def main(discretization='shooting_nodes'):
# create ocp object to formulate the OCP
ocp = AcadosOcp()
# set model
model = export_pendulum_ode_model()
ocp.model = model
integrator_type = 'LIFTED_IRK' # ERK, IRK, GNSF, LIFTED_IRK
if integrator_type == 'GNSF':
acados_dae_model_json_dump(model)
# structure detection in Matlab/Octave -> produces 'pendulum_ode_gnsf_functions.json'
status = os.system('octave detect_gnsf_from_json.m')
# load gnsf from json
with open(model.name + '_gnsf_functions.json', 'r') as f:
gnsf_dict = json.load(f)
ocp.gnsf_model = gnsf_dict
Tf = 1.0
nx = model.x.size()[0]
nu = model.u.size()[0]
ny = nx + nu
ny_e = nx
N = 15
# discretization
ocp.dims.N = N
# shooting_nodes = np.linspace(0, Tf, N+1)
time_steps = np.linspace(0, 1, N)
time_steps = Tf * time_steps / sum(time_steps)
shooting_nodes = np.zeros((N + 1, ))
for i in range(len(time_steps)):
shooting_nodes[i + 1] = shooting_nodes[i] + time_steps[i]
# nonuniform discretizations can be defined either by shooting_nodes or time_steps:
if discretization == 'shooting_nodes':
ocp.solver_options.shooting_nodes = shooting_nodes
elif discretization == 'time_steps':
ocp.solver_options.time_steps = time_steps
else:
raise NotImplementedError(
f"discretization type {discretization} not supported.")
# set num_steps
ocp.solver_options.sim_method_num_steps = 2 * np.ones((N, ))
ocp.solver_options.sim_method_num_steps[0] = 3
# set num_stages
ocp.solver_options.sim_method_num_stages = 2 * np.ones((N, ))
ocp.solver_options.sim_method_num_stages[0] = 4
# set cost
Q = 2 * np.diag([1e3, 1e3, 1e-2, 1e-2])
R = 2 * np.diag([1e-2])
ocp.cost.W_e = Q
ocp.cost.W = scipy.linalg.block_diag(Q, R)
ocp.cost.cost_type = 'LINEAR_LS'
ocp.cost.cost_type_e = 'LINEAR_LS'
ocp.cost.Vx = np.zeros((ny, nx))
ocp.cost.Vx[:nx, :nx] = np.eye(nx)
Vu = np.zeros((ny, nu))
Vu[4, 0] = 1.0
ocp.cost.Vu = Vu
ocp.cost.Vx_e = np.eye(nx)
ocp.cost.yref = np.zeros((ny, ))
ocp.cost.yref_e = np.zeros((ny_e, ))
# set constraints
Fmax = 80
ocp.constraints.lbu = np.array([-Fmax])
ocp.constraints.ubu = np.array([+Fmax])
x0 = np.array([0.0, np.pi, 0.0, 0.0])
ocp.constraints.x0 = x0
ocp.constraints.idxbu = np.array([0])
ocp.solver_options.qp_solver = 'PARTIAL_CONDENSING_HPIPM' # FULL_CONDENSING_QPOASES
ocp.solver_options.hessian_approx = 'GAUSS_NEWTON'
ocp.solver_options.integrator_type = integrator_type
ocp.solver_options.print_level = 0
ocp.solver_options.nlp_solver_type = 'SQP' # SQP_RTI, SQP
# set prediction horizon
ocp.solver_options.tf = Tf
ocp.solver_options.initialize_t_slacks = 1
# Set additional options for Simulink interface:
acados_path = get_acados_path()
json_path = os.path.join(acados_path,
'interfaces/acados_template/acados_template')
with open(json_path + '/simulink_default_opts.json', 'r') as f:
simulink_opts = json.load(f)
ocp_solver = AcadosOcpSolver(ocp,
json_file='acados_ocp.json',
simulink_opts=simulink_opts)
# ocp_solver = AcadosOcpSolver(ocp, json_file = 'acados_ocp.json')
simX = np.ndarray((N + 1, nx))
simU = np.ndarray((N, nu))
# change options after creating ocp_solver
ocp_solver.options_set("step_length", 0.99999)
ocp_solver.options_set("globalization",
"fixed_step") # fixed_step, merit_backtracking
ocp_solver.options_set("tol_eq", TOL)
ocp_solver.options_set("tol_stat", TOL)
ocp_solver.options_set("tol_ineq", TOL)
