# Define constraints
ocp.constraints() \
.initial('h-h_0', 'm') \
.initial('theta', 'rad') \
.initial('v-v_0', 'm/s') \
.initial('gam-gam_0', 'rad') \
.initial('t', 's') \
.terminal('h-h_f', 'm') \
.terminal('theta-theta_f', 'rad')
ocp.scale(m='h', s='h/v', kg='mass', rad=1)
bvp_solver = beluga.bvp_algorithm('Shooting',
algorithm='Armijo',
derivative_method='fd',
tolerance=1e-6,
max_iterations=100,
max_error=100)
guess_maker = beluga.guess_generator('auto',
start=[40000, 0, 4000, (-90) * pi / 180],
direction='forward',
costate_guess=-0.1)
continuation_steps = beluga.init_continuation()
# Start by flying straight towards the ground
continuation_steps.add_step('bisection') \
.num_cases(11) \
.const('h_f', 0)
.terminal('x-x_f','m') \
.terminal('y-y_f','m')
ocp.scale(m='y', s='y/v', kg=1, rad=1)
# bvp_solver = beluga.bvp_algorithm('MultipleShooting',
# derivative_method='fd',
# tolerance=1e-4,
# max_iterations=100,
# verbose = True,
# max_error=100
# )
bvp_solver = beluga.bvp_algorithm(
'MultipleShooting',
tolerance=1e-4,
max_iterations=50,
verbose=True,
)
# bvp_solver = beluga.bvp_algorithm('SingleShooting',
# derivative_method='fd',
# tolerance=1e-4,
# max_iterations=50,
# verbose = True,
# )
guess_maker = beluga.guess_generator(
'auto',
start=[0, 0, 1], # Starting values for states in order
direction='forward',
costate_guess=-0.1)
# Define costs
ocp.path_cost('1', '1')
# Define constraints
ocp.constraints() \
.initial('x', 'm') \
.initial('y', 'm') \
.initial('v', 'm/s') \
.initial('t', 's') \
.terminal('x-x_f', 'm') \
.terminal('y-y_f', 'm')
ocp.scale(m='y', s='y/v', kg=1, rad=1, nd=1)
bvp_solver = beluga.bvp_algorithm('Shooting')
guess_maker = beluga.guess_generator(
'auto',
start=[0, 0, 0], # Starting values for states in order
costate_guess=-0.1,
control_guess=[-pi / 2],
use_control_guess=True)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(21) \
.const('x_f', 10) \
.const('y_f', -10)
# Define constraints
ocp.initial_constraint('x', 'm')
ocp.initial_constraint('y', 'm')
ocp.initial_constraint('t', 's')
ocp.terminal_constraint('x-x_f', 'm')
ocp.terminal_constraint('y-y_f',
'm',
lower='-y_f_width',
upper='y_f_width',
activator='epsilon',
method='utm')
ocp.scale(m='x', s='x/V', rad=1)
bvp_solver = beluga.bvp_algorithm('SPBVP')
guess_maker = beluga.guess_generator('auto',
start=[0, 0],
control_guess=[0],
use_control_guess=True,
direction='forward')
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(10) \
.const('x_f', 10)
continuation_steps.add_step('bisection') \
.num_cases(10) \
# Define constraints
ocp_indirect.initial_constraint('x1 - x1_0', 'nd')
ocp_indirect.initial_constraint('x2 - x2_0', 'nd')
ocp_indirect.initial_constraint('t', 'nd')
ocp_indirect.path_constraint('u',
'rad',
lower='-2',
upper='2',
activator='epsilon1',
method='epstrig')
ocp_indirect.terminal_constraint('t - 1', 'nd')
ocp_indirect.scale(rad=1, nd=1)
