1- * FIRST * Tech Challenge Field “ Coordinate System" Definition
2- ===========================================================
1+ Field Coordinate System Definition
2+ ==================================
33
44Scope
55-----
66
7- This document defines the “standard” Coordinate System (orthogonal axes)
8- definition for a *FIRST * Tech Challenge playing field. This definition can be
7+ This document defines the Field Coordinate System
8+ for a *FIRST * Tech Challenge playing field. This definition can be
99used for consistent field-centric navigation, target localization and path
1010planning.
1111
12- Reference frame
12+ The Field Coordinate System is a
13+ `three-dimensional Cartesian coordinate system
14+ <https://en.wikipedia.org/wiki/Cartesian_coordinate_system#Three_dimensions> `__
15+ which means that the three axes are at right angles to each other.
16+ The X and Y axes will refer to a position on the field and Z axis a height above the field.
17+
18+ Reference Frame
1319---------------
1420
1521The reference frame for this definition is the field perimeter wall, adjacent
@@ -51,52 +57,68 @@ Looking at the origin from the RED WALL, the Z axis extends through the origin
5157point and runs up and down in a vertical line. Increasing Z values extend
5258upwards.
5359
54- Rotation about Axes
60+ Rotation About Axes
5561^^^^^^^^^^^^^^^^^^^
5662
5763When considering rotations about an axis, consider yourself looking down the
58- (positive) axis of rotation from the positive towards the origin. Positive
59- rotations are then CCW, and negative rotations CW.
64+ axis from the positive end towards the origin. Positive
65+ rotations are then counterclockwise and negative rotations clockwise.
66+ This rotation convention comes from the `right hand rule <https://en.wikipedia.org/wiki/Right-hand_rule >`__ of classic geometry.
6067
6168.. figure :: images/image1.jpg
6269 :width: 35%
6370 :align: center
64- :alt: Coordinate Axes
65-
66- Figure 1: Coordinate Axes
67-
68- An example: consider looking down the positive Z axis towards the origin. This
69- would be like standing in the middle of the field, looking down. A positive
70- rotation about Z (i.e. a rotation parallel to the X-Y plane) is then CCW, as
71- one would normally expect from the usual classic 2D geometry .
72-
73- Examples
74- --------
75-
76- Below are two examples illustrating this Axes definition.
77-
78- .. note ::
79- Note that in both cases the Red Alliance members are facing out,
80- along the positive Y axis.
81-
82- However, in the “Diamond” field configuration, the X axis is pointing
83- towards the Blue Alliance, but in the “Square” field configuration
84- the Y axis is pointing towards the Blue Alliance.
85-
71+ :class: no-scaled-link
72+ :alt: illustration
73+
74+ showing the counterclockwise rotations about each axis.
75+
76+ A rotation example: consider looking down the positive Z axis towards the origin.
77+ This would be like standing in the middle of the field
78+ looking down at the intersection of the tiles in the very center of the field .
79+ A positive rotation about the Z axis is then counterclockwise.
80+ Example: a robot spinning clockwise on the field is making a negative rotation about the Z axis.
81+
82+ Field Configuration Examples
83+ ----------------------------
84+
85+ Below are two examples illustrating the Field Coordinate System for different
86+ * FIRST * Tech Challenge field configurations.
87+
88+ In a diamond field configuration the two alliance walls are adjacent.
89+ The field is rotated 45 degrees such that both alliances face the audience.
90+ The red alliance will be on the right as seen from the audience.
91+ The Y axis points across the field from the RED WALL and the X axis points to
92+ the Blue Alliance on the right side of the field.
8693
8794.. figure :: images/image2.jpg
8895 :width: 75%
8996 :align: center
90- :alt: RES-Q
97+ :class: no-scaled-link
98+ :alt: a diamond field
99+
100+ from the FIRST RES-Q game
91101
92- Figure 2: FIRST Tech Challenge RES-Q game field orientation
102+ In a square field configuration the two alliances face each other across the field.
103+ The field is oriented such that the red alliance is on the right as seen from the audience.
104+ The Y axis points across the field to the Blue Alliance and the X axis points
105+ to the right side of the field, away from the audience.
93106
94107.. figure :: images/image3.jpg
95108 :width: 75%
96109 :align: center
97- :alt: Cascade Effect
110+ :class: no-scaled-link
111+ :alt: a square field
112+
113+ from the Cascade Effect game
98114
99- Figure 3: FIRST Tech Challenge Cascade Effect game field orientation
115+ .. note ::
116+ In both field configurations the Red Alliance team members are facing out along the positive Y axis
117+ and the Z axis points up from the center of the field.
118+
119+ In the diamond field configuration, the X axis is pointing
120+ towards the Blue Alliance, but in the square field configuration
121+ the Y axis is pointing towards the Blue Alliance.
100122
101123Measured Values
102124---------------
@@ -109,7 +131,7 @@ representative only, and should not be assumed to be exact, or guaranteed.
109131- Polycarbonate transparencies have a visible opening height of 255 mm
110132- The top edge of transparencies is 30 mm from the top of the perimeter
111133- Total perimeter height is 313 mm
112- - Tiles are 13mm thick
134+ - Tiles are 13 mm thick
113135
114136So, for a diamond field configuration, the corner of the field closest to the
115137audience, at a height equal to the top of the perimeter wall, would have a
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