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DeDiamondPro · Mar 15, 2024 · de9f0d8 · de9f0d8
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diff --git a/documentation/src/SUMMARY.md b/documentation/src/SUMMARY.md
@@ -3,10 +3,19 @@
 [AQLARP](title-page.md)
 # Introduction
 - [Design Principles](ch01-01-design-principles.md)
+- [Coordinate System](ch02-01-coordinate-system.md)
 # Building
-- [Materials](ch02-01-required-materials.md)
-# Documentation
+- [Required Materials](ch03-01-required-materials.md)
+- [Building](ch04-00-building.md)
+	- [Building The Legs](ch04-01-building-leg.md)
+	- [Building The Main Body](ch04-02-building-body.md)
+	- [Wiring](ch04-03-wiring.md)
+- [Installing Software](ch05-01-installing-software.md)
+# API
+- [ROS2 topics](ch06-01-ros2-topics.md)
+- [Code Structure](ch07-01-code-structure.md)
+# Concepts explained
 
-- [Inverse Kinematics](ch04-00-inverse-kinematics.md)
-	- [Inverse Kinematics Of The Legs](ch04-01-inverse-kinematics-legs.md)
-	- [Inverse Kinematics Of The Body](ch04-02-inverse-kinematics-body.md)
+- [Inverse Kinematics](ch08-00-inverse-kinematics.md)
+	- [Inverse Kinematics Of The Legs](ch08-01-inverse-kinematics-legs.md)
+	- [Inverse Kinematics Of The Body](ch08-02-inverse-kinematics-body.md)
diff --git a/documentation/src/ch-01-02-coordinate-system b/documentation/src/ch-01-02-coordinate-system
@@ -0,0 +1 @@
+# 
diff --git a/documentation/src/ch02-01-coordinate-system.md b/documentation/src/ch02-01-coordinate-system.md
@@ -0,0 +1,17 @@
+# Defining AQLARP's coordinate system
+Knowing AQLARP's coordinate system is import so you know what setting each axis will do.
+Here are the definitions for it:
+- X-axis:
+	- Increasing the value will make AQLARP move to the front
+	- Decreasing the value will make AQLARP move to the back
+- Y-axis:
+	- Increasing the value will make AQLARP go up
+	- Decreasing the value will make AQLARP go down
+- Z-axis:
+	- Increasing the value will make AQLARP go to the right
+	- Decreasing the value will make AQLARP go to the left
+
+The origin of these axis is where the leg is connected to the top joint, this is a per leg coordinate system.
+
+Below are some images to clarify what axis does what.
+![](img/Coordinate-System-XY.png)![](img/Coordinate-System-XZ.png)
diff --git a/...ntation/src/ch02-01-required-materials.md → ...ntation/src/ch03-01-required-materials.md b/...ntation/src/ch02-01-required-materials.md → ...ntation/src/ch03-01-required-materials.md
diff --git a/documentation/src/ch04-00-building.md b/documentation/src/ch04-00-building.md
diff --git a/documentation/src/ch04-01-building-leg.md b/documentation/src/ch04-01-building-leg.md
diff --git a/documentation/src/ch04-02-building-body.md b/documentation/src/ch04-02-building-body.md
diff --git a/documentation/src/ch04-02-inverse-kinematics-body.md b/documentation/src/ch04-02-inverse-kinematics-body.md
diff --git a/documentation/src/ch04-03-wiring.md b/documentation/src/ch04-03-wiring.md
diff --git a/documentation/src/ch05-01-installing-software.md b/documentation/src/ch05-01-installing-software.md
diff --git a/documentation/src/ch06-01-ros2-topics.md b/documentation/src/ch06-01-ros2-topics.md
diff --git a/documentation/src/ch07-01-code-structure.md b/documentation/src/ch07-01-code-structure.md
diff --git a/...ntation/src/ch04-00-inverse-kinematics.md → ...ntation/src/ch08-00-inverse-kinematics.md b/...ntation/src/ch04-00-inverse-kinematics.md → ...ntation/src/ch08-00-inverse-kinematics.md
diff --git a/...on/src/ch04-01-inverse-kinematics-legs.md → ...on/src/ch08-01-inverse-kinematics-legs.md b/...on/src/ch04-01-inverse-kinematics-legs.md → ...on/src/ch08-01-inverse-kinematics-legs.md
@@ -42,7 +42,7 @@ Then finally we can combine them by adding them together.
 $$A = A_{x} + A_{y}$$
 $$B = B_{y}$$
 $$C = C_{y} + C_{z}$$
-## In code
+## Code
 After transforming all these calculations into code, we get this:
 ```py
 def calc_angles(leg, x, y, z):

diff --git a/documentation/src/ch08-02-inverse-kinematics-body.md b/documentation/src/ch08-02-inverse-kinematics-body.md
@@ -0,0 +1,63 @@
+# Inverse kinematic of the body
+The inverse kinematics of the body is to transform pitch, roll and rotation into offsets for the x, y and z coordinate of a leg. 