bvp_solver_indirect = beluga.bvp_algorithm('spbvp')
guess_maker_indirect = beluga.guess_generator('auto',
start=[3, 5],
direction='forward',
costate_guess=-0.1,
control_guess=[0],
use_control_guess=True,
time_integrate=0.1)
beluga.add_logger(file_level=logging.DEBUG, display_level=logging.INFO)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(40, 'log') \
# Define costs
ocp.terminal_cost('-v**2', 'm**2/s**2')
# Define constraints
ocp.initial_constraint('h-h_0', 'm')
ocp.initial_constraint('theta', 'rad')
ocp.initial_constraint('v-v_0', 'm/s')
ocp.initial_constraint('gam-gam_0', 'rad')
ocp.initial_constraint('t', 's')
ocp.terminal_constraint('h-h_f', 'm')
ocp.terminal_constraint('theta-theta_f', 'rad')
ocp.scale(m='h', s='h/v', kg='mass', rad=1)
bvp_solver = beluga.bvp_algorithm('spbvp')
guess_maker = beluga.guess_generator(
'auto',
start=[40000, 0, 2000, (-90)*pi/180],
direction='forward',
costate_guess=-0.1,
control_guess=[0],
use_control_guess=True)
continuation_steps = beluga.init_continuation()
# Start by flying straight towards the ground
continuation_steps.add_step('bisection') \
.num_cases(5) \
.const('h_f', 0)
.terminal('zbar2-zbar2_f','nd')\
.terminal('psi2 - psi2_f', 'nd') \
# 1191 (45) - 5 vehicles with 4 path constraints
# 911 seconds for 5 v and one path constraint
# 247(31) seconds for 5 vehicle with GPOPS in background
# 68(14) seconds for 3 vehicle with u constraints
# 114(20) seconds for 4 vehicles with u constraint
# 106(14) seconds for 3 vehicle unconstrained (with u constraints)
# 75(10) seconds for 2 vehicle unconstrainted (with u constraints)
ocp.scale(m=1, s=1, kg=1, rad=1, nd=1)
bvp_solver = beluga.bvp_algorithm(
'Shooting',
tolerance=1e-3,
max_iterations=200,
verbose=True,
derivative_method='fd',
max_error=20,
)
bvp_solver = beluga.bvp_algorithm('qcpi',
tolerance=1e-3,
max_iterations=500,
verbose=True,
max_error=20,
N=81)
guess_maker = beluga.guess_generator(
'auto',
start=[-.8, 0., -.1, -pi / 12.] + [-.8, .1, -.1, 0., 1.],
direction='forward',
# Define constraints
ocp.constraints() \
.initial('h-h_0', 'm') \
.initial('theta-theta_0', 'rad') \
.initial('v-v_0', 'm/s') \
.initial('gam-gam_0', 'rad') \
.terminal('h-h_f', 'm') \
.terminal('theta-theta_f', 'rad')
ocp.scale(m='h', s='h/v', kg='mass', rad=1)
bvp_solver = beluga.bvp_algorithm(
'ArmijoShooting',
derivative_method='fd',
tolerance=1e-4,
max_iterations=100,
verbose=True,
max_error=100,
)
# bvp_solver = beluga.bvp_algorithm('Collocation')
guess_maker = beluga.guess_generator(
'auto',
start=[40000, 0, 4000, (-90) * pi / 180],
direction='forward',
costate_guess=-0.1)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
# Define costs
ocp.terminal_cost('-v^2', 'm^2/s^2')
# Define constraints
ocp.constraints() \
.initial('h-h_0', 'm') \
.initial('theta', 'rad') \
.initial('v-v_0', 'm/s') \
.initial('t', 's') \
.terminal('h-h_f', 'm') \
.terminal('theta-theta_f', 'rad')
ocp.scale(m='h', s='h/v', kg='mass', rad=1)