ocp_solver.options_set("tol_comp", TOL)
# initialize solver
for i in range(N):
ocp_solver.set(i, "x", x0)
status = ocp_solver.solve()
if status not in [0, 2]:
raise Exception('acados returned status {}. Exiting.'.format(status))
# get primal solution
for i in range(N):
simX[i, :] = ocp_solver.get(i, "x")
simU[i, :] = ocp_solver.get(i, "u")
simX[N, :] = ocp_solver.get(N, "x")
print("inequality multipliers at stage 1")
print(ocp_solver.get(1, "lam")) # inequality multipliers at stage 1
print("slack values at stage 1")
print(ocp_solver.get(1, "t")) # slack values at stage 1
print("multipliers of dynamic conditions between stage 1 and 2")
print(ocp_solver.get(
1, "pi")) # multipliers of dynamic conditions between stage 1 and 2
# initialize ineq multipliers and slacks at stage 1
ocp_solver.set(1, "lam", np.zeros(2, ))
ocp_solver.set(1, "t", np.zeros(2, ))
ocp_solver.print_statistics(
) # encapsulates: stat = ocp_solver.get_stats("statistics")
# timings
time_tot = ocp_solver.get_stats("time_tot")
time_lin = ocp_solver.get_stats("time_lin")
time_sim = ocp_solver.get_stats("time_sim")
time_qp = ocp_solver.get_stats("time_qp")
print(
f"timings OCP solver: total: {1e3*time_tot}ms, lin: {1e3*time_lin}ms, sim: {1e3*time_sim}ms, qp: {1e3*time_qp}ms"
)
# print("simU", simU)
# print("simX", simX)
iterate_filename = f'final_iterate_{discretization}.json'
ocp_solver.store_iterate(filename=iterate_filename, overwrite=True)
plot_pendulum(shooting_nodes, Fmax, simU, simX, latexify=False)
del ocp_solver
def main(interface_type='ctypes'):
# create ocp object to formulate the OCP
ocp = AcadosOcp()
# set model
model = export_pendulum_ode_model()
ocp.model = model
nx = model.x.size()[0]
nu = model.u.size()[0]
ny = nx + nu
ny_e = nx
# define the different options for the use-case demonstration
N0 = 20 # original number of shooting nodes
N12 = 15 # change the number of shooting nodes for use-cases 1 and 2
condN12 = max(1, round(N12/1)) # change the number of cond_N for use-cases 1 and 2 (for PARTIAL_* solvers only)
Tf_01 = 1.0 # original final time and for use-case 1
Tf_2 = Tf_01 * 0.7 # change final time for use-case 2 (but keep N identical)
# set dimensions
ocp.dims.N = N0
# set cost
Q = 2 * np.diag([1e3, 1e3, 1e-2, 1e-2])
R = 2 * np.diag([1e-2])
ocp.cost.W_e = Q
ocp.cost.W = scipy.linalg.block_diag(Q, R)
ocp.cost.cost_type = 'LINEAR_LS'
ocp.cost.cost_type_e = 'LINEAR_LS'
ocp.cost.Vx = np.zeros((ny, nx))
ocp.cost.Vx[:nx, :nx] = np.eye(nx)
Vu = np.zeros((ny, nu))
Vu[4, 0] = 1.0
ocp.cost.Vu = Vu
ocp.cost.Vx_e = np.eye(nx)
ocp.cost.yref = np.zeros((ny,))
ocp.cost.yref_e = np.zeros((ny_e,))
# set constraints
Fmax = 80
ocp.constraints.lbu = np.array([-Fmax])
ocp.constraints.ubu = np.array([+Fmax])
ocp.constraints.idxbu = np.array([0])
ocp.constraints.x0 = np.array([0.0, np.pi, 0.0, 0.0])
# set options
ocp.solver_options.qp_solver = 'PARTIAL_CONDENSING_HPIPM' # FULL_CONDENSING_QPOASES
# PARTIAL_CONDENSING_HPIPM, FULL_CONDENSING_QPOASES, FULL_CONDENSING_HPIPM,
# PARTIAL_CONDENSING_QPDUNES, PARTIAL_CONDENSING_OSQP
ocp.solver_options.hessian_approx = 'GAUSS_NEWTON'
ocp.solver_options.integrator_type = 'ERK'
# ocp.solver_options.print_level = 1
ocp.solver_options.nlp_solver_type = 'SQP' # SQP_RTI, SQP
# set prediction horizon
ocp.solver_options.tf = Tf_01
print(80*'-')
print('generate code and compile...')
