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.. _first field coordinate system :
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- *FIRST * Tech Challenge Field “Coordinate System" Definition
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- ===========================================================
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+ *FIRST * Tech Challenge Field Coordinate System Definition
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+ =========================================================
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+
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+ .. meta ::
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+ :description: This document defines the FIRST Tech Challenge Field Coordinate System which can be used to specify position on the playing field.
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+
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+ Summary: The *FIRST * Tech Challenge Field Coordinate System is a Cartesian Coordinate System of three dimensions.
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+ The X and Y axes will refer to a position on the field and the Z axis a height above the field.
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Scope
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-----
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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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+
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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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+ 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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- to the RED Alliance Station ( known here as the: RED WALL) . The definition is
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+ to the red Alliance Area, known here after as the Red Wall . The definition is
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from the perspective of a person, standing outside the field, in the center of
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- RED WALL, looking towards the center of the field.
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-
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- Caveat: If the Red Alliance Station is ever adjacent to two perimeter walls,
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- the RED WALL will be the one with *most * contact with the Alliance Station. If
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- the red Alliance Station is ever adjacent to two perimeter walls EQUALLY, then
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- the most clockwise of the two walls will be considered to be the RED WALL.
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+ Red Wall, looking towards the center of the field.
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+
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+ .. note ::
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+ If the red Alliance Area is ever adjacent to two perimeter walls,
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+ the Red Wall will be the one with *most * contact with the Alliance Area. If
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+ the red Alliance Area is ever adjacent to two perimeter walls *equally *, then
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+ the most clockwise of the two walls will be considered to be the Red Wall.
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+
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+ Coordinate System
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+ -----------------
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+
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+ The Field Coordinate System is a Cartesian Coordinate System of three dimensions.
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+ X and Y will refer to a position on the field.
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+ Z will refer to a height above the field.
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+ You may use any length measure as long as the same measure is used for all three axes.
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+ The coordinates are ordered (X, Y, Z).
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+ Example: coordinate position (10, -10, 0) has X = 10, Y = -10 and Z = 0.
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Origin
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^^^^^^
@@ -35,85 +52,131 @@ mat.
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X Axis
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^^^^^^
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- Looking at the origin from the RED WALL , the X axis extends through the origin
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- point and runs to the right and left, parallel with the RED WALL . The X axis
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+ Looking at the origin from the Red Wall , the X axis extends through the origin
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+ point and runs to the right and left, parallel with the Red Wall . The X axis
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values increase to the right.
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Y Axis
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^^^^^^
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- Looking at the origin from the RED WALL , the Y axis extends through the origin
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- point and runs out and in, perpendicular to the RED WALL. Increasing Y values
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- run out (away) from the RED WALL .
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+ Looking at the origin from the Red Wall , the Y axis extends through the origin
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+ point and runs out and in, perpendicular to the Red Wall. Increasing Y values
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+ run out (away) from the Red Wall .
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Z Axis
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^^^^^^
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- Looking at the origin from the RED WALL , the Z axis extends through the origin
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+ Looking at the origin from the Red Wall , the Z axis extends through the origin
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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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-
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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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+
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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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-
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- Figure 1: Coordinate Axes
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+ :alt: X, Y and Z coordinate axes.
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+
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+ Counterclockwise rotations about each axis
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+
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+ Imagine looking down the positive Z axis towards the origin.
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+ This would be like standing in the middle of the field looking down.
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+ A positive rotation about the Z axis would be counterclockwise.
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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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+ Example: a robot spinning clockwise on the Field is making a negative rotation about the Z axis.
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- Examples
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- --------
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+ Field Configuration Examples
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+ ----------------------------
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- Below are two examples illustrating this Axes definition.
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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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.. 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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-
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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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-
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-
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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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-
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- Figure 2: FIRST Tech Challenge RES-Q game field orientation
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-
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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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-
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- Figure 3: FIRST Tech Challenge Cascade Effect game field orientation
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+ In both field configurations the red Alliance is 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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+
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+ Diamond Field
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+ ^^^^^^^^^^^^^
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+
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+ .. figure :: images/first-res-q-field.png
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+ :alt: A diamond field with X, Y and Z axes shown.
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+
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+ The FIRST RES-Q game field
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+
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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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+ From the audience perspective the field forms a diamond shape.
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+ The Red Wall will be on the right as seen from the audience.
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+ The Y axis points across the field as seen from the Red Wall.
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+ The X axis points to the Blue Alliance.
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+
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+ Square Field
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+ ^^^^^^^^^^^^
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+
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+ .. figure :: images/into-the-deep-field.png
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+ :alt: A square field with X, Y and Z axes shown.
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+
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+ The Into The Deep game field
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+
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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 Wall is on the right as seen from the audience.
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+ The Y axis points across the field from the Red Wall towards the Blue Alliance.
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+ The X axis points away from the audience to the rear of the field.
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+
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+ Coordinate Position Example
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+ ---------------------------
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+
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+ Let's consider the coordinates (0, -24, 26) in inches on the Into The Deep field, which is a square field.
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+ Given the order of coordinates then X = 0, Y = -24, and Z = 26.
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+
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+ The X axis value of 0 is located at the origin in the center of the field.
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+ The Y axis value of negative 24 would be located closer to the Red Wall, away from the origin by the width of one tile.
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+ This the center of the wall of the submersible structure on the red side of the field.
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+
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+ The Z axis value of 26 indicates the coordinates refer to the center and top of the Red Alliance "high chamber"
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+ (which is the higher of the two red crossbars).
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Measured Values
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---------------
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- The following values have been measured from a 2016 competition field. They are
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+ The following metric values have been measured from a 2016 competition field. They are
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representative only, and should not be assumed to be exact, or guaranteed.
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- - Distance between opposite inside faces of panels: 3580 mm
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- (if field assembled well: the straps give some adjustment tolerance)
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+ - Distance between opposite inside faces of panels: 3580 mm,
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+ (if the field is assembled well: the straps give some adjustment tolerance)
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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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- coordinate position of: (-1790, 1790, 300).
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+ coordinate position of: (-1790, 1790, 300) in millimeters.
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+
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+ Additional Information
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+ ----------------------
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+
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+ See this Wikipedia article on `Cartesian coordinate system
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+ <https://en.wikipedia.org/wiki/Cartesian_coordinate_system#Three_dimensions> `__
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+ in three dimensions.
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+ The Field Coordinate System rotation convention comes from the
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+ `right hand rule <https://en.wikipedia.org/wiki/Right-hand_rule >`__
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+ of classic geometry.
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+
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+ Robots with a webcam can use :ref: `AprilTags <apriltag/vision_portal/apriltag_intro/apriltag-intro:apriltag introduction >`
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+ to determine where an :ref: `AprilTag is located
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+ <apriltag/understanding_apriltag_detection_values/understanding-apriltag-detection-values:introduction>`
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+ with respect to the robot.
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+ Since AprilTags are in known locations on the field, you can also determine the
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+ :ref: `location of the robot <apriltag/vision_portal/apriltag_localization/apriltag-localization:apriltag localization >`
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+ on the field.
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+
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+ Robots can use an inertial measurement unit (IMU) to measure rotations about axes
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+ with respect to the robot. See :ref: `IMU axes definition. <programming_resources/imu/imu:axes definition >`
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+ The yaw value from the IMU, also known the heading, measures rotation about the Z axis
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+ which points up from the robot.
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+ You can use the IMU to determine which direction a robot is facing.
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