roboticsas1.3A

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import ode

Ts = 0.1

t = np.arange(0, 10, Ts)

x0 = 0
y0 = 0
phi0 = 0


x = []
y = []
phi = []

x.append(x0)
y.append(y0)
phi.append(phi0)

def fun(t, y):
    return [np.sqrt(1+4*t**2)* np.cos(y[2]), np.sqrt(1+4*t**2)*np.sin(y[2]), 2/(4*t**2+1)]

r = ode(fun).set_integrator('dopri5')
r.set_initial_value([x0, y0, phi0])

for i in t:

    if r.successful():
        r.integrate(r.t + Ts)
    x.append(r.y[0])
    y.append(r.y[1])
    phi.append((r.y[2]) % (2 * np.pi))  #Just to keep phi in range 0 to 2pi


x = np.array(x)
y = np.array(y)
plt.grid()
plt.plot(x, y)
plt.annotate("Starting point",(x0,y0))
plt.scatter(x0,y0)
plt.xlabel("x")
plt.ylabel("y")
plt.show()