bvp_solver = beluga.bvp_algorithm('Shooting', algorithm='Armijo')
guess_maker = beluga.guess_generator(
'auto',
start=[80000, 0, 4000, -90*pi/180],
direction='forward',
costate_guess=-0.1
)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(11) \
.const('h_f', 0) \
.const('theta_f', 0.01*pi/180)
.initial('x-x_0','m') \
.initial('y-y_0','m') \
.initial('v-v_0','m/s') \
.terminal('x-x_f','m') \
.terminal('y-y_f','m') \
.path('constraint1','y + x','>',-1.0,'m',start_eps=1e-1)
# .path('constraint2','y + 0.75*x','>',-2,'m') #\
# ocp.scale(m='y', s='y/v', kg=1, rad=1, nd=1)
ocp.scale(m=1, s=1, kg=1, rad=1, nd=1)
bvp_solver = beluga.bvp_algorithm(
'MultipleShooting',
derivative_method='fd',
tolerance=1e-5,
max_iterations=20,
verbose=True,
max_error=50,
use_numba=True,
# N = 30,
)
guess_maker = beluga.guess_generator(
'auto',
start=[0, 0, 1], # Starting values for states in order
direction='forward',
costate_guess=0.1,
)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
ocp.constant('theta_f', 0, 'rad')
# Define costs
ocp.terminal_cost('-v^2', 'm^2/s^2')
# Define constraints
ocp.constraints() \
.initial('h-h_0','m') \
.initial('theta','rad') \
.initial('v-v_0','m/s') \
.terminal('h-h_f','m') \
.terminal('theta-theta_f','rad')
ocp.scale(m='h', s='h/v', kg='mass', rad=1)
bvp_solver = beluga.bvp_algorithm('Shooting', algorithm='SLSQP')
guess_maker = beluga.guess_generator('auto',
start=[80000, 0, 4000, -90 * pi / 180],
direction='forward',
costate_guess=-0.1)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(11) \
.const('h_f',0) \
.const('theta_f',0.01*pi/180)
continuation_steps.add_step('bisection') \
.num_cases(11) \
def test_planarhypersonic():
from math import pi
import beluga
ocp = beluga.OCP('planarHypersonic')
# Define independent variables
ocp.independent('t', 's')
# Define equations of motion
ocp.state('h', 'v*sin(gam)', 'm') \
.state('theta', 'v*cos(gam)/r', 'rad') \
.state('v', '-D/mass - mu*sin(gam)/r**2', 'm/s') \
.state('gam', 'L/(mass*v) + (v/r - mu/(v*r^2))*cos(gam)', 'rad')
# Define quantities used in the problem
ocp.quantity('rho', 'rho0*exp(-h/H)')
ocp.quantity('Cl', '(1.5658*alfa + -0.0000)')
ocp.quantity('Cd', '(1.6537*alfa^2 + 0.0612)')
ocp.quantity('D', '0.5*rho*v^2*Cd*Aref')
ocp.quantity('L', '0.5*rho*v^2*Cl*Aref')
ocp.quantity('r', 're+h')
# Define controls
ocp.control('alfa', 'rad')
# Define constants
ocp.constant('mu', 3.986e5 * 1e9,
'm^3/s^2') # Gravitational parameter, m^3/s^2
ocp.constant('rho0', 0.0001 * 1.2,
'kg/m^3') # Sea-level atmospheric density, kg/m^3
ocp.constant('H', 7500, 'm') # Scale height for atmosphere of Earth, m
ocp.constant('mass', 750 / 2.2046226, 'kg') # Mass of vehicle, kg
ocp.constant('re', 6378000, 'm') # Radius of planet, m
ocp.constant('Aref',
pi * (24 * .0254 / 2)**2,
'm^2') # Reference area of vehicle, m^2
ocp.constant('h_0', 80000, 'm')
ocp.constant('v_0', 4000, 'm/s')
