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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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.. 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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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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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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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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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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.. 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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Coordinate System
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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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^^^^^^
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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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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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.. 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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:alt: X, Y and Z coordinate axes.
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Counterclockwise rotations about each axis
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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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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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.. 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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Figure 2: FIRST Tech Challenge RES-Q game field orientation
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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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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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Diamond Field
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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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The FIRST RES-Q game field
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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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Square Field
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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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The Into The Deep game field
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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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Coordinate Position Example
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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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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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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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Additional Information
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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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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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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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