+## Definitions
+\\(l\\) length of the body
+
+\\(w\\) width of the body
+
+\\(pitch\\) desired pitch
+
+\\(roll\\) desired roll
+
+\\(rotation\\) desired rotation
+
+\\(rotation\\) desired rotation
+
+\\(m_{x}\\) leg movement x
+
+\\(m_{y}\\) leg movement y
+
+\\(m_{z}\\) leg movement z
+
+\\(x\\) x position of a leg relative to the center
+
+\\(z\\) z position of a leg relative to the center
+## Pitch
+The calculations for pitch are as follows:
+$$m_{x} = \frac{l(1-\cos(pitch))}{2}$$
+$$m_{y} = \frac{l\sin(pitch)}{2}$$
+## Roll
+The calculations for roll are as follows:
+$$m_{z} = \frac{w(1-\cos(roll))}{2}$$
+$$m_{y} = \frac{w\sin(roll)}{2}$$
+## Rotation
+The calculations for rotation are based on a [rotation matrix](https://en.wikipedia.org/wiki/Rotation_matrix). These calculations are as follows:
+
+$$m_{x} = (x \times \cos(rotation) - z \times \sin(rotation)) - x$$
+$$m_{z} = (x \times \sin(rotation) + z \times \cos(rotation)) - z$$
+## Combining Calculations
+To combine these calculations you just calculate each one separately and then calculate the sum of all x calculations, then the sum of all y calculations and finally the sum of all z calculations.
+## Code
+After transforming these calculations into code, we get this:
+```py
+def calc_leg_offsets(leg, pitch, roll, rotation):
+    # Get the X and Z coordinate of the leg
+    x = (body_length / 2) if leg < 2 else -(body_length / 2)
+    z = -(body_width / 2) if leg == 0 or leg == 3 else (body_width / 2)
+    # Calculate the height difference of the leg to reach the target pitch
+    height_diff_pitch = x * sin(radians(pitch))
+    # Calculate the height difference of the leg to reach the target roll
+    height_diff_roll = z * sin(radians(roll))
+    # Calculate the X and Z offsets to keep the body centered
+    movement_x_pitch = x * (1 - cos(radians(pitch)))
+    movement_z_roll = z * (1 - cos(radians(roll)))
+    # Calculate the rotation offsets
+    movement_x_rotation = (x * cos(radians(rotation)) - z * sin(radians(rotation))) - x
+    movement_z_rotation = (x * sin(radians(rotation)) + z * cos(radians(rotation))) - z
+    # Merge the offsets and return them
+    return (
+        movement_x_pitch + movement_x_rotation,
+        height_diff_pitch - height_diff_roll,
+        movement_z_roll + movement_z_rotation
+    )
+```
diff --git a/documentation/src/img/Coordinate-System-XY.png b/documentation/src/img/Coordinate-System-XY.png
diff --git a/documentation/src/img/Coordinate-System-XZ.png b/documentation/src/img/Coordinate-System-XZ.png
diff --git a/documentation/src/title-page.md b/documentation/src/title-page.md
@@ -5,8 +5,6 @@ AQLARP stands for **A**ffordable **Q**uadruped **L**earning **A**nd **R**esearch
 
 AQLARP is licensed under the [MIT license](https://github.com/DeDiamondPro/AQLARP/blob/master/LICENSE).
 
-<div class = "warning">
-This documentation is incomplete
-
-It is advisable to have a basic understanding of the parts of the robot to effectively address encountered issues. If you need help, feel free to open an issue on [AQLARP's GitHub](https://github.com/DeDiamondPro/AQLARP). However no guarantees can be provided that I will be able to help you.
-</div>
+> **🚨 This documentation is incomplete**
+>
+> It is advisable to have a basic understanding of the parts of the robot to effectively address encountered issues. If you need help, feel free to open an issue on [AQLARP's GitHub](https://github.com/DeDiamondPro/AQLARP). However there is no gaurantee that I will be able to help you.