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Page 70 - Toucpad robotics C11
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    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.

                  68
                  Touchpad Robotics - XI

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