# The desired speed can be computed from the circumference of the circle:
#
# \begin{align*}
# v &= \frac{d}{t}\\
# &= \frac{2 \pi 10}{20}\\
# &= \pi
# \end{align*}
#
# We can now implement this in a loop to step through the model equations. We will also run our bicycle model solution along with your model to show you the expected trajectory. This will help you verify the correctness of your model.
# In[46]:
sample_time = 0.01
time_end = 20
model = Bicycle()
solution_model = BicycleSolution()
# set delta directly
model.delta = np.arctan(2 / 10)
solution_model.delta = np.arctan(2 / 10)
t_data = np.arange(0, time_end, sample_time)
x_data = np.zeros_like(t_data)
y_data = np.zeros_like(t_data)
x_solution = np.zeros_like(t_data)
y_solution = np.zeros_like(t_data)
for i in range(t_data.shape[0]):
x_data[i] = model.xc
y_data[i] = model.yc
model.step(np.pi, 0)
# ==================================
# Implement kinematic model here
# ==================================
self.xc += v * np.cos(self.theta + self.beta) * self.sample_time
self.yc += v * np.sin(self.theta + self.beta) * self.sample_time
self.theta += v * np.cos(self.beta) * np.tan(self.delta) / self.L * self.sample_time
self.delta += w * self.sample_time
self.beta = np.arctan2(self.lr * np.tan(self.delta), self.L)
pass
sample_time = 0.01
time_end = 20
model = Bicycle()
solution_model = BicycleSolution()
# set delta directly
model.delta = np.arctan(2/10)
solution_model.delta = np.arctan(2/10)
t_data = np.arange(0,time_end,sample_time)
x_data = np.zeros_like(t_data)
y_data = np.zeros_like(t_data)
x_solution = np.zeros_like(t_data)
y_solution = np.zeros_like(t_data)
for i in range(t_data.shape[0]):
x_data[i] = model.xc
y_data[i] = model.yc
model.step(np.pi, 0)