update doc

docs/modules/cgmres_nmpc.rst

@@ -61,28 +61,32 @@ Mathematical Formulation
 
 Motion model is
 
-:math:`\dot{x}=vcos\theta`
+.. math:: \dot{x}=vcos\theta
 
-:math:`\dot{y}=vsin\theta`
+.. math:: \dot{y}=vsin\theta
 
-:math:`\dot{\theta}=\frac{v}{WB}sin(u_{\delta})` (tan is not good for
-optimization)
+.. math:: \dot{\theta}=\frac{v}{WB}sin(u_{\delta})
 
-:math:`\dot{v}=u_a`
+\ (tan is not good for optimization)
+
+.. math:: \dot{v}=u_a
 
 Cost function is
 
-:math:`J=\frac{1}{2}(u_a^2+u_{\delta}^2)-\phi_a d_a-\phi_\delta d_\delta`
+.. math:: J=\frac{1}{2}(u_a^2+u_{\delta}^2)-\phi_a d_a-\phi_\delta d_\delta
 
 Input constraints are
 
-:math:`|u_a| \leq u_{a,max}`
+.. math:: |u_a| \leq u_{a,max}
 
-:math:`|u_\delta| \leq u_{\delta,max}`
+.. math:: |u_\delta| \leq u_{\delta,max}
 
 So, Hamiltonian　is
 
-:math:`J=\frac{1}{2}(u_a^2+u_{\delta}^2)-\phi_a d_a-\phi_\delta d_\delta\\ +\lambda_1vcos\theta+\lambda_2vsin\theta+\lambda_3\frac{v}{WB}sin(u_{\delta})+\lambda_4u_a\\ +\rho_1(u_a^2+d_a^2+u_{a,max}^2)+\rho_2(u_\delta^2+d_\delta^2+u_{\delta,max}^2)`
+.. math::
+
+   J=\frac{1}{2}(u_a^2+u_{\delta}^2)-\phi_a d_a-\phi_\delta d_\delta\\ +\lambda_1vcos\theta+\lambda_2vsin\theta+\lambda_3\frac{v}{WB}sin(u_{\delta})+\lambda_4u_a\\ 
+   +\rho_1(u_a^2+d_a^2+u_{a,max}^2)+\rho_2(u_\delta^2+d_\delta^2+u_{\delta,max}^2)
 
 Partial differential equations of the Hamiltonian are:
 

docs/modules/extended_kalman_filter_localization.rst

@@ -39,9 +39,9 @@ Filter design
 In this simulation, the robot has a state vector includes 4 states at
 time :math:`t`.
 
-.. math:: \textbf{x}_t=[x_t, y_t, \theta_t, v_t]
+.. math:: \textbf{x}_t=[x_t, y_t, \phi_t, v_t]
 
-x, y are a 2D x-y position, :math:`\theta` is orientation, and v is
+x, y are a 2D x-y position, :math:`\phi` is orientation, and v is
 velocity.
 
 In the code, “xEst” means the state vector.

docs/modules/rocket_powered_landing.rst

@@ -1,6 +1,6 @@
 
 Simulation
-----------
+~~~~~~~~~~
 
 .. code-block:: ipython3
 
@@ -21,7 +21,7 @@ Simulation
    gif
 
 Equation generation
--------------------
+~~~~~~~~~~~~~~~~~~~
 
 .. code-block:: ipython3