def create_ocp_solver(model, Tf, dt, kq, kr, n, m, max_abs_roll_rate,
max_abs_pitch_rate, max_abs_yaw_rate, x0):
'''
creates ACADOS ocp solver with conditions and costs
'''
# create ocp object to formulate the OCP
ocp = AcadosOcp()
ocp.model = model
nx = model.x.size()[0]
nu = model.u.size()[0]
ny = nx + nu
ny_e = nx
N = int(Tf / dt)
ocp.dims.N = N
# set cost
Q = kq * np.eye(n)
R = kr * np.eye(m)
ocp.cost.W_e = Q
ocp.cost.W = la.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[nx:, :] = np.eye(nu)
ocp.cost.Vu = Vu
ocp.cost.Vx_e = np.eye(nx)
# solver options
ocp.solver_options.qp_solver = 'PARTIAL_CONDENSING_HPIPM' # FULL_CONDENSING_QPOASES
# ocp.solver_options.qp_solver = 'FULL_CONDENSING_QPOASES'
ocp.solver_options.hessian_approx = 'GAUSS_NEWTON'
ocp.solver_options.integrator_type = 'ERK'
ocp.solver_options.print_level = 0
ocp.solver_options.nlp_solver_type = 'SQP_RTI' # SQP_RTI, SQP
ocp.solver_options.tf = Tf
# constraints on control
ocp.constraints.lbu = np.array(
[-max_abs_roll_rate, -max_abs_pitch_rate, -max_abs_pitch_rate, 0])
ocp.constraints.ubu = np.array(
[max_abs_roll_rate, max_abs_pitch_rate, max_abs_pitch_rate, 1])
ocp.constraints.idxbu = np.array([0, 1, 2, 3])
ocp.constraints.x0 = x0
ocp.cost.yref = np.zeros((n + m, ))
ocp.cost.yref_e = np.zeros((n, ))
ocp_solver = AcadosOcpSolver(ocp, json_file='acados_ocp.json')
return ocp_solver
def __init__(self, ocp, **solver_options):
if not isinstance(ocp.CX(), SX):
raise RuntimeError(
"CasADi graph must be SX to be solved with ACADOS. Use use_SX "
)
super().__init__(ocp)
# If Acados is installed using the acados_install.sh file, you probably can leave this to unset
acados_path = ""
if "acados_dir" in solver_options:
acados_path = solver_options["acados_dir"]
self.acados_ocp = AcadosOcp(acados_path=acados_path)
self.acados_model = AcadosModel()
if "cost_type" in solver_options:
self.__set_cost_type(solver_options["cost_type"])
else:
self.__set_cost_type()
self.lagrange_costs = SX()
self.mayer_costs = SX()
self.y_ref = []
self.y_ref_end = []
self.__acados_export_model(ocp)
self.__prepare_acados(ocp)
self.ocp_solver = None
self.W = np.zeros((0, 0))
self.W_e = np.zeros((0, 0))
def __init__(self, ocp, solver_options: Solver.ACADOS = None):
"""
Parameters
----------
ocp: OptimalControlProgram
A reference to the current OptimalControlProgram
solver_options: ACADOS
The options to pass to the solver
"""
if not isinstance(ocp.cx(), SX):
raise RuntimeError(
"CasADi graph must be SX to be solved with ACADOS. Please set use_sx to True in OCP"
)
super().__init__(ocp)
# solver_options = solver_options.__dict__
if solver_options is None:
solver_options = Solver.ACADOS()
self.acados_ocp = AcadosOcp(acados_path=solver_options.acados_dir)
self.acados_model = AcadosModel()
self.__set_cost_type(solver_options.cost_type)
self.__set_constr_type(solver_options.constr_type)
self.lagrange_costs = SX()
self.mayer_costs = SX()
self.y_ref = []
self.y_ref_end = []
self.nparams = 0
self.params_initial_guess = None
self.params_bounds = None
self.__acados_export_model(ocp)
self.__prepare_acados(ocp)
self.ocp_solver = None
self.W = np.zeros((0, 0))
self.W_e = np.zeros((0, 0))
self.status = None
self.out = {}
self.real_time_to_optimize = -1
self.all_constr = None
self.end_constr = SX()
self.all_g_bounds = Bounds(interpolation=InterpolationType.CONSTANT)
self.end_g_bounds = Bounds(interpolation=InterpolationType.CONSTANT)
self.x_bound_max = np.ndarray((self.acados_ocp.dims.nx, 3))
self.x_bound_min = np.ndarray((self.acados_ocp.dims.nx, 3))
self.Vu = np.array([],
dtype=np.int64).reshape(0,
ocp.nlp[0].controls.shape)
self.Vx = np.array([], dtype=np.int64).reshape(0,
ocp.nlp[0].states.shape)
self.Vxe = np.array([],
dtype=np.int64).reshape(0, ocp.nlp[0].states.shape)
self.opts = Solver.ACADOS(
) if solver_options is None else solver_options
def __init__(self, ocp, **solver_options):
"""
Parameters
----------
ocp: OptimalControlProgram
A reference to the current OptimalControlProgram
solver_options: dict
The options to pass to the solver
"""
if not isinstance(ocp.cx(), SX):
raise RuntimeError(
"CasADi graph must be SX to be solved with ACADOS. Please set use_sx to True in OCP"
)
super().__init__(ocp)
# If Acados is installed using the acados_install.sh file, you probably can leave this to unset
acados_path = ""
if "acados_dir" in solver_options:
acados_path = solver_options["acados_dir"]
self.acados_ocp = AcadosOcp(acados_path=acados_path)
self.acados_model = AcadosModel()
if "cost_type" in solver_options:
self.__set_cost_type(solver_options["cost_type"])
else:
self.__set_cost_type()
if "constr_type" in solver_options:
self.__set_constr_type(solver_options["constr_type"])
else:
self.__set_constr_type()
self.lagrange_costs = SX()
self.mayer_costs = SX()
self.y_ref = []
self.y_ref_end = []
self.params = None
self.__acados_export_model(ocp)
self.__prepare_acados(ocp)
self.ocp_solver = None
self.W = np.zeros((0, 0))
self.W_e = np.zeros((0, 0))
self.status = None
self.out = {}
self.all_constr = None
self.end_constr = SX()
self.all_g_bounds = Bounds(interpolation=InterpolationType.CONSTANT)
self.end_g_bounds = Bounds(interpolation=InterpolationType.CONSTANT)
self.x_bound_max = np.ndarray((self.acados_ocp.dims.nx, 3))
self.x_bound_min = np.ndarray((self.acados_ocp.dims.nx, 3))
self.Vu = np.array([], dtype=np.int64).reshape(0, ocp.nlp[0].nu)
self.Vx = np.array([], dtype=np.int64).reshape(0, ocp.nlp[0].nx)
self.Vxe = np.array([], dtype=np.int64).reshape(0, ocp.nlp[0].nx)
def solve_marathos_ocp(setting):
globalization = setting['globalization']
line_search_use_sufficient_descent = setting[
'line_search_use_sufficient_descent']
globalization_use_SOC = setting['globalization_use_SOC']
qp_solver = setting['qp_solver']
# create ocp object to formulate the OCP
ocp = AcadosOcp()
# set model
model = export_linear_mass_model()
ocp.model = model
nx = model.x.size()[0]
nu = model.u.size()[0]
ny = nu
# discretization
Tf = 2
N = 20
shooting_nodes = np.linspace(0, Tf, N + 1)
ocp.dims.N = N
# set cost
Q = 2 * np.diag([])
R = 2 * np.diag([1e1, 1e1])
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))
Vu = np.eye((nu))
ocp.cost.Vu = Vu
ocp.cost.yref = np.zeros((ny, ))
# set constraints
Fmax = 5
ocp.constraints.lbu = -Fmax * np.ones((nu, ))
ocp.constraints.ubu = +Fmax * np.ones((nu, ))
ocp.constraints.idxbu = np.array(range(nu))
x0 = np.array([1e-1, 1.1, 0, 0])
ocp.constraints.x0 = x0
# terminal constraint
x_goal = np.array([0, -1.1, 0, 0])
ocp.constraints.idxbx_e = np.array(range(nx))
ocp.constraints.lbx_e = x_goal
ocp.constraints.ubx_e = x_goal
if SOFTEN_TERMINAL:
ocp.constraints.idxsbx_e = np.array(range(nx))
ocp.cost.zl_e = 1e4 * np.ones(nx)
ocp.cost.zu_e = 1e4 * np.ones(nx)
ocp.cost.Zl_e = 1e6 * np.ones(nx)
ocp.cost.Zu_e = 1e6 * np.ones(nx)
# add obstacle
if OBSTACLE:
obs_rad = 1.0
obs_x = 0.0
obs_y = 0.0
circle = (obs_x, obs_y, obs_rad)
ocp.constraints.uh = np.array([100.0]) # doenst matter
ocp.constraints.lh = np.array([obs_rad**2])
x_square = model.x[0]**OBSTACLE_POWER + model.x[1]**OBSTACLE_POWER
ocp.model.con_h_expr = x_square
# copy for terminal
ocp.constraints.uh_e = ocp.constraints.uh
ocp.constraints.lh_e = ocp.constraints.lh
ocp.model.con_h_expr_e = ocp.model.con_h_expr
else:
circle = None
# soften
if OBSTACLE and SOFTEN_OBSTACLE:
ocp.constraints.idxsh = np.array([0])
ocp.constraints.idxsh_e = np.array([0])
Zh = 1e6 * np.ones(1)
zh = 1e4 * np.ones(1)
ocp.cost.zl = zh
ocp.cost.zu = zh
ocp.cost.Zl = Zh
ocp.cost.Zu = Zh
ocp.cost.zl_e = np.concatenate((ocp.cost.zl_e, zh))
ocp.cost.zu_e = np.concatenate((ocp.cost.zu_e, zh))
ocp.cost.Zl_e = np.concatenate((ocp.cost.Zl_e, Zh))
ocp.cost.Zu_e = np.concatenate((ocp.cost.Zu_e, Zh))
# set options
ocp.solver_options.qp_solver = qp_solver # 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
ocp.solver_options.globalization = globalization
ocp.solver_options.alpha_min = 0.01
# ocp.solver_options.__initialize_t_slacks = 0
# ocp.solver_options.levenberg_marquardt = 1e-2
ocp.solver_options.qp_solver_cond_N = 0
ocp.solver_options.print_level = 1
ocp.solver_options.nlp_solver_max_iter = 200
ocp.solver_options.qp_solver_iter_max = 400
# NOTE: this is needed for PARTIAL_CONDENSING_HPIPM to get expected behavior
qp_tol = 5e-7
ocp.solver_options.qp_solver_tol_stat = qp_tol
ocp.solver_options.qp_solver_tol_eq = qp_tol
ocp.solver_options.qp_solver_tol_ineq = qp_tol
ocp.solver_options.qp_solver_tol_comp = qp_tol
ocp.solver_options.qp_solver_ric_alg = 1
# ocp.solver_options.qp_solver_cond_ric_alg = 1
# set prediction horizon
ocp.solver_options.tf = Tf
ocp_solver = AcadosOcpSolver(ocp, json_file=f'{model.name}_ocp.json')
ocp_solver.options_set('line_search_use_sufficient_descent',
line_search_use_sufficient_descent)
ocp_solver.options_set('globalization_use_SOC', globalization_use_SOC)
ocp_solver.options_set('full_step_dual', 1)
if INITIALIZE: # initialize solver
# [ocp_solver.set(i, "x", x0 + (i/N) * (x_goal-x0)) for i in range(N+1)]
[ocp_solver.set(i, "x", x0) for i in range(N + 1)]
# [ocp_solver.set(i, "u", 2*(np.random.rand(2) - 0.5)) for i in range(N)]
# solve
status = ocp_solver.solve()
ocp_solver.print_statistics(
) # encapsulates: stat = ocp_solver.get_stats("statistics")
sqp_iter = ocp_solver.get_stats('sqp_iter')[0]
print(f'acados returned status {status}.')
