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docs/source/game_specific_resources/field_coordinate_system/field-coordinate-system.rst

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*FIRST* Tech Challenge Field Coordinate System" Definition
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===========================================================
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Field Coordinate System Definition
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==================================
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Scope
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-----
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This document defines the “standard” Coordinate System (orthogonal axes)
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definition for a *FIRST* Tech Challenge playing field. This definition can be
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This document defines the Field Coordinate System
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for a *FIRST* Tech Challenge playing field. This definition can be
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used for consistent field-centric navigation, target localization and path
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planning.
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Reference frame
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The Field Coordinate System is a
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`three-dimensional Cartesian coordinate system
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<https://en.wikipedia.org/wiki/Cartesian_coordinate_system#Three_dimensions>`__
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which means that the three axes are at right angles to each other.
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The X and Y axes will refer to a position on the field and Z axis a height above the field.
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Reference Frame
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---------------
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The reference frame for this definition is the field perimeter wall, adjacent
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point and runs up and down in a vertical line. Increasing Z values extend
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upwards.
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Rotation about Axes
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Rotation About Axes
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^^^^^^^^^^^^^^^^^^^
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When considering rotations about an axis, consider yourself looking down the
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(positive) axis of rotation from the positive towards the origin. Positive
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rotations are then CCW, and negative rotations CW.
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axis from the positive end towards the origin. Positive
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rotations are then counterclockwise and negative rotations clockwise.
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This rotation convention comes from the `right hand rule <https://en.wikipedia.org/wiki/Right-hand_rule>`__ of classic geometry.
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.. figure:: images/image1.jpg
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:width: 35%
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:align: center
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:alt: Coordinate Axes
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Figure 1: Coordinate Axes
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An example: consider looking down the positive Z axis towards the origin. This
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would be like standing in the middle of the field, looking down. A positive
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rotation about Z (i.e. a rotation parallel to the X-Y plane) is then CCW, as
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one would normally expect from the usual classic 2D geometry.
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Examples
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--------
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Below are two examples illustrating this Axes definition.
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.. note::
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Note that in both cases the Red Alliance members are facing out,
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along the positive Y axis.
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However, in the “Diamond” field configuration, the X axis is pointing
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towards the Blue Alliance, but in the “Square” field configuration
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the Y axis is pointing towards the Blue Alliance.
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:class: no-scaled-link
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:alt: illustration
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showing the counterclockwise rotations about each axis.
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A rotation example: consider looking down the positive Z axis towards the origin.
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This would be like standing in the middle of the field
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looking down at the intersection of the tiles in the very center of the field.
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A positive rotation about the Z axis is then counterclockwise.
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Example: a robot spinning clockwise on the field is making a negative rotation about the Z axis.
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Field Configuration Examples
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----------------------------
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Below are two examples illustrating the Field Coordinate System for different
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*FIRST* Tech Challenge field configurations.
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In a diamond field configuration the two alliance walls are adjacent.
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The field is rotated 45 degrees such that both alliances face the audience.
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The red alliance will be on the right as seen from the audience.
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The Y axis points across the field from the RED WALL and the X axis points to
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the Blue Alliance on the right side of the field.
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.. figure:: images/image2.jpg
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:width: 75%
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:align: center
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:alt: RES-Q
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:class: no-scaled-link
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:alt: a diamond field
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from the FIRST RES-Q game
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Figure 2: FIRST Tech Challenge RES-Q game field orientation
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In a square field configuration the two alliances face each other across the field.
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The field is oriented such that the red alliance is on the right as seen from the audience.
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The Y axis points across the field to the Blue Alliance and the X axis points
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to the right side of the field, away from the audience.
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.. figure:: images/image3.jpg
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:width: 75%
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:align: center
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:alt: Cascade Effect
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:class: no-scaled-link
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:alt: a square field
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from the Cascade Effect game
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Figure 3: FIRST Tech Challenge Cascade Effect game field orientation
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.. note::
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In both field configurations the Red Alliance team members are facing out along the positive Y axis
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and the Z axis points up from the center of the field.
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In the diamond field configuration, the X axis is pointing
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towards the Blue Alliance, but in the square field configuration
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the Y axis is pointing towards the Blue Alliance.
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Measured Values
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---------------
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- Polycarbonate transparencies have a visible opening height of 255 mm
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- The top edge of transparencies is 30 mm from the top of the perimeter
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- Total perimeter height is 313 mm
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- Tiles are 13mm thick
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- Tiles are 13 mm thick
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So, for a diamond field configuration, the corner of the field closest to the
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audience, at a height equal to the top of the perimeter wall, would have a

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