensors on a
u
rotating platform) naturally produce data in polar coordinates.
Advantages

Intuitive for Rotational Motion: It’s very easy to describe and control rotational movements.
u
Simple for Radial Movement: Describing the extension or retraction of a link is a straightforward change in the
u
radius ‘r’.
Disadvantages
Less Intuitive for Linear Motion: Moving in a straight line with polar coordinates is more complex to calculate and
u
control.

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Touchpad Robotics - XI