ocp.constant('h_f', 80000, 'm')
ocp.constant('theta_f', 0, 'rad')
# Define costs
ocp.terminal_cost('-v^2', 'm^2/s^2')
# Define constraints
ocp.constraints() \
.initial('h-h_0', 'm') \
.initial('theta', 'rad') \
.initial('v-v_0', 'm/s') \
.terminal('h-h_f', 'm') \
.terminal('theta-theta_f', 'rad')
ocp.scale(m='h', s='h/v', kg='mass', rad=1)
bvp_solver = beluga.bvp_algorithm('Shooting',
algorithm='SLSQP',
tolerance=1e-6)
guess_maker = beluga.guess_generator(
'auto',
start=[80000, 0, 4000, -90 * pi / 180],
direction='forward',
costate_guess=-0.1)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(11) \
.const('h_f', 0) \
.const('theta_f', 0.01 * pi / 180)
continuation_steps.add_step('bisection') \
.num_cases(11) \
.const('theta_f', 5.0 * pi / 180)
continuation_steps.add_step('bisection') \
.num_cases(11) \
.const('rho0', 1.2)
sol = beluga.solve(ocp,
method='traditional',
bvp_algorithm=bvp_solver,
steps=continuation_steps,
guess_generator=guess_maker)
y0 = sol.y[0]
yf = sol.y[-1]
y0e = [
8.00000000e+04, 0.00000000e+00, 4.00000000e+03, 1.95069984e-02,
-1.68249327e+01, 1.21634197e+06, -2.83598229e+03, -6.15819100e-17
]
yfe = [
5.23214346e-04, 8.72664626e-02, 2.69147623e+03, -9.38246813e-01,
5.46455659e+02, 1.21634197e+06, -5.38295257e+03, 1.67911185e-01
]
tfe = 144.5678
assert sol.t.shape[0] == sol.y.shape[0]
assert sol.t.shape[0] == sol.u.shape[0]
assert sol.y.shape[1] == 8
assert sol.u.shape[1] == 1
assert abs((y0[0] - y0e[0]) / y0e[0]) < tol
assert abs((y0[1] - y0e[1])) < tol
assert abs((y0[2] - y0e[2]) / y0e[2]) < tol
assert abs((y0[3] - y0e[3]) / y0e[3]) < tol
assert abs((y0[4] - y0e[4]) / y0e[4]) < tol
assert abs((y0[5] - y0e[5]) / y0e[5]) < tol
assert abs((y0[6] - y0e[6]) / y0e[6]) < tol
assert abs((y0[7] - y0e[7])) < tol
assert abs((sol.t[-1] - tfe) / tfe) < tol
assert abs((yf[0] - yfe[0])) < tol
assert abs((yf[1] - yfe[1]) / yfe[1]) < tol
assert abs((yf[2] - yfe[2]) / yfe[2]) < tol
assert abs((yf[3] - yfe[3]) / yfe[3]) < tol
assert abs((yf[4] - yfe[4]) / yfe[4]) < tol
assert abs((yf[5] - yfe[5]) / yfe[5]) < tol
assert abs((yf[6] - yfe[6]) / yfe[6]) < tol
assert abs((yf[7] - yfe[7]) / yfe[7]) < tol
def test_zermelo_custom_functions():
import beluga
ocp = beluga.OCP('zermelos_problem')
def drift_x(x, y):
return 0
def drift_y(x, y):
return ((x - 5)**4 - 625) / 625
ocp.custom_function('drift_x', drift_x)
ocp.custom_function('drift_y', drift_y)
# Define independent variables
ocp.independent('t', 's')
# Define equations of motion
ocp.state('x', 'V*cos(theta) + epsilon*drift_x(x,y)', 'm') \
.state('y', 'V*sin(theta) + epsilon*drift_y(x,y)', 'm')
# Define controls
ocp.control('theta', 'rad')
# Define constants
ocp.constant('V', 10, 'm/s')
ocp.constant('epsilon', 0.001, '1')
ocp.constant('x_f', 0, 'm')
ocp.constant('y_f', 0, 'm')
# Define costs
ocp.path_cost('1', '1')
# Define constraints
ocp.constraints() \
.initial('x', 'm') \
.initial('y', 'm') \
.terminal('x-x_f', 'm') \
