Rune Harlyk
34 lines
1.2 KiB
Markdown
34 lines
1.2 KiB
Markdown
# 🦾 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 -->
|
|
|
|
<!-- $$
|
|
R_{body} =
|
|
\begin{bmatrix}
|
|
\cos\psi\cos\theta & \cos\psi\sin\theta\sin\phi - \sin\psi\cos\phi & \cos\psi\sin\theta\cos\phi + \sin\psi\sin\phi \\
|
|
\sin\psi\cos\theta & \sin\psi\sin\theta\sin\phi + \cos\psi\cos\phi & \sin\psi\sin\theta\cos\phi - \cos\psi\sin\phi \\
|
|
-\sin\theta & \cos\theta\sin\phi & \cos\theta\cos\phi
|
|
\end{bmatrix}
|
|
$$ -->
|