# ocp_solver.store_iterate(f'it{ocp.solver_options.nlp_solver_max_iter}_{model.name}.json')
# get solution
simX = np.array([ocp_solver.get(i, "x") for i in range(N + 1)])
simU = np.array([ocp_solver.get(i, "u") for i in range(N)])
pi_multiplier = [ocp_solver.get(i, "pi") for i in range(N)]
print(f"cost function value = {ocp_solver.get_cost()}")
# print summary
print(f"solved Marathos test problem with settings {setting}")
print(
f"cost function value = {ocp_solver.get_cost()} after {sqp_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}")
# checks
if status != 0:
raise Exception(f"acados solver returned status {status} != 0.")
if globalization == "FIXED_STEP":
if sqp_iter != 18:
raise Exception(
f"acados solver took {sqp_iter} iterations, expected 18.")
elif globalization == "MERIT_BACKTRACKING":
if globalization_use_SOC == 1 and line_search_use_sufficient_descent == 0 and sqp_iter not in range(
21, 23):
raise Exception(
f"acados solver took {sqp_iter} iterations, expected range(21, 23)."
)
elif globalization_use_SOC == 1 and line_search_use_sufficient_descent == 1 and sqp_iter not in range(
21, 24):
raise Exception(
f"acados solver took {sqp_iter} iterations, expected range(21, 24)."
)
elif globalization_use_SOC == 0 and line_search_use_sufficient_descent == 0 and sqp_iter not in range(
155, 165):
raise Exception(
f"acados solver took {sqp_iter} iterations, expected range(155, 165)."
)
elif globalization_use_SOC == 0 and line_search_use_sufficient_descent == 1 and sqp_iter not in range(
160, 175):
raise Exception(
f"acados solver took {sqp_iter} iterations, expected range(160, 175)."
)
if PLOT:
plot_linear_mass_system_X_state_space(simX,
circle=circle,
x_goal=x_goal)
plot_linear_mass_system_U(shooting_nodes, simU)
# plot_linear_mass_system_X(shooting_nodes, simX)
# import pdb; pdb.set_trace()
print(f"\n\n----------------------\n")
def run_nominal_control(chain_params):
# create ocp object to formulate the OCP
ocp = AcadosOcp()
# chain parameters
n_mass = chain_params["n_mass"]
M = chain_params["n_mass"] - 2 # number of intermediate masses
Ts = chain_params["Ts"]
Tsim = chain_params["Tsim"]
N = chain_params["N"]
u_init = chain_params["u_init"]
with_wall = chain_params["with_wall"]
yPosWall = chain_params["yPosWall"]
m = chain_params["m"]
D = chain_params["D"]
L = chain_params["L"]
perturb_scale = chain_params["perturb_scale"]
nlp_iter = chain_params["nlp_iter"]
nlp_tol = chain_params["nlp_tol"]
save_results = chain_params["save_results"]
show_plots = chain_params["show_plots"]
seed = chain_params["seed"]
np.random.seed(seed)
nparam = 3*M
W = perturb_scale * np.eye(nparam)
# export model
model = export_disturbed_chain_mass_model(n_mass, m, D, L)
# set model
ocp.model = model
nx = model.x.size()[0]
nu = model.u.size()[0]
ny = nx + nu
ny_e = nx
Tf = N * Ts
# initial state
xPosFirstMass = np.zeros((3,1))
xEndRef = np.zeros((3,1))
xEndRef[0] = L * (M+1) * 6
pos0_x = np.linspace(xPosFirstMass[0], xEndRef[0], n_mass)
xrest = compute_steady_state(n_mass, m, D, L, xPosFirstMass, xEndRef)
x0 = xrest
# set dimensions
ocp.dims.N = N
# set cost module
ocp.cost.cost_type = 'LINEAR_LS'
ocp.cost.cost_type_e = 'LINEAR_LS'
Q = 2*np.diagflat( np.ones((nx, 1)) )
q_diag = np.ones((nx,1))
strong_penalty = M+1
q_diag[3*M] = strong_penalty
q_diag[3*M+1] = strong_penalty
q_diag[3*M+2] = strong_penalty
Q = 2*np.diagflat( q_diag )
R = 2*np.diagflat( 1e-2 * np.ones((nu, 1)) )
ocp.cost.W = scipy.linalg.block_diag(Q, R)
ocp.cost.W_e = Q
ocp.cost.Vx = np.zeros((ny, nx))
ocp.cost.Vx[:nx,:nx] = np.eye(nx)
Vu = np.zeros((ny, nu))
Vu[nx:nx+nu, :] = np.eye(nu)
ocp.cost.Vu = Vu
ocp.cost.Vx_e = np.eye(nx)
# import pdb; pdb.set_trace()
yref = np.vstack((xrest, np.zeros((nu,1)))).flatten()
ocp.cost.yref = yref
ocp.cost.yref_e = xrest.flatten()
# set constraints
umax = 1*np.ones((nu,))
ocp.constraints.constr_type = 'BGH'
ocp.constraints.lbu = -umax
ocp.constraints.ubu = umax
ocp.constraints.x0 = x0.reshape((nx,))
ocp.constraints.idxbu = np.array(range(nu))
# disturbances
nparam = 3*M
ocp.parameter_values = np.zeros((nparam,))
# wall constraint
if with_wall:
nbx = M + 1
Jbx = np.zeros((nbx,nx))
for i in range(nbx):
Jbx[i, 3*i+1] = 1.0
ocp.constraints.Jbx = Jbx
ocp.constraints.lbx = yPosWall * np.ones((nbx,))
ocp.constraints.ubx = 1e9 * np.ones((nbx,))
# slacks
ocp.constraints.Jsbx = np.eye(nbx)
L2_pen = 1e3
L1_pen = 1
ocp.cost.Zl = L2_pen * np.ones((nbx,))
ocp.cost.Zu = L2_pen * np.ones((nbx,))
ocp.cost.zl = L1_pen * np.ones((nbx,))
ocp.cost.zu = L1_pen * np.ones((nbx,))
# solver options
ocp.solver_options.qp_solver = 'PARTIAL_CONDENSING_HPIPM' # FULL_CONDENSING_QPOASES
ocp.solver_options.hessian_approx = 'GAUSS_NEWTON'
ocp.solver_options.integrator_type = 'IRK'
ocp.solver_options.nlp_solver_type = 'SQP' # SQP_RTI
ocp.solver_options.nlp_solver_max_iter = nlp_iter
ocp.solver_options.sim_method_num_stages = 2
ocp.solver_options.sim_method_num_steps = 2
ocp.solver_options.qp_solver_cond_N = N
ocp.solver_options.qp_tol = nlp_tol
ocp.solver_options.tol = nlp_tol
# ocp.solver_options.nlp_solver_tol_eq = 1e-9
# set prediction horizon
ocp.solver_options.tf = Tf
acados_ocp_solver = AcadosOcpSolver(ocp, json_file = 'acados_ocp_' + model.name + '.json')
# acados_integrator = AcadosSimSolver(ocp, json_file = 'acados_ocp_' + model.name + '.json')
acados_integrator = export_chain_mass_integrator(n_mass, m, D, L)
#%% get initial state from xrest
xcurrent = x0.reshape((nx,))
for i in range(5):
acados_integrator.set("x", xcurrent)
acados_integrator.set("u", u_init)
status = acados_integrator.solve()
if status != 0:
raise Exception('acados integrator returned status {}. Exiting.'.format(status))
# update state
xcurrent = acados_integrator.get("x")
#%% actual simulation
N_sim = int(np.floor(Tsim/Ts))
simX = np.ndarray((N_sim+1, nx))
simU = np.ndarray((N_sim, nu))
wall_dist = np.zeros((N_sim,))
timings = np.zeros((N_sim,))
simX[0,:] = xcurrent
# closed loop
for i in range(N_sim):
# solve ocp
acados_ocp_solver.set(0, "lbx", xcurrent)
acados_ocp_solver.set(0, "ubx", xcurrent)
status = acados_ocp_solver.solve()
timings[i] = acados_ocp_solver.get_stats("time_tot")[0]
if status != 0:
raise Exception('acados acados_ocp_solver returned status {} in time step {}. Exiting.'.format(status, i))
simU[i,:] = acados_ocp_solver.get(0, "u")
print("control at time", i, ":", simU[i,:])
# simulate system
acados_integrator.set("x", xcurrent)
acados_integrator.set("u", simU[i,:])
pertubation = sampleFromEllipsoid(np.zeros((nparam,)), W)
acados_integrator.set("p", pertubation)
status = acados_integrator.solve()
if status != 0:
raise Exception('acados integrator returned status {}. Exiting.'.format(status))
# update state
xcurrent = acados_integrator.get("x")
simX[i+1,:] = xcurrent
# xOcpPredict = acados_ocp_solver.get(1, "x")
# print("model mismatch = ", str(np.max(xOcpPredict - xcurrent)))
yPos = xcurrent[range(1,3*M+1,3)]
wall_dist[i] = np.min(yPos - yPosWall)
print("time i = ", str(i), " dist2wall ", str(wall_dist[i]))
print("dist2wall (minimum over simulation) ", str(np.min(wall_dist)))
#%% plot results
if os.environ.get('ACADOS_ON_TRAVIS') is None and show_plots:
plot_chain_control_traj(simU)
plot_chain_position_traj(simX, yPosWall=yPosWall)
plot_chain_velocity_traj(simX)
animate_chain_position(simX, xPosFirstMass, yPosWall=yPosWall)
# animate_chain_position_3D(simX, xPosFirstMass)
plt.show()
if __name__ == "__main__":
parser = argparse.ArgumentParser(
description='test Python interface on pendulum example.')
