Difference between revisions of "Gravity Turn Maneuver (Casadi)"
From mintOC
(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...") |
m |
||
| Line 1: | Line 1: | ||
| − | 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 === | ||
| Line 104: | Line 104: | ||
== 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 === | ||
Revision as of 16:03, 9 December 2015
This page contains a discretized version of the OCP Gravity Turn Maneuver in 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
# ---------------------------------------------------------------- # 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 })
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 
. IPOPT finds the solution in 22 iterations (20.085 seconds proc time).