.terminal('y-y_f', 'm')
ocp.scale(m='x', s='x/V', rad=1)
bvp_solver = beluga.bvp_algorithm('Shooting',
derivative_method='fd',
tolerance=1e-4,
max_error=100,
max_iterations=100)
guess_maker = beluga.guess_generator('auto',
start=[0, 0],
control_guess=[0],
use_control_guess=True,
direction='forward')
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(10) \
.const('x_f', 10)
continuation_steps.add_step('bisection') \
.num_cases(10) \
.const('y_f', 10)
continuation_steps.add_step('bisection') \
.num_cases(10) \
.const('epsilon', 1)
sol = beluga.solve(ocp,
method='icrm',
bvp_algorithm=bvp_solver,
steps=continuation_steps,
guess_generator=guess_maker)
from beluga.ivpsol import Trajectory
assert isinstance(sol, Trajectory)
guess_maker = beluga.guess_generator(
'ones',
start=[1.0], # Starting values for states in order
costate_guess=0.1,
control_guess=[0.35],
use_control_guess=True)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(10, 'log') \
.const('eps1', 2e-1)
beluga.add_logger(logging_level=logging.DEBUG, display_level=logging.INFO)
bvp_solver = beluga.bvp_algorithm('spbvp')
beluga.solve(ocp=ocp,
method='indirect',
optim_options={
'control_method': 'icrm',
'analytical_jacobian': True
},
bvp_algorithm=bvp_solver,
steps=continuation_steps,
guess_generator=guess_maker,
autoscale=False,
save='indirect_data.blg')
bvp_solver = beluga.bvp_algorithm('Collocation', num_nodes=60)
ocp.terminal_cost('-r^2', 'L')
# Define constraints
ocp.initial_constraint('r-r_0', 'L')
ocp.initial_constraint('theta - theta_0', 'rad')
ocp.initial_constraint('v_r - v_r_0', 'L/s')
ocp.initial_constraint('v_theta - v_theta_0', 'L/s')
ocp.initial_constraint('m - m_0', 'M')
ocp.initial_constraint('t', 's')
ocp.terminal_constraint('v_r - v_r_f', 'L/s')
ocp.terminal_constraint('v_theta - sqrt(mu / r)', 'L/s')
ocp.terminal_constraint('t - t_f', 's')
ocp.scale(L='r', s='r/v_theta', M='m', rad=1)
bvp_solver_shooting = beluga.bvp_algorithm('Shooting', algorithm='Armijo')
bvp_solver_collocation = beluga.bvp_algorithm('spbvp')
guess_maker = beluga.guess_generator('auto',
start=[1, 0, 0, 1, 1],
direction='forward',
costate_guess=-0.1)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(3) \
.const('v_r_f', 0)
continuation_steps.add_step('bisection') \
.num_cases(40) \
def test_planarhypersonic():
from math import pi
import beluga
ocp = beluga.OCP('planarHypersonic')
# Define independent variables
ocp.independent('t', 's')
# Define equations of motion
ocp.state('h', 'v*sin(gam)', 'm') \
.state('theta', 'v*cos(gam)/r', 'rad') \
.state('v', '-D/mass - mu*sin(gam)/r**2', 'm/s') \
.state('gam', 'L/(mass*v) + (v/r - mu/(v*r^2))*cos(gam)', 'rad')
# Define quantities used in the problem
ocp.quantity('rho', 'rho0*exp(-h/H)')
ocp.quantity('Cl', '(1.5658*alfa + -0.0000)')
ocp.quantity('Cd', '(1.6537*alfa^2 + 0.0612)')
ocp.quantity('D', '0.5*rho*v^2*Cd*Aref')
ocp.quantity('L', '0.5*rho*v^2*Cl*Aref')
ocp.quantity('r', 're+h')
# Define controls
ocp.control('alfa', 'rad')
# Define constants
ocp.constant('mu', 3.986e5 * 1e9, 'm^3/s^2') # Gravitational parameter, m^3/s^2
ocp.constant('rho0', 0.0001 * 1.2, 'kg/m^3') # Sea-level atmospheric density, kg/m^3
ocp.constant('H', 7500, 'm') # Scale height for atmosphere of Earth, m
ocp.constant('mass', 750 / 2.2046226, 'kg') # Mass of vehicle, kg
ocp.constant('re', 6378000, 'm') # Radius of planet, m
ocp.constant('Aref', pi * (24 * .0254 / 2) ** 2, 'm^2') # Reference area of vehicle, m^2
# Define costs
ocp.terminal_cost('-v^2', 'm^2/s^2')
# Define constraints
ocp.constraints() \
.initial('h-h_0', 'm') \
.initial('theta-theta_0', 'rad') \
.initial('v-v_0', 'm/s') \
.terminal('h-h_f', 'm') \
.terminal('theta-theta_f', 'rad')
ocp.scale(m='h', s='h/v', kg='mass', rad=1)
bvp_solver = beluga.bvp_algorithm('Shooting')
guess_maker = beluga.guess_generator('auto', start=[80000, 0, 4000, -90 * pi / 180], direction='forward', costate_guess=-0.1)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(11) \
.terminal('h', 0) \
.terminal('theta', 0.01 * pi / 180)
continuation_steps.add_step('bisection') \
.num_cases(11) \
.terminal('theta', 5.0 * pi / 180)
continuation_steps.add_step('bisection') \
.num_cases(11) \
.const('rho0', 1.2)
sol = beluga.solve(ocp, method='traditional', bvp_algorithm=bvp_solver, steps=continuation_steps, guess_generator=guess_maker)
y0 = sol.y[0]
yf = sol.y[-1]
y0e = [80000, 0, 4000, 0.0195, -16.8243, 1212433.8085, -2836.0620, 0]
yfe = [0, 0.0873, 2691.4733, -0.9383, 546.4540, 1212433.8085, -5382.9467, 0.1840]
tfe = 144.5677
assert sol.t.shape[0] == sol.y.shape[0]
assert sol.t.shape[0] == sol.u.shape[0]
assert sol.y.shape[1] == 8
assert sol.u.shape[1] == 1
assert abs((y0[0] - y0e[0]) / y0e[0]) < tol
assert abs((y0[1] - y0e[1])) < tol
assert abs((y0[2] - y0e[2]) / y0e[2]) < tol
assert abs((y0[3] - y0e[3]) / y0e[3]) < tol
assert abs((y0[4] - y0e[4]) / y0e[4]) < tol
assert abs((y0[5] - y0e[5]) / y0e[5]) < tol
assert abs((y0[6] - y0e[6]) / y0e[6]) < tol
assert abs((y0[7] - y0e[7])) < tol
assert abs((sol.t[-1] - tfe) / tfe) < tol
assert abs((yf[0] - yfe[0])) < tol
assert abs((yf[1] - yfe[1]) / yfe[1]) < tol
assert abs((yf[2] - yfe[2]) / yfe[2]) < tol
assert abs((yf[3] - yfe[3]) / yfe[3]) < tol
assert abs((yf[4] - yfe[4]) / yfe[4]) < tol
assert abs((yf[5] - yfe[5]) / yfe[5]) < tol
assert abs((yf[6] - yfe[6]) / yfe[6]) < tol
assert abs((yf[7] - yfe[7]) / yfe[7]) < tol
# Define costs
ocp.path_cost('1', '1')
# Define constraints
ocp.constraints() \
.initial('x', 'm') \
.initial('y', 'm') \
.initial('t', 's') \
.terminal('x-x_f', 'm') \
.terminal('y-y_f', 'm')
ocp.scale(m='x', s='x/V', rad=1)
bvp_solver = beluga.bvp_algorithm(
'Shooting',
derivative_method='fd',
tolerance=1e-4
)
guess_maker = beluga.guess_generator(
'auto',
start=[0, 0],
control_guess=[0],
use_control_guess=True,
direction='forward'
)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(10) \
def test_brachistochrone_shooting():
from math import pi
import beluga
from beluga.ivpsol import Trajectory
from beluga.bvpsol import Solution
ocp = beluga.OCP('brachisto')
# Define independent variables
ocp.independent('t', 's')
# Define equations of motion
ocp.state('x', 'v*cos(theta)', 'm') \
.state('y', 'v*sin(theta)', 'm') \
.state('v', 'g*sin(theta)', 'm/s')
# Define controls
ocp.control('theta', 'rad')
# Define constants
ocp.constant('g', -9.81, 'm/s^2')
# Define costs
ocp.path_cost('1', '1')
# Define constraints
ocp.constraints() \
.initial('x-x_0', 'm') \
.initial('y-y_0', 'm') \
.initial('v-v_0', 'm/s') \
.terminal('x-x_f', 'm') \
.terminal('y-y_f', 'm')
ocp.scale(m='y', s='y/v', kg=1, rad=1)
shooting_solver = beluga.bvp_algorithm('Shooting')
guess_maker = beluga.guess_generator('auto', start=[0, 0, 0], direction='forward', costate_guess=-0.1, control_guess = [-pi/2], use_control_guess=True)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(21) \
.terminal('x', 10) \
.terminal('y', -10)
sol = beluga.solve(ocp, method='icrm', bvp_algorithm=shooting_solver, steps=continuation_steps,
guess_generator=guess_maker)
assert isinstance(sol, Trajectory)
assert isinstance(sol, Solution)
assert sol.t.shape[0] == sol.y.shape[0]
assert sol.t.shape[0] == sol.u.shape[0]
assert sol.y.shape[1] == 7
assert sol.u.shape[1] == 1
y0 = sol.y[0]
yf = sol.y[-1]
assert abs(y0[0] - 0) < tol
assert abs(y0[1] - 0) < tol
assert abs(y0[2] - 0) < tol
assert abs(y0[3] + 0.0667) < tol
assert abs(y0[4] - 0.0255) < tol
assert abs(y0[5] + 0.1019) < tol
assert abs(sol.t[-1] - 1.8433) < tol
assert abs(yf[0] - 10) < tol
assert abs(yf[1] + 10) < tol
assert abs(yf[2] - 14.0071) < tol
assert abs(yf[3] + 0.0667) < tol
assert abs(yf[4] - 0.0255) < tol
assert abs(yf[5] - 0) < tol
assert abs(y0[3] - yf[3]) < tol
assert abs(y0[4] - yf[4]) < tol
sol = beluga.solve(ocp, method='traditional', bvp_algorithm=shooting_solver, steps=continuation_steps, guess_generator=guess_maker)
y0 = sol.y[0]
yf = sol.y[-1]
assert sol.t.shape[0] == sol.y.shape[0]
assert sol.t.shape[0] == sol.u.shape[0]
assert sol.y.shape[1] == 6
assert sol.u.shape[1] == 1
assert abs(y0[0] - 0) < tol
assert abs(y0[1] - 0) < tol
assert abs(y0[2] - 0) < tol
assert abs(y0[3] + 0.0667) < tol
assert abs(y0[4] - 0.0255) < tol
assert abs(y0[5] + 0.1019) < tol
assert abs(sol.t[-1] - 1.8433) < tol
assert abs(yf[0] - 10) < tol
assert abs(yf[1] + 10) < tol
assert abs(yf[2] - 14.0071) < tol
assert abs(yf[3] + 0.0667) < tol
assert abs(yf[4] - 0.0255) < tol
assert abs(yf[5] - 0) < tol
assert abs(y0[3] - yf[3]) < tol
assert abs(y0[4] - yf[4]) < tol
ocp.constraints() \
.initial('x-x_0','m') \
.initial('v-v_0','m/s') \
.terminal('x-x_f','m') \
.terminal('v-v_f','m/s') \
.path('xlim','x - 0.18','<',0.00,'m') \
.independent('tf - 1','s') # Fixed final time (not working for multiarc)