parser.add_argument('--INTEGRATOR_TYPE',
dest='INTEGRATOR_TYPE',
help='INTEGRATOR_TYPE: ERK, IRK, GNSF, DISCRETE')
args = parser.parse_args()
integrator_type = args.INTEGRATOR_TYPE
INTEGRATOR_TYPE_values = ['ERK', 'IRK', 'GNSF', 'DISCRETE']
if integrator_type not in INTEGRATOR_TYPE_values:
raise Exception('Invalid unit test value {} for parameter INTEGRATOR_TYPE. Possible values are' \
' {}. Exiting.'.format(integrator_type, INTEGRATOR_TYPE_values))
# create ocp object to formulate the OCP
ocp = AcadosOcp()
Tf = 1.0
N = 20
# set model
if integrator_type == 'DISCRETE':
model = export_pendulum_ode_model_with_discrete_rk4(Tf / N)
else:
model = export_pendulum_ode_model()
ocp.model = model
nx = model.x.size()[0]
nu = model.u.size()[0]
ny = nx + nu
Tf = 1.5 # prediction horizon N = round(Tf * 20) # number of discretization steps T = 12.0 # maximum simulation time[s] mb = 4 mw = 2 mt = mb + mw Rw = 0.17 Iw = (mw * (Rw**2)) g = 9.81 car_model = CarModel_mpc_noise(mb, mw, Iw, Rw, Tf / N) model = car_model.model ocp = AcadosOcp() ocp.model = model print(model) # set dimensions nx = model.x.size()[0] nu = model.u.size()[0] ny = nx + nu ny_e = nx ocp.dims.N = N # set cost Q = np.diag([5, 50, 0.5, 1, 50, 500]) R = np.diag([10, 1]) Qe = np.diag([5, 50, 0.5, 1, 10, 500])
def acados_settings(Tf, N, track_file):
# create render arguments
ocp = AcadosOcp()
# export model
model, constraint = bicycle_model(track_file)
# define acados ODE
model_ac = AcadosModel()
model_ac.f_impl_expr = model.f_impl_expr
model_ac.f_expl_expr = model.f_expl_expr
model_ac.x = model.x
model_ac.xdot = model.xdot
model_ac.u = model.u
model_ac.z = model.z
model_ac.p = model.p
model_ac.name = model.name
ocp.model = model_ac
# define constraint
model_ac.con_h_expr = constraint.expr
# set dimensions
nx = model.x.size()[0]
nu = model.u.size()[0]
ny = nx + nu
ny_e = nx
ocp.dims.N = N
ns = 2
nsh = 2
# set cost
Q = np.diag([1e-1, 1e-8, 1e-8, 1e-8, 1e-3, 5e-3])
R = np.eye(nu)
R[0, 0] = 1e-3
R[1, 1] = 5e-3
Qe = np.diag([5e0, 1e1, 1e-8, 1e-8, 5e-3, 2e-3])
ocp.cost.cost_type = "LINEAR_LS"
ocp.cost.cost_type_e = "LINEAR_LS"
unscale = N / Tf
ocp.cost.W = unscale * scipy.linalg.block_diag(Q, R)
ocp.cost.W_e = Qe / unscale
Vx = np.zeros((ny, nx))
Vx[:nx, :nx] = np.eye(nx)
ocp.cost.Vx = Vx
Vu = np.zeros((ny, nu))
Vu[6, 0] = 1.0
Vu[7, 1] = 1.0
ocp.cost.Vu = Vu
Vx_e = np.zeros((ny_e, nx))
Vx_e[:nx, :nx] = np.eye(nx)
ocp.cost.Vx_e = Vx_e
ocp.cost.zl = 100 * np.ones((ns, ))
ocp.cost.Zl = 0 * np.ones((ns, ))
ocp.cost.zu = 100 * np.ones((ns, ))
ocp.cost.Zu = 0 * np.ones((ns, ))
# set intial references
ocp.cost.yref = np.array([1, 0, 0, 0, 0, 0, 0, 0])
ocp.cost.yref_e = np.array([0, 0, 0, 0, 0, 0])
# setting constraints
ocp.constraints.lbx = np.array([-12])
ocp.constraints.ubx = np.array([12])
ocp.constraints.idxbx = np.array([1])
ocp.constraints.lbu = np.array([model.dthrottle_min, model.ddelta_min])
ocp.constraints.ubu = np.array([model.dthrottle_max, model.ddelta_max])
ocp.constraints.idxbu = np.array([0, 1])
# ocp.constraints.lsbx=np.zero s([1])
# ocp.constraints.usbx=np.zeros([1])
# ocp.constraints.idxsbx=np.array([1])
ocp.constraints.lh = np.array([
constraint.along_min,
constraint.alat_min,
model.n_min,
model.throttle_min,
model.delta_min,
])
ocp.constraints.uh = np.array([
constraint.along_max,
constraint.alat_max,
model.n_max,
model.throttle_max,
model.delta_max,
])
ocp.constraints.lsh = np.zeros(nsh)
ocp.constraints.ush = np.zeros(nsh)
ocp.constraints.idxsh = np.array([0, 2])
# set intial condition
ocp.constraints.x0 = model.x0
# set QP solver and integration
ocp.solver_options.tf = Tf
# ocp.solver_options.qp_solver = 'FULL_CONDENSING_QPOASES'
ocp.solver_options.qp_solver = "PARTIAL_CONDENSING_HPIPM"
ocp.solver_options.nlp_solver_type = "SQP_RTI"
ocp.solver_options.hessian_approx = "GAUSS_NEWTON"
ocp.solver_options.integrator_type = "ERK"
ocp.solver_options.sim_method_num_stages = 4
ocp.solver_options.sim_method_num_steps = 3
# ocp.solver_options.qp_solver_tol_stat = 1e-2
# ocp.solver_options.qp_solver_tol_eq = 1e-2
# ocp.solver_options.qp_solver_tol_ineq = 1e-2
# ocp.solver_options.qp_solver_tol_comp = 1e-2
# create solver
acados_solver = AcadosOcpSolver(ocp, json_file="acados_ocp.json")
return constraint, model, acados_solver
def acados_settings(Tf, N):
# create render arguments
ocp = AcadosOcp()
# export model
model, constraint = usv_model()
# define acados ODE
model_ac = AcadosModel()
model_ac.f_impl_expr = model.f_impl_expr
model_ac.f_expl_expr = model.f_expl_expr
model_ac.x = model.x
model_ac.xdot = model.xdot
model_ac.u = model.U
model_ac.z = model.z
model_ac.p = model.p
model_ac.name = model.name
ocp.model = model_ac
# define constraint
model_ac.con_h_expr = constraint.expr
# set dimensions
nx = model.x.size()[0]
nu = model.U.size()[0]
ny = nx + nu
ny_e = nx
ocp.dims.N = N
ns = 8
nsh = 8
# set cost
Q = np.diag([0, 0, 0.05, 0.01, 0, 0, 0, 0])
R = np.eye(nu)
R[0, 0] = 0.2
Qe = np.diag([0, 0, 0.1, 0.05, 0, 0, 0, 0])
ocp.cost.cost_type = "LINEAR_LS"
ocp.cost.cost_type_e = "LINEAR_LS"
#unscale = N / Tf
#ocp.cost.W = unscale * scipy.linalg.block_diag(Q, R)
#ocp.cost.W_e = Qe / unscale
ocp.cost.W = scipy.linalg.block_diag(Q, R)
ocp.cost.W_e = Qe
Vx = np.zeros((ny, nx))
Vx[:nx, :nx] = np.eye(nx)
ocp.cost.Vx = Vx
Vu = np.zeros((ny, nu))
Vu[8, 0] = 1.0
ocp.cost.Vu = Vu
Vx_e = np.zeros((ny_e, nx))
Vx_e[:nx, :nx] = np.eye(nx)
ocp.cost.Vx_e = Vx_e
ocp.cost.zl = 10 * np.ones((ns, )) #previously 100
ocp.cost.Zl = 0 * np.ones((ns, ))
ocp.cost.zu = 10 * np.ones((ns, )) #previously 100
ocp.cost.Zu = 0 * np.ones((ns, ))
# set intial references
ocp.cost.yref = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0])
ocp.cost.yref_e = np.array([0, 0, 0, 0, 0, 0, 0, 0])
# setting constraints
#ocp.constraints.lbx = np.array([model.psieddot_min])
#ocp.constraints.ubx = np.array([model.psieddot_max])
#ocp.constraints.idxbx = np.array([8])
ocp.constraints.lbu = np.array([model.Upsieddot_min])
ocp.constraints.ubu = np.array([model.Upsieddot_max])
ocp.constraints.idxbu = np.array([0])
# ocp.constraints.lsbx=np.zero s([1])
# ocp.constraints.usbx=np.zeros([1])
# ocp.constraints.idxsbx=np.array([1])
ocp.constraints.lh = np.array([
constraint.distance_min, constraint.distance_min,
constraint.distance_min, constraint.distance_min,
constraint.distance_min, constraint.distance_min,
constraint.distance_min, constraint.distance_min
])
ocp.constraints.uh = np.array([
1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000
])
'''ocp.constraints.lsh = np.zeros(nsh)
ocp.constraints.ush = np.zeros(nsh)
ocp.constraints.idxsh = np.array([0, 2])'''
ocp.constraints.lsh = np.array(
[-0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2])
ocp.constraints.ush = np.array([0, 0, 0, 0, 0, 0, 0, 0])
ocp.constraints.idxsh = np.array([0, 1, 2, 3, 4, 5, 6, 7])
# set intial condition
ocp.constraints.x0 = model.x0
#ocp.parameter_values = np.array([4,4,4,8,4,12,4,20,100,100,100,100,100,100,100,100])
ocp.parameter_values = np.array([
100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100,
100, 100
])
# set QP solver and integration
ocp.solver_options.tf = Tf
#ocp.solver_options.qp_solver = 'FULL_CONDENSING_QPOASES'
ocp.solver_options.qp_solver = "PARTIAL_CONDENSING_HPIPM"
ocp.solver_options.nlp_solver_type = "SQP_RTI"
#ocp.solver_options.nlp_solver_type = "SQP"
ocp.solver_options.hessian_approx = "GAUSS_NEWTON"
ocp.solver_options.integrator_type = "ERK"
#ocp.solver_options.sim_method_num_stages = 4
#ocp.solver_options.sim_method_num_steps = 3
#ocp.solver_options.nlp_solver_max_iter = 200
#ocp.solver_options.tol = 1e-4
#ocp.solver_options.qp_solver_tol_stat = 1e-2
#ocp.solver_options.qp_solver_tol_eq = 1e-2
#ocp.solver_options.qp_solver_tol_ineq = 1e-2
#ocp.solver_options.qp_solver_tol_comp = 1e-2
# create solver
acados_solver = AcadosOcpSolver(ocp, json_file="acados_ocp.json")
return constraint, model, acados_solver
def generate(self, dae=None, quad=None, name='tunempc', opts={}):
""" Create embeddable NLP solver
"""
from acados_template import AcadosModel, AcadosOcp, AcadosOcpSolver, AcadosSimSolver
# extract dimensions
nx = self.__nx
nu = self.__nu + self.__ns # treat slacks as pseudo-controls
# extract reference
ref = self.__ref
xref = np.squeeze(self.__ref[0][:nx], axis=1)
uref = np.squeeze(self.__ref[0][nx:nx + nu], axis=1)
# sampling time
self.__ts = opts['tf'] / self.__N
# create acados model
model = AcadosModel()
model.x = ca.MX.sym('x', nx)
model.u = ca.MX.sym('u', nu)
model.p = []
model.name = name
# detect input type
if dae is None:
model.f_expl_expr = self.__F(x0=model.x,
p=model.u)['xf'] / self.__ts
opts['integrator_type'] = 'ERK'
opts['sim_method_num_stages'] = 1
opts['sim_method_num_steps'] = 1
else:
n_in = dae.n_in()
if n_in == 2:
# xdot = f(x, u)
if 'integrator_type' in opts:
if opts['integrator_type'] in ['IRK', 'GNSF']:
xdot = ca.MX.sym('xdot', nx)
model.xdot = xdot
model.f_impl_expr = xdot - dae(model.x,
model.u[:self.__nu])
model.f_expl_expr = xdot
elif opts['integrator_type'] == 'ERK':
model.f_expl_expr = dae(model.x, model.u[:self.__nu])
else:
raise ValueError('Provide numerical integrator type!')
else:
xdot = ca.MX.sym('xdot', nx)
model.xdot = xdot
model.f_expl_expr = xdot
if n_in == 3:
# f(xdot, x, u) = 0
model.f_impl_expr = dae(xdot, model.x, model.u[:self.__nu])
elif n_in == 4:
# f(xdot, x, u, z) = 0
nz = dae.size1_in(3)
z = ca.MX.sym('z', nz)
model.z = z
model.f_impl_expr = dae(xdot, model.x, model.u[:self.__nu],
z)
else:
raise ValueError(
'Invalid number of inputs for system dynamics function.'
)
if self.__gnl is not None:
model.con_h_expr = self.__gnl(model.x, model.u[:self.__nu],
model.u[self.__nu:])
if self.__type == 'economic':
if quad is None:
model.cost_expr_ext_cost = self.__cost(
model.x, model.u[:self.__nu]) / self.__ts
else:
model.cost_expr_ext_cost = self.__cost(model.x,
model.u[:self.__nu])
# create acados ocp
ocp = AcadosOcp()
ocp.model = model
ny = nx + nu
ny_e = nx
if 'integrator_type' in opts and opts['integrator_type'] == 'GNSF':
from acados_template import acados_dae_model_json_dump
import os
acados_dae_model_json_dump(model)
# Set up Octave to be able to run the following:
## if using a virtual python env, the following lines can be added to the env/bin/activate script:
# export OCTAVE_PATH=$OCTAVE_PATH:$ACADOS_INSTALL_DIR/external/casadi-octave
# export OCTAVE_PATH=$OCTAVE_PATH:$ACADOS_INSTALL_DIR/interfaces/acados_matlab_octave/
# export OCTAVE_PATH=$OCTAVE_PATH:$ACADOS_INSTALL_DIR/interfaces/acados_matlab_octave/acados_template_mex/
# echo
# echo "OCTAVE_PATH=$OCTAVE_PATH"
status = os.system(
"octave --eval \"convert({})\"".format("\'" + model.name +
"_acados_dae.json\'"))
# load gnsf from json
with open(model.name + '_gnsf_functions.json', 'r') as f:
import json
gnsf_dict = json.load(f)
ocp.gnsf_model = gnsf_dict
# set horizon length
ocp.dims.N = self.__N
# set cost module
if self.__type == 'economic':
# set cost function type to external (provided in model)
ocp.cost.cost_type = 'EXTERNAL'
if quad is not None:
ocp.solver_options.cost_discretization = 'INTEGRATOR'
elif self.__type == 'tracking':
# set weighting matrices
ocp.cost.W = self.__Href[0][0]
# set-up linear least squares cost
ocp.cost.cost_type = 'LINEAR_LS'
ocp.cost.W_e = np.zeros((nx, nx))
ocp.cost.Vx = np.zeros((ny, nx))
ocp.cost.Vx[:nx, :nx] = np.eye(nx)
Vu = np.zeros((ny, nu))
Vu[nx:, :] = np.eye(nu)
ocp.cost.Vu = Vu
ocp.cost.Vx_e = np.eye(nx)
ocp.cost.yref = np.squeeze(
ca.vertcat(xref,uref).full() - \
ct.mtimes(np.linalg.inv(ocp.cost.W),self.__qref[0][0].T).full(), # gradient term
axis = 1
)
ocp.cost.yref_e = np.zeros((ny_e, ))
if n_in == 4: # DAE flag
ocp.cost.Vz = np.zeros((ny, nz))
# if 'custom_hessian' in opts:
# self.__custom_hessian = opts['custom_hessian']
# initial condition
ocp.constraints.x0 = xref
# set inequality constraints
ocp.constraints.constr_type = 'BGH'
if self.__S['C'] is not None:
C = self.__S['C'][0][:, :nx]
D = self.__S['C'][0][:, nx:]
lg = -self.__S['e'][0] + ct.mtimes(C, xref).full() + ct.mtimes(
D, uref).full()
ug = 1e8 - self.__S['e'][0] + ct.mtimes(
C, xref).full() + ct.mtimes(D, uref).full()
ocp.constraints.lg = np.squeeze(lg, axis=1)
ocp.constraints.ug = np.squeeze(ug, axis=1)
ocp.constraints.C = C
ocp.constraints.D = D
if 'usc' in self.__vars:
if 'us' in self.__vars:
arg = [
self.__vars['x'], self.__vars['u'], self.__vars['us'],
self.__vars['usc']
]
else:
arg = [
self.__vars['x'], self.__vars['u'], self.__vars['usc']
]
Jsg = ca.Function(
'Jsg', [self.__vars['usc']],
[ca.jacobian(self.__h(*arg), self.__vars['usc'])])(0.0)
self.__Jsg = Jsg.full()[:-self.__nsc, :]
ocp.constraints.Jsg = self.__Jsg
ocp.cost.Zl = np.zeros((self.__nsc, ))
ocp.cost.Zu = np.zeros((self.__nsc, ))
ocp.cost.zl = np.squeeze(self.__scost.full(),
axis=1) / self.__ts
ocp.cost.zu = np.squeeze(self.__scost.full(),
axis=1) / self.__ts
# set nonlinear equality constraints
if self.__gnl is not None:
ocp.constraints.lh = np.zeros(self.__ns, )
ocp.constraints.uh = np.zeros(self.__ns, )
# terminal constraint:
x_term = self.__p_operator(model.x)
Jbx = ca.Function('Jbx', [model.x],
[ca.jacobian(x_term, model.x)])(0.0)
ocp.constraints.Jbx_e = Jbx.full()
ocp.constraints.lbx_e = np.squeeze(self.__p_operator(xref).full(),
axis=1)
ocp.constraints.ubx_e = np.squeeze(self.__p_operator(xref).full(),
axis=1)
for option in list(opts.keys()):
if hasattr(ocp.solver_options, option):
setattr(ocp.solver_options, option, opts[option])
self.__acados_ocp_solver = AcadosOcpSolver(ocp,
json_file='acados_ocp_' +
model.name + '.json')
self.__acados_integrator = AcadosSimSolver(ocp,
json_file='acados_ocp_' +
model.name + '.json')
# set initial guess
self.__set_acados_initial_guess()
return self.__acados_ocp_solver, self.__acados_integrator
def acados_settings_dyn(Tf, N, modelparams = "modelparams.yaml"):
#create render arguments
ocp = AcadosOcp()
#load model
model, constraints = dynamic_model(modelparams)
# define acados ODE
model_ac = AcadosModel()
model_ac.f_impl_expr = model.f_impl_expr
model_ac.f_expl_expr = model.f_expl_expr
model_ac.x = model.x
model_ac.xdot = model.xdot
#inputvector
model_ac.u = model.u
#parameter vector
model_ac.p = model.p
#parameter vector
model_ac.z = model.z
#external cost function
model_ac.cost_expr_ext_cost = model.stage_cost
#model_ac.cost_expr_ext_cost_e = 0
model_ac.con_h_expr = model.con_h_expr
model_ac.name = model.name
ocp.model = model_ac
# set dimensions
nx = model.x.size()[0]
nu = model.u.size()[0]
nz = model.z.size()[0]
np = model.p.size()[0]
#ny = nu + nx
#ny_e = nx
ocp.dims.nx = nx
ocp.dims.nz = nz
#ocp.dims.ny = ny
#ocp.dims.ny_e = ny_e
ocp.dims.nu = nu
ocp.dims.np = np
ocp.dims.nh = 1
#ocp.dims.ny = ny
#ocp.dims.ny_e = ny_e
ocp.dims.nbx = 3
ocp.dims.nsbx = 0
ocp.dims.nbu = nu
#number of soft on h constraints
ocp.dims.nsh = 1
ocp.dims.ns = 1
ocp.dims.N = N
# set cost to casadi expression defined above
ocp.cost.cost_type = "EXTERNAL"
#ocp.cost.cost_type_e = "EXTERNAL"
ocp.cost.zu = 1000 * npy.ones((ocp.dims.ns,))
ocp.cost.Zu = 1000 * npy.ones((ocp.dims.ns,))
ocp.cost.zl = 1000 * npy.ones((ocp.dims.ns,))
ocp.cost.Zl = 1000 * npy.ones((ocp.dims.ns,))
#not sure if needed
#unscale = N / Tf
#constraints
#stagewise constraints for tracks with slack
ocp.constraints.uh = npy.array([0.00])
ocp.constraints.lh = npy.array([-10])
ocp.constraints.lsh = 0.1*npy.ones(ocp.dims.nsh)
ocp.constraints.ush = -0.1*npy.ones(ocp.dims.nsh)
ocp.constraints.idxsh = npy.array([0])
#ocp.constraints.Jsh = 1
# boxconstraints
# xvars = ['posx', 'posy', 'phi', 'vx', 'vy', 'omega', 'd', 'delta', 'theta']
ocp.constraints.lbx = npy.array([10, 10, 100, model.vx_min, model.vy_min, model.omega_min, model.d_min, model.delta_min, model.theta_min])
ocp.constraints.ubx = npy.array([10, 10, 100, model.vx_max, model.vy_max, model.omega_max, model.d_max, model.delta_max, model.theta_max])
ocp.constraints.idxbx = npy.arange(nx)
#ocp.constraints.lsbx= -0.1 * npy.ones(ocp.dims.nbx)
#ocp.constraints.usbx= 0.1 * npy.ones(ocp.dims.nbx)
#ocp.constraints.idxsbx= npy.array([6,7,8])
#print("ocp.constraints.idxbx: ",ocp.constraints.idxbx)
ocp.constraints.lbu = npy.array([model.ddot_min, model.deltadot_min, model.thetadot_min])
ocp.constraints.ubu = npy.array([model.ddot_max, model.deltadot_max, model.thetadot_max])
ocp.constraints.idxbu = npy.array([0, 1, 2])
# set intial condition
ocp.constraints.x0 = model.x0
# set QP solver and integration
ocp.solver_options.tf = Tf
# ocp.solver_options.qp_solver = 'FULL_CONDENSING_QPOASES'
ocp.solver_options.qp_solver = "PARTIAL_CONDENSING_HPIPM"
ocp.solver_options.nlp_solver_type = "SQP"#"SQP_RTI" #
ocp.solver_options.hessian_approx = "GAUSS_NEWTON"
ocp.solver_options.integrator_type = "ERK"
ocp.parameter_values = npy.zeros(np)
#ocp.solver_options.sim_method_num_stages = 4
#ocp.solver_options.sim_method_num_steps = 3
ocp.solver_options.nlp_solver_step_length = 0.01
ocp.solver_options.nlp_solver_max_iter = 50
ocp.solver_options.tol = 1e-4
#ocp.solver_options.print_level = 1
# ocp.solver_options.nlp_solver_tol_comp = 1e-1
# create solver
acados_solver = AcadosOcpSolver(ocp, json_file="acados_ocp_dynamic.json")
return constraints, model, acados_solver, ocp
def quadrotor_optimizer_setup(self, ):
# Q_m_ = np.diag([80.0, 80.0, 120.0, 20.0, 20.0,
# 30.0, 10.0, 10.0, 0.0]) # position, velocity, roll, pitch, (not yaw)
# P_m_ = np.diag([86.21, 86.21, 120.95,
# 6.94, 6.94, 11.04]) # only p and v
# P_m_[0, 3] = 6.45
# P_m_[3, 0] = 6.45
# P_m_[1, 4] = 6.45
# P_m_[4, 1] = 6.45
# P_m_[2, 5] = 10.95
# P_m_[5, 2] = 10.95
# R_m_ = np.diag([50.0, 60.0, 1.0])
Q_m_ = np.diag(
[
10.0,
10.0,
10.0,
3e-1,
3e-1,
3e-1,
#3e-1, 3e-1, 3e-2, 3e-2,
100.0,
100.0,
1e-3,
1e-3,
10.5,
10.5,
10.5
]
) # position, velocity, load_position, load_velocity, [roll, pitch, yaw]
P_m_ = np.diag([
10.0, 10.0, 10.0, 0.05, 0.05, 0.05
# 10.0, 10.0, 10.0,
# 0.05, 0.05, 0.05
]) # only p and v
# P_m_[0, 8] = 6.45
# P_m_[8, 0] = 6.45
# P_m_[1, 9] = 6.45
# P_m_[9, 1] = 6.45
# P_m_[2, 10] = 10.95
# P_m_[10, 2] = 10.95
R_m_ = np.diag([3.0, 3.0, 3.0, 1.0])
nx = self.model.x.size()[0]
self.nx = nx
nu = self.model.u.size()[0]
self.nu = nu
ny = nx + nu
n_params = self.model.p.size()[0] if isinstance(self.model.p,
ca.SX) else 0
acados_source_path = os.environ['ACADOS_SOURCE_DIR']
sys.path.insert(0, acados_source_path)
# create OCP
ocp = AcadosOcp()
ocp.acados_include_path = acados_source_path + '/include'
ocp.acados_lib_path = acados_source_path + '/lib'
ocp.model = self.model
ocp.dims.N = self.N
ocp.solver_options.tf = self.T
# initialize parameters
ocp.dims.np = n_params
ocp.parameter_values = np.zeros(n_params)
# cost type
ocp.cost.cost_type = 'LINEAR_LS'
ocp.cost.cost_type_e = 'LINEAR_LS'
ocp.cost.W = scipy.linalg.block_diag(Q_m_, R_m_)
ocp.cost.W_e = P_m_ # np.zeros((nx-3, nx-3))
ocp.cost.Vx = np.zeros((ny, nx))
ocp.cost.Vx[:nx, :nx] = np.eye(nx)
ocp.cost.Vu = np.zeros((ny, nu))
ocp.cost.Vu[-nu:, -nu:] = np.eye(nu)
ocp.cost.Vx_e = np.zeros((nx - 7, nx)) # only consider p and v
ocp.cost.Vx_e[:nx - 7, :nx - 7] = np.eye(nx - 7)
# initial reference trajectory_ref
x_ref = np.zeros(nx)
x_ref_e = np.zeros(nx - 7)
u_ref = np.zeros(nu)
u_ref[-1] = self.g
ocp.cost.yref = np.concatenate((x_ref, u_ref))
ocp.cost.yref_e = x_ref_e
# Set constraints
ocp.constraints.lbu = np.array([
self.constraints.roll_min, self.constraints.pitch_min,
self.constraints.yaw_min, self.constraints.thrust_min
])
ocp.constraints.ubu = np.array([
self.constraints.roll_max, self.constraints.pitch_max,
self.constraints.yaw_max, self.constraints.thrust_max
])
ocp.constraints.idxbu = np.array([0, 1, 2, 3])
# initial state
ocp.constraints.x0 = x_ref
# solver options
ocp.solver_options.qp_solver = 'FULL_CONDENSING_HPIPM'
ocp.solver_options.hessian_approx = 'GAUSS_NEWTON'
# explicit Runge-Kutta integrator
ocp.solver_options.integrator_type = 'ERK'
ocp.solver_options.print_level = 0
ocp.solver_options.nlp_solver_type = 'SQP' # 'SQP_RTI'
ocp.solver_options.levenberg_marquardt = 0.12 # 0.0
# compile acados ocp
json_file = os.path.join('./' + self.model.name + '_acados_ocp.json')
self.solver = AcadosOcpSolver(ocp, json_file=json_file)
if self.simulation_required:
self.integrator = AcadosSimSolver(ocp, json_file=json_file)
def generate(self, dae, name='tunempc', opts={}):
""" Create embeddable NLP solver
"""
from acados_template import AcadosModel, AcadosOcp, AcadosOcpSolver, AcadosSimSolver
# extract dimensions
nx = self.__nx
nu = self.__nu + self.__ns # treat slacks as pseudo-controls
# extract reference
ref = self.__ref
xref = np.squeeze(self.__ref[0][:nx], axis=1)
uref = np.squeeze(self.__ref[0][nx:nx + nu], axis=1)
# create acados model
model = AcadosModel()
model.x = ca.MX.sym('x', nx)
model.u = ca.MX.sym('u', nu)
model.p = []
model.name = name
# detect input type
n_in = dae.n_in()
if n_in == 2:
# xdot = f(x, u)
if 'integrator_type' in opts:
if opts['integrator_type'] == 'IRK':
xdot = ca.MX.sym('xdot', nx)
model.xdot = xdot
model.f_impl_expr = xdot - dae(model.x,
model.u[:self.__nu])
model.f_expl_expr = xdot
elif opts['integrator_type'] == 'ERK':
model.f_expl_expr = dae(model.x, model.u[:self.__nu])
else:
raise ValueError('Provide numerical integrator type!')
else:
xdot = ca.MX.sym('xdot', nx)
model.xdot = xdot
model.f_expl_expr = xdot
if n_in == 3:
# f(xdot, x, u) = 0
model.f_impl_expr = dae(xdot, model.x, model.u[:self.__nu])
elif n_in == 4:
# f(xdot, x, u, z) = 0
nz = dae.size1_in(3)
z = ca.MX.sym('z', nz)
model.z = z
model.f_impl_expr = dae(xdot, model.x, model.u[:self.__nu], z)
else:
raise ValueError(
'Invalid number of inputs for system dynamics function.')
if self.__gnl is not None:
model.con_h_expr = self.__gnl(model.x, model.u[:self.__nu],
model.u[self.__nu:])
if self.__type == 'economic':
model.cost_expr_ext_cost = self.__cost(model.x,
model.u[:self.__nu])
# create acados ocp
ocp = AcadosOcp()
ocp.model = model
ny = nx + nu
ny_e = nx
# set horizon length
ocp.dims.N = self.__N
# set cost module
if self.__type == 'economic':
# set cost function type to external (provided in model)
ocp.cost.cost_type = 'EXTERNAL'
else:
# set weighting matrices
if self.__type == 'tracking':
ocp.cost.W = self.__Href[0][0]
# set-up linear least squares cost
ocp.cost.cost_type = 'LINEAR_LS'
ocp.cost.W_e = np.zeros((nx, nx))
ocp.cost.Vx = np.zeros((ny, nx))
ocp.cost.Vx[:nx, :nx] = np.eye(nx)
Vu = np.zeros((ny, nu))
Vu[nx:, :] = np.eye(nu)
ocp.cost.Vu = Vu
ocp.cost.Vx_e = np.eye(nx)
ocp.cost.yref = np.squeeze(
ca.vertcat(xref,uref).full() - \
ct.mtimes(np.linalg.inv(ocp.cost.W),self.__qref[0][0].T).full(), # gradient term
axis = 1
)
ocp.cost.yref_e = np.zeros((ny_e, ))
if n_in == 4: # DAE flag
ocp.cost.Vz = np.zeros((ny, nz))
# initial condition
ocp.constraints.x0 = xref
# set inequality constraints
ocp.constraints.constr_type = 'BGH'
if self.__S['C'] is not None:
C = self.__S['C'][0][:, :nx]
D = self.__S['C'][0][:, nx:]
lg = -self.__S['e'][0] + ct.mtimes(C, xref).full() + ct.mtimes(
D, uref).full()
ug = 1e8 - self.__S['e'][0] + ct.mtimes(
C, xref).full() + ct.mtimes(D, uref).full()
ocp.constraints.lg = np.squeeze(lg, axis=1)
ocp.constraints.ug = np.squeeze(ug, axis=1)
ocp.constraints.C = C
ocp.constraints.D = D
if 'usc' in self.__vars:
if 'us' in self.__vars:
arg = [
self.__vars['x'], self.__vars['u'], self.__vars['us'],
self.__vars['usc']
]
else:
arg = [
self.__vars['x'], self.__vars['u'], self.__vars['usc']
]
Jsg = ca.Function(
'Jsg', [self.__vars['usc']],
[ca.jacobian(self.__h(*arg), self.__vars['usc'])])(0.0)
self.__Jsg = Jsg.full()[:-self.__nsc, :]
ocp.constraints.Jsg = self.__Jsg
ocp.cost.Zl = np.zeros((self.__nsc, ))
ocp.cost.Zu = np.zeros((self.__nsc, ))
ocp.cost.zl = np.squeeze(self.__scost.full(), axis=1)
ocp.cost.zu = np.squeeze(self.__scost.full(), axis=1)
# set nonlinear equality constraints
if self.__gnl is not None:
ocp.constraints.lh = np.zeros(self.__ns, )
ocp.constraints.uh = np.zeros(self.__ns, )
# terminal constraint:
x_term = self.__p_operator(model.x)
Jbx = ca.Function('Jbx', [model.x],
[ca.jacobian(x_term, model.x)])(0.0)
ocp.constraints.Jbx_e = Jbx.full()
ocp.constraints.lbx_e = np.squeeze(self.__p_operator(xref).full(),
axis=1)
ocp.constraints.ubx_e = np.squeeze(self.__p_operator(xref).full(),
axis=1)
for option in list(opts.keys()):
setattr(ocp.solver_options, option, opts[option])
self.__acados_ocp_solver = AcadosOcpSolver(ocp,
json_file='acados_ocp_' +
model.name + '.json')
self.__acados_integrator = AcadosSimSolver(ocp,
json_file='acados_ocp_' +
model.name + '.json')
# set initial guess
self.__set_acados_initial_guess()
return self.__acados_ocp_solver, self.__acados_integrator
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 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}')
def quadrotor_optimizer_setup(self, ):
Q_m_ = np.diag([
10,
10,
10,
0.3,
0.3,
0.3,
0.3,
0.05,
0.05,
0.05,
]) # position, q, v
P_m_ = np.diag([10, 10, 10, 0.05, 0.05, 0.05]) # only p and v
R_m_ = np.diag([5.0, 5.0, 5.0, 0.6])
nx = self.model.x.size()[0]
self.nx = nx
nu = self.model.u.size()[0]
self.nu = nu
ny = nx + nu
n_params = self.model.p.size()[0] if isinstance(self.model.p,
ca.SX) else 0
acados_source_path = os.environ['ACADOS_SOURCE_DIR']
sys.path.insert(0, acados_source_path)
# create OCP
ocp = AcadosOcp()
ocp.acados_include_path = acados_source_path + '/include'
ocp.acados_lib_path = acados_source_path + '/lib'
ocp.model = self.model
ocp.dims.N = self.N
ocp.solver_options.tf = self.T
# initialize parameters
ocp.dims.np = n_params
ocp.parameter_values = np.zeros(n_params)
# cost type
ocp.cost.cost_type = 'LINEAR_LS'
ocp.cost.cost_type_e = 'LINEAR_LS'
ocp.cost.W = scipy.linalg.block_diag(Q_m_, R_m_)
ocp.cost.W_e = P_m_
ocp.cost.Vx = np.zeros((ny, nx))
ocp.cost.Vx[:nx, :nx] = np.eye(nx)
ocp.cost.Vu = np.zeros((ny, nu))
ocp.cost.Vu[-nu:, -nu:] = np.eye(nu)
ocp.cost.Vx_e = np.zeros((nx - 4, nx))
# ocp.cost.Vx_e[:6, :6] = np.eye(6)
ocp.cost.Vx_e[:3, :3] = np.eye(3)
ocp.cost.Vx_e[-3:, -3:] = np.eye(3)
# initial reference trajectory_ref
x_ref = np.zeros(nx)
x_ref[3] = 1.0
x_ref_e = np.zeros(nx - 4)
u_ref = np.zeros(nu)
u_ref[-1] = self.g_
ocp.cost.yref = np.concatenate((x_ref, u_ref))
ocp.cost.yref_e = x_ref_e
# Set constraints
ocp.constraints.lbu = np.array([
self.constraints.roll_rate_min, self.constraints.pitch_rate_min,
self.constraints.yaw_rate_min, self.constraints.thrust_min
])
ocp.constraints.ubu = np.array([
self.constraints.roll_rate_max, self.constraints.pitch_rate_max,
self.constraints.yaw_rate_max, self.constraints.thrust_max
])
ocp.constraints.idxbu = np.array([0, 1, 2, 3])
# initial state
ocp.constraints.x0 = x_ref
# solver options
ocp.solver_options.qp_solver = 'FULL_CONDENSING_HPIPM'
ocp.solver_options.hessian_approx = 'GAUSS_NEWTON'
# explicit Runge-Kutta integrator
ocp.solver_options.integrator_type = 'ERK'
ocp.solver_options.print_level = 0
ocp.solver_options.nlp_solver_type = 'SQP' # 'SQP_RTI'
ocp.solver_options.nlp_solver_max_iter = 400
# compile acados ocp
## files are stored in .ros/
json_file = os.path.join('./' + self.model.name + '_acados_ocp.json')
self.solver = AcadosOcpSolver(ocp, json_file=json_file)
if self.simulation_required:
self.integrator = AcadosSimSolver(ocp, json_file=json_file)
def main(use_cython=True):
# (very) simple crane model
beta = 0.001
k = 0.9
a_max = 10
dt_max = 2.0
# states
p1 = SX.sym('p1')
v1 = SX.sym('v1')
p2 = SX.sym('p2')
v2 = SX.sym('v2')
x = vertcat(p1, v1, p2, v2)
# controls
a = SX.sym('a')
dt = SX.sym('dt')
u = vertcat(a, dt)
f_expl = dt * vertcat(v1, a, v2, -beta * v2 - k * (p2 - p1))
model = AcadosModel()
model.f_expl_expr = f_expl
model.x = x
model.u = u
model.name = 'crane_time_opt'
# create ocp object to formulate the OCP
x0 = np.array([2.0, 0.0, 2.0, 0.0])
xf = np.array([0.0, 0.0, 0.0, 0.0])
ocp = AcadosOcp()
ocp.model = model
# N - maximum number of bangs
N = 7
Tf = N
nx = model.x.size()[0]
nu = model.u.size()[0]
# set dimensions
ocp.dims.N = N
# set cost
ocp.cost.cost_type = 'EXTERNAL'
ocp.cost.cost_type_e = 'EXTERNAL'
ocp.model.cost_expr_ext_cost = dt
ocp.model.cost_expr_ext_cost_e = 0
ocp.constraints.lbu = np.array([-a_max, 0.0])
ocp.constraints.ubu = np.array([+a_max, dt_max])
ocp.constraints.idxbu = np.array([0, 1])
ocp.constraints.x0 = x0
ocp.constraints.lbx_e = xf
ocp.constraints.ubx_e = xf
ocp.constraints.idxbx_e = np.array([0, 1, 2, 3])
# set prediction horizon
ocp.solver_options.tf = Tf
# set options
ocp.solver_options.qp_solver = 'FULL_CONDENSING_QPOASES' #'PARTIAL_CONDENSING_HPIPM' # FULL_CONDENSING_QPOASES
ocp.solver_options.integrator_type = 'ERK'
ocp.solver_options.print_level = 3
ocp.solver_options.nlp_solver_type = 'SQP' # SQP_RTI, SQP
ocp.solver_options.globalization = 'MERIT_BACKTRACKING'
ocp.solver_options.nlp_solver_max_iter = 5000
ocp.solver_options.nlp_solver_tol_stat = 1e-6
ocp.solver_options.levenberg_marquardt = 0.1
ocp.solver_options.sim_method_num_steps = 15
ocp.solver_options.qp_solver_iter_max = 100
ocp.code_export_directory = 'c_generated_code'
ocp.solver_options.hessian_approx = 'EXACT'
ocp.solver_options.exact_hess_constr = 0
ocp.solver_options.exact_hess_dyn = 0
if use_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')
else: # ctypes
## Note: skip generate and build assuming this is done before (in cython run)
ocp_solver = AcadosOcpSolver(ocp,
json_file='acados_ocp.json',
build=False,
generate=False)
ocp_solver.reset()
for i, tau in enumerate(np.linspace(0, 1, N)):
ocp_solver.set(i, 'x', (1 - tau) * x0 + tau * xf)
ocp_solver.set(i, 'u', np.array([0.1, 0.5]))
simX = np.zeros((N + 1, nx))
simU = np.zeros((N, nu))
status = ocp_solver.solve()
if status != 0:
ocp_solver.print_statistics()
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")
dts = simU[:, 1]
print(
"acados solved OCP successfully, creating integrator to simulate the solution"
)
# simulate on finer grid
sim = AcadosSim()
# set model
sim.model = model
# set options
sim.solver_options.integrator_type = 'ERK'
sim.solver_options.num_stages = 4
sim.solver_options.num_steps = 3
sim.solver_options.T = 1.0 # dummy value
dt_approx = 0.0005
dts_fine = np.zeros((N, ))
Ns_fine = np.zeros((N, ), dtype='int16')
# compute number of simulation steps for bang interval + dt_fine
for i in range(N):
N_approx = max(int(dts[i] / dt_approx), 1)
dts_fine[i] = dts[i] / N_approx
Ns_fine[i] = int(round(dts[i] / dts_fine[i]))
N_fine = int(np.sum(Ns_fine))
simU_fine = np.zeros((N_fine, nu))
ts_fine = np.zeros((N_fine + 1, ))
simX_fine = np.zeros((N_fine + 1, nx))
simX_fine[0, :] = x0
acados_integrator = AcadosSimSolver(sim)
k = 0
for i in range(N):
u = simU[i, 0]
acados_integrator.set("u", np.hstack((u, np.ones(1, ))))
# set simulation time
acados_integrator.set("T", dts_fine[i])
for j in range(Ns_fine[i]):
acados_integrator.set("x", simX_fine[k, :])
status = acados_integrator.solve()
if status != 0:
raise Exception(f'acados returned status {status}.')
simX_fine[k + 1, :] = acados_integrator.get("x")
simU_fine[k, :] = u
ts_fine[k + 1] = ts_fine[k] + dts_fine[i]
k += 1
# visualize
if os.environ.get('ACADOS_ON_TRAVIS'):
plt.figure()
state_labels = ['p1', 'v1', 'p2', 'v2']
for i, l in enumerate(state_labels):
plt.subplot(5, 1, i + 1)
plt.plot(ts_fine, simX_fine[:, i], label='time optimal solution')
plt.grid(True)
plt.ylabel(l)
if i == 0:
plt.legend(loc=1)
plt.subplot(5, 1, 5)
plt.step(ts_fine,
np.hstack((simU_fine[:, 0], simU_fine[-1, 0])),
'-',
where='post')
plt.grid(True)
plt.ylabel('a')
plt.xlabel('t')
plt.show()
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")
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE # POSSIBILITY OF SUCH DAMAGE.; # import sys sys.path.insert(0, '../getting_started/common') from acados_template import AcadosOcp, AcadosOcpSolver from export_pendulum_ode_model import export_pendulum_ode_model import numpy as np import scipy.linalg from utils import plot_pendulum from casadi import SX # create ocp object to formulate the OCP ocp = AcadosOcp() # set model model = export_pendulum_ode_model() ocp.model = model Tf = 1.0 nx = model.x.size()[0] nu = model.u.size()[0] ny = nx + nu ny_e = nx N = 20 # set dimensions ocp.dims.N = N
def create_ocp_solver_separate_gains(model, Tf, dt, n, m,
max_abs_roll_rate, max_abs_pitch_rate,
max_abs_yaw_rate, x0, kqxy, kqz, kqrp, kqy,
kqxyv, kqzv, krt, krrpr, kryr):
# create ocp object to formulate the OCP
ocp = AcadosOcp()
ocp.model = model
nx = model.x.size()[0]
nu = model.u.size()[0]
ny = nx + nu
# ny_e = nx
N = int(Tf/dt)
ocp.dims.N = N
# set cost
Q = np.eye(n)
Q[0,0] = kqxy
Q[1,1] = kqxy
Q[2,2] = kqz
Q[3,3] = kqrp
Q[4,4] = kqrp
Q[5,5] = kqy
Q[6,6] = kqxyv
Q[7,7] = kqxyv
Q[8,8] = kqzv
R = np.eye(m)
R[0,0] = krrpr
R[1,1] = krrpr
R[2,2] = kryr
R[3,3] = krt
ocp.cost.W_e = Q
ocp.cost.W = la.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[nx:,:] = np.eye(nu)
ocp.cost.Vu = Vu
ocp.cost.Vx_e = np.eye(nx)
# solver options
# ocp.solver_options.qp_solver = 'PARTIAL_CONDENSING_HPIPM' # FULL_CONDENSING_QPOASES
ocp.solver_options.qp_solver = 'FULL_CONDENSING_QPOASES'
ocp.solver_options.hessian_approx = 'GAUSS_NEWTON'
ocp.solver_options.integrator_type = 'ERK'
ocp.solver_options.print_level = 0
ocp.solver_options.nlp_solver_type = 'SQP_RTI' # SQP_RTI, SQP
ocp.solver_options.tf = Tf
# constraints on control
ocp.constraints.lbu = np.array([-max_abs_roll_rate, -max_abs_pitch_rate, -max_abs_pitch_rate,0])
ocp.constraints.ubu = np.array([max_abs_roll_rate, max_abs_pitch_rate, max_abs_pitch_rate,1])
ocp.constraints.idxbu = np.array([0,1,2,3])
ocp.constraints.x0 = x0
ocp.cost.yref = np.zeros((n+m,))
ocp.cost.yref_e = np.zeros((n,))
ocp_solver = AcadosOcpSolver(ocp, json_file = 'acados_ocp.json')
return ocp_solver
def run_closed_loop_experiment(FORMULATION):
# create ocp object to formulate the OCP
ocp = AcadosOcp()
# set model
model = export_pendulum_ode_model()
ocp.model = model
Tf = 1.0
nx = model.x.size()[0]
nu = model.u.size()[0]
ny = nx + nu
ny_e = nx
N = 20
# set dimensions
# NOTE: all dimensions but N ar detected
ocp.dims.N = N
# set cost module
ocp.cost.cost_type = 'LINEAR_LS'
ocp.cost.cost_type_e = 'LINEAR_LS'
Q = 2 * np.diag([1e3, 1e3, 1e-2, 1e-2])
R = 2 * np.diag([1e-2])
ocp.cost.W = scipy.linalg.block_diag(Q, R)
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.W_e = Q
ocp.cost.yref = np.zeros((ny, ))
ocp.cost.yref_e = np.zeros((ny_e, ))
ocp.cost.zl = 2000 * np.ones((1, ))
ocp.cost.Zl = 1 * np.ones((1, ))
ocp.cost.zu = 2000 * np.ones((1, ))
ocp.cost.Zu = 1 * np.ones((1, ))
# set constraints
Fmax = 80
vmax = 5
x0 = np.array([0.0, np.pi, 0.0, 0.0])
ocp.constraints.x0 = x0
# bound on u
ocp.constraints.lbu = np.array([-Fmax])
ocp.constraints.ubu = np.array([+Fmax])
ocp.constraints.idxbu = np.array([0])
if FORMULATION == 0:
# soft bound on x
ocp.constraints.lbx = np.array([-vmax])
ocp.constraints.ubx = np.array([+vmax])
ocp.constraints.idxbx = np.array([2]) # v is x[2]
# indices of slacked constraints within bx
ocp.constraints.idxsbx = np.array([0])
elif FORMULATION == 1:
# soft bound on x, using constraint h
v1 = ocp.model.x[2]
ocp.model.con_h_expr = v1
ocp.constraints.lh = np.array([-vmax])
ocp.constraints.uh = np.array([+vmax])
# indices of slacked constraints within h
ocp.constraints.idxsh = np.array([0])
# set options
ocp.solver_options.qp_solver = 'PARTIAL_CONDENSING_HPIPM'
ocp.solver_options.hessian_approx = 'GAUSS_NEWTON'
ocp.solver_options.integrator_type = 'ERK'
ocp.solver_options.tf = Tf
ocp.solver_options.nlp_solver_type = 'SQP'
ocp.solver_options.tol = 1e-1 * tol
json_filename = 'pendulum_soft_constraints.json'
acados_ocp_solver = AcadosOcpSolver(ocp, json_file=json_filename)
acados_integrator = AcadosSimSolver(ocp, json_file=json_filename)
# closed loop
Nsim = 20
simX = np.ndarray((Nsim + 1, nx))
simU = np.ndarray((Nsim, nu))
xcurrent = x0
for i in range(Nsim):
simX[i, :] = xcurrent
# solve ocp
acados_ocp_solver.set(0, "lbx", xcurrent)
acados_ocp_solver.set(0, "ubx", xcurrent)
status = acados_ocp_solver.solve()
if status != 0:
raise Exception(
'acados acados_ocp_solver returned status {}. Exiting.'.format(
status))
simU[i, :] = acados_ocp_solver.get(0, "u")
# simulate system
acados_integrator.set("x", xcurrent)
acados_integrator.set("u", simU[i, :])
status = acados_integrator.solve()
if status != 0:
raise Exception(
'acados integrator returned status {}. Exiting.'.format(
status))
# update state
xcurrent = acados_integrator.get("x")
simX[Nsim, :] = xcurrent
# get slack values at stage 1
sl = acados_ocp_solver.get(1, "sl")
su = acados_ocp_solver.get(1, "su")
print("sl", sl, "su", su)
# plot results
# plot_pendulum(np.linspace(0, Tf, N+1), Fmax, simU, simX, latexify=False)
# store results
np.savetxt('test_results/simX_soft_formulation_' + str(FORMULATION), simX)
np.savetxt('test_results/simU_soft_formulation_' + str(FORMULATION), simU)
print("soft constraint example: ran formulation", FORMULATION,
"successfully.")
def main(cost_type='NONLINEAR_LS', hessian_approximation='EXACT', ext_cost_use_num_hess=0,
integrator_type='ERK'):
print(f"using: cost_type {cost_type}, integrator_type {integrator_type}")
# create ocp object to formulate the OCP
ocp = AcadosOcp()
# set model
model = export_pendulum_ode_model()
ocp.model = model
Tf = 1.0
nx = model.x.size()[0]
nu = model.u.size()[0]
ny = nx + nu
ny_e = nx
N = 20
ocp.dims.N = N
# set cost
Q = 2*np.diag([1e3, 1e3, 1e-2, 1e-2])
R = 2*np.diag([1e-2])
x = ocp.model.x
u = ocp.model.u
cost_W = scipy.linalg.block_diag(Q, R)
if cost_type == 'LS':
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)
elif cost_type == 'NONLINEAR_LS':
ocp.cost.cost_type = 'NONLINEAR_LS'
ocp.cost.cost_type_e = 'NONLINEAR_LS'
ocp.model.cost_y_expr = vertcat(x, u)
ocp.model.cost_y_expr_e = x
elif cost_type == 'EXTERNAL':
ocp.cost.cost_type = 'EXTERNAL'
ocp.cost.cost_type_e = 'EXTERNAL'
ocp.model.cost_expr_ext_cost = vertcat(x, u).T @ cost_W @ vertcat(x, u)
ocp.model.cost_expr_ext_cost_e = x.T @ Q @ x
else:
raise Exception('Unknown cost_type. Possible values are \'LS\' and \'NONLINEAR_LS\'.')
if cost_type in ['LS', 'NONLINEAR_LS']:
ocp.cost.yref = np.zeros((ny, ))
ocp.cost.yref_e = np.zeros((ny_e, ))
ocp.cost.W_e = Q
ocp.cost.W = cost_W
# set constraints
Fmax = 80
ocp.constraints.constr_type = 'BGH'
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 = hessian_approximation
ocp.solver_options.regularize_method = 'CONVEXIFY'
ocp.solver_options.integrator_type = integrator_type
if ocp.solver_options.integrator_type == 'GNSF':
import json
with open('../getting_started/common/' + model.name + '_gnsf_functions.json', 'r') as f:
gnsf_dict = json.load(f)
ocp.gnsf_model = gnsf_dict
ocp.solver_options.qp_solver_cond_N = 5
# set prediction horizon
ocp.solver_options.tf = Tf
ocp.solver_options.nlp_solver_type = 'SQP' # SQP_RTI
ocp.solver_options.ext_cost_num_hess = ext_cost_use_num_hess
# create solver
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')
# time create
Ncreate = 1
create_time = []
for i in range(Ncreate):
t0 = time.time()
# ocp_solver = AcadosOcpSolver(ocp, json_file = 'acados_ocp.json', build=False, generate=False)
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)
create_time.append( time.time() - t0)
print(f"create_time: min {np.min(create_time)*1e3:.4f} ms mean {np.mean(create_time)*1e3:.4f} ms max {np.max(create_time)*1e3:.4f} ms over {Ncreate} executions")
# create_time: min 0.2189 ms mean 0.2586 ms max 0.6881 ms over 10000 executions
# RESET
Nreset = 3
reset_time = []
for i in range(Nreset):
# set NaNs as input to test reset() -> NOT RECOMMENDED!!!
# ocp_solver.options_set('print_level', 2)
for i in range(N):
ocp_solver.set(i, 'x', np.NaN * np.ones((nx,)))
ocp_solver.set(i, 'u', np.NaN * np.ones((nu,)))
status = ocp_solver.solve()
ocp_solver.print_statistics() # encapsulates: stat = ocp_solver.get_stats("statistics")
if status == 0:
raise Exception(f'acados returned status {status}, although NaNs were given.')
else:
print(f'acados returned status {status}, which is expected, since NaNs were given.')
t0 = time.time()
ocp_solver.reset()
reset_time.append( time.time() - t0)
print(f"reset_time: min {np.min(reset_time)*1e3:.4f} ms mean {np.mean(reset_time)*1e3:.4f} ms max {np.max(reset_time)*1e3:.4f} ms over {Nreset} executions")
# OLD: without HPIPM mem reset:
# reset_time: min 0.0019 ms mean 0.0022 ms max 0.0250 ms over 10000 executions
# NEW: with HPIPM mem reset:
# reset_time: min 0.0036 ms mean 0.0047 ms max 0.0906 ms over 10000 executions
for i in range(N):
ocp_solver.set(i, 'x', x0)
if cost_type == 'EXTERNAL':
# NOTE: hessian is wrt [u,x]
if ext_cost_use_num_hess:
for i in range(N):
ocp_solver.cost_set(i, "ext_cost_num_hess", np.diag([0.04, 4000, 4000, 0.04, 0.04, ]))
ocp_solver.cost_set(N, "ext_cost_num_hess", np.diag([4000, 4000, 0.04, 0.04, ]))
simX = np.ndarray((N+1, nx))
simU = np.ndarray((N, nu))
status = ocp_solver.solve()
ocp_solver.print_statistics()
if status != 0:
raise Exception(f'acados returned status {status} for cost_type {cost_type}\n'
f'integrator_type = {integrator_type}.')
# 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")
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN # CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) # ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE # POSSIBILITY OF SUCH DAMAGE.; # from acados_template import AcadosOcp, AcadosOcpSolver, AcadosSimSolver from export_quad_ode_model import export_quad_ode_model from utils import * import numpy as nmp import scipy.linalg COST_MODULE = 'NLS' USE_QUAT_SLACK = 1 # create ocp object to formulate the OCP ocp = AcadosOcp() # set model model = export_quad_ode_model() ocp.model = model # model parameters rho = 1.225 A = 0.1 Cl = 0.125 Cd = 0.075 m = 10.0 g = 9.81 J3 = 0.25 J2 = J3 * 4 J1 = J3 * 4
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
import sys sys.path.insert(0, '../common') from acados_template import AcadosOcp, AcadosOcpSolver from export_pendulum_ode_model import export_pendulum_ode_model import numpy as np import scipy.linalg from utils import plot_pendulum from casadi import vertcat COST_MODULE = 'EXTERNAL' # 'LS', 'EXTERNAL' HESSIAN_APPROXIMATION = 'EXACT' # 'GAUSS_NEWTON EXTERNAL_COST_USE_NUM_HESS = 1 # create ocp object to formulate the OCP ocp = AcadosOcp() # set model model = export_pendulum_ode_model() ocp.model = model Tf = 1.0 nx = model.x.size()[0] nu = model.u.size()[0] ny = nx + nu ny_e = nx N = 20 # set dimensions ocp.dims.nx = nx ocp.dims.ny = ny
def __init__(self, quad, t_horizon=1, n_nodes=20,
q_cost=None, r_cost=None, q_mask=None,
B_x=None, gp_regressors=None, rdrv_d_mat=None,
model_name="quad_3d_acados_mpc", solver_options=None):
"""
:param quad: quadrotor object
:type quad: Quadrotor3D
:param t_horizon: time horizon for MPC optimization
:param n_nodes: number of optimization nodes until time horizon
:param q_cost: diagonal of Q matrix for LQR cost of MPC cost function. Must be a numpy array of length 12.
:param r_cost: diagonal of R matrix for LQR cost of MPC cost function. Must be a numpy array of length 4.
:param B_x: dictionary of matrices that maps the outputs of the gp regressors to the state space.
:param gp_regressors: Gaussian Process ensemble for correcting the nominal model
:type gp_regressors: GPEnsemble
:param q_mask: Optional boolean mask that determines which variables from the state compute towards the cost
function. In case no argument is passed, all variables are weighted.
:param solver_options: Optional set of extra options dictionary for solvers.
:param rdrv_d_mat: 3x3 matrix that corrects the drag with a linear model according to Faessler et al. 2018. None
if not used
"""
# Weighted squared error loss function q = (p_xyz, a_xyz, v_xyz, r_xyz), r = (u1, u2, u3, u4)
if q_cost is None:
q_cost = np.array([10, 10, 10, 0.1, 0.1, 0.1, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05])
if r_cost is None:
r_cost = np.array([0.1, 0.1, 0.1, 0.1])
self.T = t_horizon # Time horizon
self.N = n_nodes # number of control nodes within horizon
self.quad = quad
self.max_u = quad.max_input_value
self.min_u = quad.min_input_value
# Declare model variables
self.p = cs.MX.sym('p', 3) # position
self.q = cs.MX.sym('a', 4) # angle quaternion (wxyz)
self.v = cs.MX.sym('v', 3) # velocity
self.r = cs.MX.sym('r', 3) # angle rate
# Full state vector (13-dimensional)
self.x = cs.vertcat(self.p, self.q, self.v, self.r)
self.state_dim = 13
# Control input vector
u1 = cs.MX.sym('u1')
u2 = cs.MX.sym('u2')
u3 = cs.MX.sym('u3')
u4 = cs.MX.sym('u4')
self.u = cs.vertcat(u1, u2, u3, u4)
# Nominal model equations symbolic function (no GP)
self.quad_xdot_nominal = self.quad_dynamics(rdrv_d_mat)
# Linearized model dynamics symbolic function
self.quad_xdot_jac = self.linearized_quad_dynamics()
# Initialize objective function, 0 target state and integration equations
self.L = None
self.target = None
# Check if GP ensemble has an homogeneous feature space (if actual Ensemble)
if gp_regressors is not None and gp_regressors.homogeneous:
self.gp_reg_ensemble = gp_regressors
self.B_x = [B_x[dim] for dim in gp_regressors.dim_idx]
self.B_x = np.squeeze(np.stack(self.B_x, axis=1))
self.B_x = self.B_x[:, np.newaxis] if len(self.B_x.shape) == 1 else self.B_x
self.B_z = gp_regressors.B_z
elif gp_regressors and gp_regressors.no_ensemble:
# If not homogeneous, we have to treat each z feature vector independently
self.gp_reg_ensemble = gp_regressors
self.B_x = [B_x[dim] for dim in gp_regressors.dim_idx]
self.B_x = np.squeeze(np.stack(self.B_x, axis=1))
self.B_x = self.B_x[:, np.newaxis] if len(self.B_x.shape) == 1 else self.B_x
self.B_z = gp_regressors.B_z
else:
self.gp_reg_ensemble = None
# Declare model variables for GP prediction (only used in real quadrotor flight with EKF estimator).
# Will be used as initial state for GP prediction as Acados parameters.
self.gp_p = cs.MX.sym('gp_p', 3)
self.gp_q = cs.MX.sym('gp_a', 4)
self.gp_v = cs.MX.sym('gp_v', 3)
self.gp_r = cs.MX.sym('gp_r', 3)
self.gp_x = cs.vertcat(self.gp_p, self.gp_q, self.gp_v, self.gp_r)
# The trigger variable is used to tell ACADOS to use the additional GP state estimate in the first optimization
# node and the regular integrated state in the rest
self.trigger_var = cs.MX.sym('trigger', 1)
# Build full model. Will have 13 variables. self.dyn_x contains the symbolic variable that
# should be used to evaluate the dynamics function. It corresponds to self.x if there are no GP's, or
# self.x_with_gp otherwise
acados_models, nominal_with_gp = self.acados_setup_model(
self.quad_xdot_nominal(x=self.x, u=self.u)['x_dot'], model_name)
# Convert dynamics variables to functions of the state and input vectors
self.quad_xdot = {}
for dyn_model_idx in nominal_with_gp.keys():
dyn = nominal_with_gp[dyn_model_idx]
self.quad_xdot[dyn_model_idx] = cs.Function('x_dot', [self.x, self.u], [dyn], ['x', 'u'], ['x_dot'])
# ### Setup and compile Acados OCP solvers ### #
self.acados_ocp_solver = {}
# Check if GP's have been loaded
self.with_gp = self.gp_reg_ensemble is not None
# Add one more weight to the rotation (use quaternion norm weighting in acados)
q_diagonal = np.concatenate((q_cost[:3], np.mean(q_cost[3:6])[np.newaxis], q_cost[3:]))
if q_mask is not None:
q_mask = np.concatenate((q_mask[:3], np.zeros(1), q_mask[3:]))
q_diagonal *= q_mask
# Ensure current working directory is current folder
os.chdir(os.path.dirname(os.path.realpath(__file__)))
self.acados_models_dir = '../../acados_models'
safe_mkdir_recursive(os.path.join(os.getcwd(), self.acados_models_dir))
for key, key_model in zip(acados_models.keys(), acados_models.values()):
nx = key_model.x.size()[0]
nu = key_model.u.size()[0]
ny = nx + nu
n_param = key_model.p.size()[0] if isinstance(key_model.p, cs.MX) else 0
acados_source_path = os.environ['ACADOS_SOURCE_DIR']
sys.path.insert(0, '../common')
# Create OCP object to formulate the optimization
ocp = AcadosOcp()
ocp.acados_include_path = acados_source_path + '/include'
ocp.acados_lib_path = acados_source_path + '/lib'
ocp.model = key_model
ocp.dims.N = self.N
ocp.solver_options.tf = t_horizon
# Initialize parameters
ocp.dims.np = n_param
ocp.parameter_values = np.zeros(n_param)
ocp.cost.cost_type = 'LINEAR_LS'
ocp.cost.cost_type_e = 'LINEAR_LS'
ocp.cost.W = np.diag(np.concatenate((q_diagonal, r_cost)))
ocp.cost.W_e = np.diag(q_diagonal)
terminal_cost = 0 if solver_options is None or not solver_options["terminal_cost"] else 1
ocp.cost.W_e *= terminal_cost
ocp.cost.Vx = np.zeros((ny, nx))
ocp.cost.Vx[:nx, :nx] = np.eye(nx)
ocp.cost.Vu = np.zeros((ny, nu))
ocp.cost.Vu[-4:, -4:] = np.eye(nu)
ocp.cost.Vx_e = np.eye(nx)
# Initial reference trajectory (will be overwritten)
x_ref = np.zeros(nx)
ocp.cost.yref = np.concatenate((x_ref, np.array([0.0, 0.0, 0.0, 0.0])))
ocp.cost.yref_e = x_ref
# Initial state (will be overwritten)
ocp.constraints.x0 = x_ref
# Set constraints
ocp.constraints.lbu = np.array([self.min_u] * 4)
ocp.constraints.ubu = np.array([self.max_u] * 4)
ocp.constraints.idxbu = np.array([0, 1, 2, 3])
# Solver options
ocp.solver_options.qp_solver = 'FULL_CONDENSING_HPIPM'
ocp.solver_options.hessian_approx = 'GAUSS_NEWTON'
ocp.solver_options.integrator_type = 'ERK'
ocp.solver_options.print_level = 0
ocp.solver_options.nlp_solver_type = 'SQP_RTI' if solver_options is None else solver_options["solver_type"]
# Compile acados OCP solver if necessary
json_file = os.path.join(self.acados_models_dir, key_model.name + '_acados_ocp.json')
self.acados_ocp_solver[key] = AcadosOcpSolver(ocp, json_file=json_file)
