def solve_marathos_problem_with_setting(setting):
globalization = setting['globalization']
line_search_use_sufficient_descent = setting[
'line_search_use_sufficient_descent']
globalization_use_SOC = setting['globalization_use_SOC']
# create ocp object to formulate the OCP
ocp = AcadosOcp()
# set model
model = AcadosModel()
x1 = SX.sym('x1')
x2 = SX.sym('x2')
x = vertcat(x1, x2)
# dynamics: identity
model.disc_dyn_expr = x
model.x = x
model.u = SX.sym('u', 0, 0) # [] / None doesnt work
model.p = []
model.name = f'marathos_problem'
ocp.model = model
# discretization
Tf = 1
N = 1
ocp.dims.N = N
ocp.solver_options.tf = Tf
# cost
ocp.cost.cost_type_e = 'EXTERNAL'
ocp.model.cost_expr_ext_cost_e = x1
# constarints
ocp.model.con_h_expr = x1**2 + x2**2
ocp.constraints.lh = np.array([1.0])
ocp.constraints.uh = np.array([1.0])
# # soften
# ocp.constraints.idxsh = np.array([0])
# ocp.cost.zl = 1e5 * np.array([1])
# ocp.cost.zu = 1e5 * np.array([1])
# ocp.cost.Zl = 1e5 * np.array([1])
# ocp.cost.Zu = 1e5 * np.array([1])
# add bounds on x
# nx = 2
# ocp.constraints.idxbx_0 = np.array(range(nx))
# ocp.constraints.lbx_0 = -2 * np.ones((nx))
# ocp.constraints.ubx_0 = 2 * np.ones((nx))
# 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 = 'EXACT'
ocp.solver_options.integrator_type = 'DISCRETE'
# ocp.solver_options.print_level = 1
ocp.solver_options.tol = TOL
ocp.solver_options.nlp_solver_type = 'SQP' # SQP_RTI, SQP
ocp.solver_options.globalization = globalization
ocp.solver_options.alpha_min = 1e-2
# ocp.solver_options.__initialize_t_slacks = 0
# ocp.solver_options.regularize_method = 'CONVEXIFY'
ocp.solver_options.levenberg_marquardt = 1e-1
# ocp.solver_options.print_level = 2
SQP_max_iter = 300
ocp.solver_options.qp_solver_iter_max = 400
ocp.solver_options.regularize_method = 'MIRROR'
# ocp.solver_options.exact_hess_constr = 0
ocp.solver_options.line_search_use_sufficient_descent = line_search_use_sufficient_descent
ocp.solver_options.globalization_use_SOC = globalization_use_SOC
ocp.solver_options.eps_sufficient_descent = 1e-1
ocp.solver_options.qp_tol = 5e-7
if FOR_LOOPING: # call solver in for loop to get all iterates
ocp.solver_options.nlp_solver_max_iter = 1
ocp_solver = AcadosOcpSolver(ocp, json_file=f'{model.name}.json')
else:
ocp.solver_options.nlp_solver_max_iter = SQP_max_iter
ocp_solver = AcadosOcpSolver(ocp, json_file=f'{model.name}.json')
# initialize solver
rad_init = 0.1 #0.1 #np.pi / 4
xinit = np.array([np.cos(rad_init), np.sin(rad_init)])
# xinit = np.array([0.82120912, 0.58406911])
[ocp_solver.set(i, "x", xinit) for i in range(N + 1)]
# solve
if FOR_LOOPING: # call solver in for loop to get all iterates
iterates = np.zeros((SQP_max_iter + 1, 2))
iterates[0, :] = xinit
alphas = np.zeros((SQP_max_iter, ))
qp_iters = np.zeros((SQP_max_iter, ))
iter = SQP_max_iter
residuals = np.zeros((4, SQP_max_iter))
# solve
for i in range(SQP_max_iter):
status = ocp_solver.solve()
ocp_solver.print_statistics(
) # encapsulates: stat = ocp_solver.get_stats("statistics")
