Cartpole
Description
Environment to simulate a Cartpole System.
Equation
\[\begin{split}\ddot{\theta_t}= \frac{g\sin{\theta_t}+\cos{\theta_t}[\frac{-F_t-ml{\dot{\theta_t}}^2 \sin{\theta_t}+\mu_c \textrm{sgn}({\dot{x_t}})}{m_c+m_p}]-\frac{\mu_p \dot{\theta_t}}{m_p l}}{l [\frac{4}{3}- \frac{m_p {\cos^2{\theta_t}}}{m_c + m_p}]} \\
\ddot{x_t}= \frac{F_t + m l [{\dot{\theta_t}}^2 \sin{\theta_t}- \ddot{\theta_t} \cos{\theta_t}]-\mu_c \textrm{sgn}(\dot{x_t})}{m_c + m_p}\end{split}\]
Parameters
\(\mu_{p}\): Coefficient of friction of pole on cart
\(\mu_{c}\): Coefficient of friction of cart on track
\(l\): Half-pole length
\(m_{c}\): Mass of cart
\(m_{p}\): Mass of pole
\(g\): Gravitational acceleration
Action
Num |
Term in Equation |
Term in Class |
|---|---|---|
0 |
\(F_t\) |
force |
States
Num |
Term in Equation |
Term in Class |
|---|---|---|
0 |
\(x_t\) |
deflection |
1 |
\(\dot{x_t}\) |
velocity |
2 |
\(\theta_t\) |
theta |
3 |
\(\dot{\theta_t}\) |
omega |