def solve(problem_spec):
# system state boundary values for a = 0.0 [s] and b = 2.0 [s]
xa = problem_spec.xx_start
xb = problem_spec.xx_end
T_end = problem_spec.T_transition
# constraints dictionary
con = problem_spec.constraints
ua = problem_spec.u_start
ub = problem_spec.u_end
def f_pytrajectory(xx, uu, uuref, t, pp):
""" Right hand side of the vectorfield defining the system dynamics
This function wraps the rhs-function of the problem_spec to make it compatible to
pytrajectory.
:param xx: state
:param uu: input
:param uuref: reference input (not used)
:param t: time (not used)
:param pp: additionial free parameters (not used)
:return: xdot
"""
return problem_spec.rhs(xx, uu)
first_guess = problem_spec.first_guess
# create the trajectory object
S = TransitionProblem(f_pytrajectory,
a=0.0,
b=T_end,
xa=xa,
xb=xb,
ua=ua,
ub=ub,
constraints=con,
use_chains=True,
first_guess=first_guess)
# alter some method parameters to increase performance
S.set_param('su', 10)
# start
x, u = S.solve()
solution_data = SolutionData()
solution_data.x_func = x
solution_data.u_func = u
save_plot(problem_spec, solution_data)
return solution_data
return ff
# system state boundary values for a = 0.0 [s] and b = 2.0 [s]
xa = [0.0, 0.0, np.pi, 0.0, np.pi, 0.0]
xb = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
# boundary values for the input
ua = [0.0]
ub = [0.0]
# create trajectory object
S = TransitionProblem(f, a=0.0, b=2.0, xa=xa, xb=xb, ua=ua, ub=ub)
# alter some method parameters to increase performance
S.set_param('su', 10)
S.set_param('eps', 8e-2)
# run iteration
S.solve()
# the following code provides an animation of the system above
# for a more detailed explanation have a look at the 'Visualisation' section in the documentation
import sys
import matplotlib as mpl
from pytrajectory.visualisation import Animation
def draw(xti, image):
x, phi1, phi2 = xti[0], xti[2], xti[4]
(M * l + m * l * s**2) + c / (M * l + l * m * s**2) * u1
])
return ff
# boundary values at the start (a = 0.0 [s])
xa = [0.0, 0.0, 0.0, 0.0]
# boundary values at the end (b = 2.0 [s])
xb = [1.0, 0.0, 0.0, 0.0]
# create trajectory object
S = TransitionProblem(f, a=0.0, b=2.0, xa=xa, xb=xb)
# change method parameter to increase performance
S.set_param('use_chains', False)
# run iteration
S.solve()
# the following code provides an animation of the system above
# for a more detailed explanation have a look at the 'Visualisation' section in the documentation
import sys
import matplotlib as mpl
from pytrajectory.visualisation import Animation
def draw(xti, image):
x = xti[0]
phi = xti[2]
ub = [0.0]
# create System
first_guess = {'seed': 1529} # choose a seed which leads to quick convergence
S = TransitionProblem(f,
a=0.0,
b=2.0,
xa=xa,
xb=xb,
ua=ua,
ub=ub,
use_chains=True,
first_guess=first_guess)
# alter some method parameters to increase performance
S.set_param('su', 10)
# run iteration
S.solve()
# the following code provides an animation of the system above
# for a more detailed explanation have a look at the 'Visualisation' section in the documentation
import sys
import matplotlib as mpl
from pytrajectory.visualisation import Animation
def draw(xti, image):
phi1, phi2 = xti[0], xti[2]
L = 0.5
0.0]
xb = [ 0.2*np.pi,
0.0,
0.2*np.pi,
0.0]
# boundary values for the inputs
ua = [0.0]
ub = [0.0]
# create trajectory object
S = TransitionProblem(f, a=0.0, b=1.8, xa=xa, xb=xb, ua=ua, ub=ub)
# also alter some method parameters to increase performance
S.set_param('su', 20)
S.set_param('kx', 3)
# run iteration
S.solve()
# the following code provides an animation of the system above
# for a more detailed explanation have a look at the 'Visualisation' section in the documentation
import sys
import matplotlib as mpl
from pytrajectory.visualisation import Animation
def draw(xti, image):
phi1, phi2 = xti[0], xti[2]