# print(f'acados returned status {status}.')
iterates[i + 1, :] = ocp_solver.get(0, "x")
if status in [0, 4]:
iter = i
break
alphas[i] = ocp_solver.get_stats('alpha')[1]
qp_iters[i] = ocp_solver.get_stats('qp_iter')[1]
residuals[:, i] = ocp_solver.get_stats('residuals')
else:
ocp_solver.solve()
ocp_solver.print_statistics()
iter = ocp_solver.get_stats('sqp_iter')[0]
alphas = ocp_solver.get_stats('alpha')[1:]
qp_iters = ocp_solver.get_stats('qp_iter')
residuals = ocp_solver.get_stats('statistics')[1:5, 1:iter]
# get solution
solution = ocp_solver.get(0, "x")
# print summary
print(f"solved Marathos test problem with settings {setting}")
print(
f"cost function value = {ocp_solver.get_cost()} after {iter} SQP iterations"
)
print(f"alphas: {alphas[:iter]}")
print(f"total number of QP iterations: {sum(qp_iters[:iter])}")
max_infeasibility = np.max(residuals[1:3])
print(f"max infeasibility: {max_infeasibility}")
# compare to analytical solution
exact_solution = np.array([-1, 0])
sol_err = max(np.abs(solution - exact_solution))
# checks
if sol_err > TOL * 1e1:
raise Exception(
f"error of numerical solution wrt exact solution = {sol_err} > tol = {TOL*1e1}"
)
else:
print(f"matched analytical solution with tolerance {TOL}")
try:
if globalization == 'FIXED_STEP':
# import pdb; pdb.set_trace()
if max_infeasibility < 5.0:
raise Exception(
f"Expected max_infeasibility > 5.0 when using full step SQP on Marathos problem"
)
if iter != 10:
raise Exception(
f"Expected 10 SQP iterations when using full step SQP on Marathos problem, got {iter}"
)
if any(alphas[:iter] != 1.0):
raise Exception(
f"Expected all alphas = 1.0 when using full step SQP on Marathos problem"
)
elif globalization == 'MERIT_BACKTRACKING':
if max_infeasibility > 0.5:
raise Exception(
f"Expected max_infeasibility < 0.5 when using globalized SQP on Marathos problem"
)
if globalization_use_SOC == 0:
if FOR_LOOPING and iter != 57:
raise Exception(
f"Expected 57 SQP iterations when using globalized SQP without SOC on Marathos problem, got {iter}"
)
elif line_search_use_sufficient_descent == 1:
if iter not in range(29, 37):
# NOTE: got 29 locally and 36 on Github actions.
# On Github actions the inequality constraint was numerically violated in the beginning.
# This leads to very different behavior, since the merit gradient is so different.
# Github actions: merit_grad = -1.669330e+00, merit_grad_cost = -1.737950e-01, merit_grad_dyn = 0.000000e+00, merit_grad_ineq = -1.495535e+00
# Jonathan Laptop: merit_grad = -1.737950e-01, merit_grad_cost = -1.737950e-01, merit_grad_dyn = 0.000000e+00, merit_grad_ineq = 0.000000e+00
raise Exception(
f"Expected SQP iterations in range(29, 37) when using globalized SQP with SOC on Marathos problem, got {iter}"
)
else:
if iter != 12:
raise Exception(
f"Expected 12 SQP iterations when using globalized SQP with SOC on Marathos problem, got {iter}"
)
except Exception as inst:
if FOR_LOOPING and globalization == "MERIT_BACKTRACKING":
print(
"\nAcados globalized OCP solver behaves different when for looping due to different merit function weights.",
"Following exception is not raised\n")
print(inst, "\n")
else:
raise (inst)
if PLOT:
plt.figure()
axs = plt.plot(solution[0], solution[1], 'x', label='solution')
if FOR_LOOPING: # call solver in for loop to get all iterates
cm = plt.cm.get_cmap('RdYlBu')
axs = plt.scatter(iterates[:iter + 1, 0],
iterates[:iter + 1, 1],
c=range(iter + 1),
s=35,
cmap=cm,
label='iterates')
plt.colorbar(axs)
ts = np.linspace(0, 2 * np.pi, 100)
plt.plot(1 * np.cos(ts) + 0, 1 * np.sin(ts) - 0, 'r')
plt.axis('square')
plt.legend()
plt.title(
f"Marathos problem with N = {N}, x formulation, SOC {globalization_use_SOC}"
)
plt.show()
print(f"\n\n----------------------\n")
