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docs/kinematics.md

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+# 🦾 Kinematics
+
+To enable complex movements, it's beneficial to be able to describe the robot state using a world reference frame, instead of using raw joint angles.
+
+The robot's body pose in the world reference frame is represented as
+
+$$T_{body}=\left[x_b,y_b,z_b,\phi, \theta,\psi\right]$$
+
+Where
+
+- $x_b, y_b, z_b$ are cartesian coordinates of the robot's body center.
+- $\phi, \theta,\psi$ are the roll, pitch and yaw angles, describing the body orientation.
+
+The feet positions in the world reference frame are:
+
+$$P_{feet}=\left\{(x_{f_i},y_{f_i},z_{f_i})|i=1,2,3,4\right\}$$
+
+where $x_{f_i}, y_{f_i}, z_{f_i}$ are cartesian coordinates for each foot $i$.
+
+Solving the inverse kinematics yields target angles for the actuators.
+
+<!-- Write about the calculation, rotation matrix and trig -->
+
+<!-- L1, L2, L3, L4, L, W -->
+
+<!-- $$
+R_{body} =
+\begin{bmatrix}
+\cos\psi\cos\theta & \cos\psi\sin\theta\sin\phi - \sin\psi\cos\phi & \cos\psi\sin\theta\cos\phi + \sin\psi\sin\phi \\
+\sin\psi\cos\theta & \sin\psi\sin\theta\sin\phi + \cos\psi\cos\phi & \sin\psi\sin\theta\cos\phi - \cos\psi\sin\phi \\
+-\sin\theta & \cos\theta\sin\phi & \cos\theta\cos\phi
+\end{bmatrix}
+$$ -->