ocp.scale(m=1, s=1, kg=1, rad=1, nd=1)
# ocp.bvp_solver = algorithms.SingleShooting(derivative_method='fd',tolerance=1e-4, max_iterations=30, verbose = True, cached=False)
bvp_solver = beluga.bvp_algorithm('MultipleShooting',
derivative_method='fd',
tolerance=1e-3,
max_iterations=1000,
verbose = True,
max_error=200
)
guess_maker = beluga.guess_generator('auto',
start=[0,.01], # Starting values for states in order
direction='forward',
costate_guess = -0.1,
time_integrate = 1 ## REQUIRED BECAUSE OF FIXED FINAL TIME
)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection', max_divisions=30).num_cases(5) \
.terminal('x',0) \
.initial('v',1) \
'm**2') # Reference area of vehicle, m**2
ocp.constant('rn', 1 / 12 * 0.3048, 'm') # Nose radius, m
ocp.constant('h_0', 40000, 'm')
ocp.constant('theta_0', 0, 'rad')
ocp.constant('v_0', 2000, 'm/s')
ocp.constant('gam_0', -(90 - 10) * pi / 180, 'rad')
ocp.constant('psi_0', 0, 'rad')
ocp.constant('h_f', 0, 'm')
ocp.constant('theta_f', 0, 'rad')
ocp.constant('phi_f', 0, 'rad')
ocp.scale(m='h', s='h/v', kg='mass', rad=1)
bvp_solver = beluga.bvp_algorithm('Shooting',
derivative_method='fd',
tolerance=1e-4,
max_iterations=100,
max_error=400,
algorithm='SLSQP')
guess_maker = beluga.guess_generator(
'auto',
start=[40000, 0, 0, 2000, -(90 - 10) * pi / 180, 0],
direction='forward',
costate_guess=-0.1,
control_guess=[0.0, 0.0],
use_control_guess=True,
time_integrate=0.5,
)
continuation_steps = beluga.init_continuation()
guess_maker = beluga.guess_generator(
'ones',
start=[1.0], # Starting values for states in order
costate_guess=0.1,
control_guess=[0.35],
use_control_guess=True)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step('bisection') \
.num_cases(10, 'log') \
.const('eps1', 2e-1)
beluga.add_logger(file_level=logging.DEBUG, display_level=logging.INFO)
bvp_solver = beluga.bvp_algorithm('spbvp')
beluga.solve(ocp=ocp,
method='indirect',
optim_options={
'control_method': 'differential',
'analytical_jacobian': True
},
bvp_algorithm=bvp_solver,
steps=continuation_steps,
guess_generator=guess_maker,
autoscale=False,
save_sols='indirect_data.beluga')
# bvp_solver = beluga.bvp_algorithm('Collocation', num_nodes=60)
ocp.terminal_cost('-h', '1')
# Define constraints
ocp.constraints() \
.initial('h - h_0', '1') \
.initial('v - v_0', '1') \
.initial('m - m_0', '1') \
.initial('t', 's') \
.terminal('v - v_f', '1') \
.terminal('m - m_f', '1')
ocp.path_constraint('thrust', '1', lower='T_min', upper='T_max', activator='eps', method='epstrig')
ocp.scale(m=1, s=1, kg=1, rad=1, nd=1)
bvp_solver = beluga.bvp_algorithm('spbvp', algorithm='armijo', num_arcs=4)
guess_maker = beluga.guess_generator(
'auto',
start=[h_0, v_0, m_0], # Starting values for states in order
costate_guess=-0.0001,
control_guess=[pi/3],
time_integrate=0.1,
)
continuation_steps = beluga.init_continuation()
continuation_steps.add_step() \
.num_cases(3) \
.const('v_f', 0)