def solve_armijo_problem_with_setting(setting):
globalization = setting['globalization']
line_search_use_sufficient_descent = setting[
'line_search_use_sufficient_descent']
globalization_use_SOC = setting['globalization_use_SOC']
# create ocp object to formulate the OCP
ocp = AcadosOcp()
# set model
model = AcadosModel()
x = SX.sym('x')
# dynamics: identity
model.disc_dyn_expr = x
model.x = x
model.u = SX.sym('u', 0, 0) # [] / None doesnt work
model.p = []
model.name = f'armijo_problem'
ocp.model = model
# discretization
Tf = 1
N = 1
ocp.dims.N = N
ocp.solver_options.tf = Tf
# cost
ocp.cost.cost_type_e = 'EXTERNAL'
ocp.model.cost_expr_ext_cost_e = x @ x
ocp.model.cost_expr_ext_cost_custom_hess_e = 1.0 # 2.0 is the actual hessian
# constarints
ocp.constraints.idxbx = np.array([0])
ocp.constraints.lbx = np.array([-10.0])
ocp.constraints.ubx = np.array([10.0])
# options
ocp.solver_options.qp_solver = 'FULL_CONDENSING_QPOASES' # 'PARTIAL_CONDENSING_HPIPM' # FULL_CONDENSING_QPOASES
ocp.solver_options.hessian_approx = 'EXACT'
ocp.solver_options.integrator_type = 'DISCRETE'
ocp.solver_options.print_level = 0
ocp.solver_options.tol = TOL
ocp.solver_options.nlp_solver_type = 'SQP' # SQP_RTI, SQP
ocp.solver_options.globalization = globalization
ocp.solver_options.alpha_reduction = 0.9
ocp.solver_options.line_search_use_sufficient_descent = line_search_use_sufficient_descent
ocp.solver_options.globalization_use_SOC = globalization_use_SOC
ocp.solver_options.eps_sufficient_descent = 5e-1
SQP_max_iter = 200
ocp.solver_options.qp_solver_iter_max = 400
ocp.solver_options.nlp_solver_max_iter = SQP_max_iter
# create solver
ocp_solver = AcadosOcpSolver(ocp, json_file=f'{model.name}.json')
# initialize solver
xinit = np.array([1.0])
[ocp_solver.set(i, "x", xinit) for i in range(N + 1)]
# get stats
status = ocp_solver.solve()
ocp_solver.print_statistics()
iter = ocp_solver.get_stats('sqp_iter')[0]
alphas = ocp_solver.get_stats('alpha')[1:]
qp_iters = ocp_solver.get_stats('qp_iter')
print(f"acados ocp solver returned status {status}")
# get solution
solution = ocp_solver.get(0, "x")
print(f"found solution {solution}")
# print summary
print(f"solved Armijo test problem with settings {setting}")
print(
f"cost function value = {ocp_solver.get_cost()} after {iter} SQP iterations"
)
print(f"alphas: {alphas[:iter]}")
print(f"total number of QP iterations: {sum(qp_iters[:iter])}")
# compare to analytical solution
exact_solution = np.array([0.0])
sol_err = max(np.abs(solution - exact_solution))
print(f"error wrt analytical solution {sol_err}")
# checks
if ocp.model.cost_expr_ext_cost_custom_hess_e == 1.0:
if globalization == 'MERIT_BACKTRACKING':
if sol_err > TOL * 1e1:
raise Exception(
f"error of numerical solution wrt exact solution = {sol_err} > tol = {TOL*1e1}"
)
else:
print(f"matched analytical solution with tolerance {TOL}")
if status != 0:
raise Exception(
f"acados solver returned status {status} != 0.")
if line_search_use_sufficient_descent == 1:
if iter > 22:
raise Exception(f"acados ocp solver took {iter} iterations." + \
"Expected <= 22 iterations for globalized SQP method with aggressive eps_sufficient_descent condition on Armijo test problem.")
else:
if iter < 64:
raise Exception(f"acados ocp solver took {iter} iterations." + \
"Expected > 64 iterations for globalized SQP method without sufficient descent condition on Armijo test problem.")
elif globalization == 'FIXED_STEP':
if status != 2:
raise Exception(
f"acados solver returned status {status} != 2. Expected maximum iterations for full-step SQP on Armijo test problem."
)
else:
print(
f"Sucess: Expected maximum iterations for full-step SQP on Armijo test problem."
)
print(f"\n\n----------------------\n")