if interface_type == 'cython':
AcadosOcpSolver.generate(ocp, json_file='acados_ocp.json')
AcadosOcpSolver.build(ocp.code_export_directory, with_cython=True)
ocp_solver = AcadosOcpSolver.create_cython_solver('acados_ocp.json')
elif interface_type == 'ctypes':
ocp_solver = AcadosOcpSolver(ocp, json_file='acados_ocp.json')
elif interface_type == 'cython_prebuilt':
from c_generated_code.acados_ocp_solver_pyx import AcadosOcpSolverCython
ocp_solver = AcadosOcpSolverCython(ocp.model.name, ocp.solver_options.nlp_solver_type, ocp.dims.N)
# test setting HPIPM options
ocp_solver.options_set('qp_tol_ineq', 1e-8)
ocp_solver.options_set('qp_tau_min', 1e-10)
ocp_solver.options_set('qp_mu0', 1e0)
# --------------------------------------------------------------------------------
# 0) solve the problem defined here (original from code export), analog to 'minimal_example_ocp.py'
nvariant = 0
simX0 = np.ndarray((N0 + 1, nx))
simU0 = np.ndarray((N0, nu))
print(80*'-')
print(f'solve original code with N = {N0} and Tf = {Tf_01} s:')
status = ocp_solver.solve()
if status != 0:
ocp_solver.print_statistics() # encapsulates: stat = ocp_solver.get_stats("statistics")
raise Exception(f'acados returned status {status}.')
# get solution
for i in range(N0):
simX0[i, :] = ocp_solver.get(i, "x")
simU0[i, :] = ocp_solver.get(i, "u")
simX0[N0, :] = ocp_solver.get(N0, "x")
ocp_solver.print_statistics() # encapsulates: stat = ocp_solver.get_stats("statistics")
ocp_solver.store_iterate(filename=f'final_iterate_{interface_type}_variant{nvariant}.json', overwrite=True)
if PLOT:# plot but don't halt
plot_pendulum(np.linspace(0, Tf_01, N0 + 1), Fmax, simU0, simX0, latexify=False, plt_show=False, X_true_label=f'original: N={N0}, Tf={Tf_01}')
ocp_solver.print_statistics()
if status != 0:
raise Exception(f'acados returned status {status}.')
# get solution
for i in range(N):
simX[i,:] = ocp_solver.get(i, "x")
simU[i,:] = ocp_solver.get(i, "u")
simX[N,:] = ocp_solver.get(N, "x")
# plot results
plot_pendulum(np.linspace(0, Tf, N+1), Fmax, simU, simX, latexify=False)
ocp_solver.store_iterate(filename='solution.json', overwrite=True)
ocp_solver.load_iterate(filename='solution.json')
# timings
# time_tot = 1e8
# time_lin = 1e8
# for k in range(1000):
# status = ocp_solver.solve()
# time_tot = min(time_tot, ocp_solver.get_stats("time_tot")[0])
# time_lin = min(time_lin, ocp_solver.get_stats("time_lin")[0])
# print("CPU time = ", time_tot * 1e3, "ms")
# print("CPU time linearization = ", time_lin * 1e3, "ms")