SebastianSager: case sensitive category

2015-12-15T10:01:54Z

case sensitive category

← Older revision		Revision as of 10:01, 15 December 2015
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	</pre>		</pre>

	[[Category:~~CasADi~~]]		[[Category:Casadi]]

MirkoHahn at 13:14, 13 December 2015

2015-12-13T13:14:47Z

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MirkoHahn: Corrected due to error in derivative of angle to vertical; added comments and intermediate expressions

2015-12-13T13:09:04Z

Corrected due to error in derivative of angle to vertical; added comments and intermediate expressions

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MirkoHahn at 15:03, 9 December 2015

2015-12-09T15:03:34Z

← Older revision		Revision as of 15:03, 9 December 2015
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	This page contains a discretized version of the OCP [[Gravity Turn Maneuver]] in [http://www.casadi.org CasADi 2.4.2] format. The continuous model was discretized using a direct multiple shooting approach with 300 shooting nodes distributed equidistantly over a variable time horizon. The control grid is equal to the DMS grid.		This page contains a discretized version of the OCP [[Gravity Turn Maneuver]] in [http://www.casadi.org CasADi 2.4.2] format. The continuous model was discretized using a direct multiple shooting approach with 300 shooting nodes distributed equidistantly over a variable time horizon. The control grid is equal to the DMS grid. An initial solution is chosen by linearly interpolating between initial and terminal state.

	=== CasADi ===		=== CasADi ===
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	== Results ==		== Results ==

			The solution is calculated using IPOPT (3.11.9, default settings with tolerance 1e-5, using linear solver MUMPS in sequential mode on Ubuntu 15.10 for x86-64 with Linux 4.2.0-19-generic, Intel(R) Core(TM) i7-4790K CPU @ 4.00GHz, 16 GB RAM). The objective function value is <math>9.63924</math>. IPOPT finds the solution in 22 iterations (20.085 seconds proc time).

	<!--=== Bonmin ===		<!--=== Bonmin ===

MirkoHahn: Created page with "This page contains a discretized version of the OCP Gravity Turn Maneuver in [http://www.casadi.org CasADi 2.4.2] format. The continuous model was discretized using a dire..."

2015-12-09T13:16:30Z

Created page with "This page contains a discretized version of the OCP Gravity Turn Maneuver in [http://www.casadi.org CasADi 2.4.2] format. The continuous model was discretized using a dire..."

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This page contains a discretized version of the OCP [[Gravity Turn Maneuver]] in [http://www.casadi.org CasADi 2.4.2] format. The continuous model was discretized using a direct multiple shooting approach with 300 shooting nodes distributed equidistantly over a variable time horizon. The control grid is equal to the DMS grid.

=== CasADi ===

<source lang="Python">
# ----------------------------------------------------------------
# Gravity Turn Maneuver with direct multiple shooting using CVodes
# (c) Mirko Hahn
# ----------------------------------------------------------------
from casadi import *

N = 300
vel_eps = 1e-6

m0 = 11.3
m1 = 1.3
g0 = 9.81e-3
r0 = 6.0e2
Isp = 300.0
Fmax = 600.0e-3

cd = 0.021
A = 1.0
H = 5.6
rho = (1.0 * 1.2230948554874)

h_obj = 75
v_obj = 2.287
q_obj = 0.5 * pi

x = SX.sym('[m, v, q, h, d]')
u = SX.sym('u')
T = SX.sym('T')

ode = [
-(Fmax / (Isp * g0)) * u,
(Fmax * u - 0.5e3 * A * cd * rho * exp(-x[3] / H) * x[1]**2) / x[0] - g0 * (r0 / (r0 + x[3]))**2 * cos(x[2]),
g0 * (r0 / (r0 + x[3]))**2 * sin(x[2]) / x[1] - x[1] * cos(x[2]) / (r0 + x[3]),
x[1] * cos(x[2]),
x[1] * sin(x[2]) / (r0 + x[3])
]
quad = u

dae = SXFunction("dae", daeIn(x=x, p=vertcat([u, T])), daeOut(ode=T*vertcat(ode), quad=T*quad))
I = Integrator("I", "cvodes", dae, {'t0': 0.0, 'tf': 1.0 / N})

p_min = [120.0]
p_max = [600.0]
p_init = [120.0]

u_min = [0.0]
u_max = [1.0]
u_init = [0.5]

x0_min = [m0, vel_eps, 0.0, 0.0, 0.0]
x0_max = [m0, vel_eps, 0.5 * pi, 0.0, 0.0]
x0_init = [m0, vel_eps, 0.05 * pi, 0.0, 0.0]

xf_min = [m1, v_obj, q_obj, h_obj, 0.0]
xf_max = [m0, v_obj, q_obj, h_obj, inf]
xf_init = [m1, v_obj, q_obj, h_obj, 0.0]

x_min = [m1, vel_eps, 0.0, 0.0, 0.0]
x_max = [m0, inf, pi, inf, inf]
x_init = [0.5 * (m0 + m1), 0.5 * v_obj, 0.5 * q_obj, 0.5 * h_obj, 0.0]

np = 1
nx = x.size1()
nu = u.size1()
ns = nx + nu

V = MX.sym('X', N * ns + nx + np)
P = V[0]
X = [V[np+i*ns:np+i*ns+nx] for i in range(0, N+1)]
U = [V[np+i*ns+nx:np+(i+1)*ns] for i in range(0, N)]

G = []
F = 0.0

x0 = p_init + x0_init
for i in range(0, N):
Y = I({'x0': X[i], 'p': vertcat([U[i], P])})
G = G + [Y['xf'] - X[i+1]]
F = F + Y['qf']

frac = float(i+1) / N
x0 = x0 + u_init + [x0_init[i] + frac * (xf_init[i] - x0_init[i]) for i in range(0, nx)]

lbg = 0.0
ubg = 0.0
lbx = p_min + x0_min + u_min + (N-1) * (x_min + u_min) + xf_min
ubx = p_max + x0_max + u_max + (N-1) * (x_max + u_max) + xf_max

nlp = MXFunction("nlp", nlpIn(x=V), nlpOut(f=m0 - X[-1][0], g=vertcat(G)))
S = NlpSolver("S", "ipopt", nlp, {'tol': 1e-5})
r = S({
'x0' : x0,
'lbx': lbx,
'ubx': ubx,
'lbg': lbg,
'ubg': ubg
})
</source>

== Results ==



[[Category:CasADi]]

Gravity Turn Maneuver (Casadi) - Revision history

SebastianSager: case sensitive category

MirkoHahn at 13:14, 13 December 2015

MirkoHahn: Corrected due to error in derivative of angle to vertical; added comments and intermediate expressions

MirkoHahn at 15:03, 9 December 2015

MirkoHahn: Created page with "This page contains a discretized version of the OCP Gravity Turn Maneuver in [http://www.casadi.org CasADi 2.4.2] format. The continuous model was discretized using a dire..."