In [11]:

    

from general_wheel import*
from mobile_ss import*


    

In [12]:

    

f1 = general_wheel(v_alpha = -pi/2, v_beta = 0, v_gamma =  pi/2, d = 0)
f1.exp


    

    




New mobile robot parameterization






    
Out[12]:





$$\left[\begin{matrix}- r\\0\end{matrix}\right] \dot{\phi} + \left[\begin{matrix}1 & 0 & L\\0 & 1 & 0\end{matrix}\right] {R(\theta)} \dot{\xi}$$

In [13]:

    

f2 = general_wheel(v_alpha = pi/2, v_beta = 0, v_gamma =  -pi/2, d = 0)
f2.exp


    

    




New mobile robot parameterization






    
Out[13]:





$$\left[\begin{matrix}- r\\0\end{matrix}\right] \dot{\phi} + \left[\begin{matrix}1 & 0 & - L\\0 & 1 & 0\end{matrix}\right] {R(\theta)} \dot{\xi}$$

In [14]:

    

b3 = Symbol('\\beta _{3c}')
a = Symbol('a')
c3 = general_wheel(v_alpha = pi, v_beta = b3 , v_gamma =  0, L=a)
c3.exp


    

    




New mobile robot parameterization






    
Out[14]:





$$\left[\begin{matrix}0\\d\end{matrix}\right] \dot{\beta} + \left[\begin{matrix}- r\\0\end{matrix}\right] \dot{\phi} + \left[\begin{matrix}- \cos{\left (\beta _{{3c}} \right )} & - \sin{\left (\beta _{{3c}} \right )} & a \sin{\left (\beta _{{3c}} \right )}\\\sin{\left (\beta _{{3c}} \right )} & - \cos{\left (\beta _{{3c}} \right )} & a \cos{\left (\beta _{{3c}} \right )} + d\end{matrix}\right] {R(\theta)} \dot{\xi}$$

In [15]:

    

mob = mobile_ss();   
mob.conf_kinematic_model([f1,f2,c3],['f','f','c'])


    

    




New mobile robot instance:






    
Out[15]:





$$\left[\begin{matrix}\cos{\left (\theta \right )} & 0\\\sin{\left (\theta \right )} & 0\\0 & 1\\- \frac{1}{d} \sin{\left (\beta _{{3c}} \right )} & - \frac{1}{d} \left(a \cos{\left (\beta _{{3c}} \right )} + d\right)\\\frac{1}{r} & \frac{L}{r}\\\frac{1}{r} & - \frac{L}{r}\\- \frac{1}{r} \cos{\left (\beta _{{3c}} \right )} & \frac{a}{r} \sin{\left (\beta _{{3c}} \right )}\end{matrix}\right]$$

In [ ]: