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test_global_stochastic_collocation.py
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test_global_stochastic_collocation.py
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import os
from sys import platform
import numpy as np
from casadi import DM, vertcat
from bioptim import Solver, SocpType
def test_arm_reaching_torque_driven_collocations():
from bioptim.examples.stochastic_optimal_control import arm_reaching_torque_driven_collocations as ocp_module
if platform != "linux":
return
final_time = 0.4
n_shooting = 4
hand_final_position = np.array([9.359873986980460e-12, 0.527332023564034])
dt = 0.05
motor_noise_std = 0.05
wPq_std = 3e-4
wPqdot_std = 0.0024
motor_noise_magnitude = DM(np.array([motor_noise_std**2 / dt, motor_noise_std**2 / dt]))
wPq_magnitude = DM(np.array([wPq_std**2 / dt, wPq_std**2 / dt]))
wPqdot_magnitude = DM(np.array([wPqdot_std**2 / dt, wPqdot_std**2 / dt]))
sensory_noise_magnitude = vertcat(wPq_magnitude, wPqdot_magnitude)
bioptim_folder = os.path.dirname(ocp_module.__file__)
ocp = ocp_module.prepare_socp(
biorbd_model_path=bioptim_folder + "/models/LeuvenArmModel.bioMod",
final_time=final_time,
n_shooting=n_shooting,
polynomial_degree=3,
hand_final_position=hand_final_position,
motor_noise_magnitude=motor_noise_magnitude,
sensory_noise_magnitude=sensory_noise_magnitude,
)
# Solver parameters
solver = Solver.IPOPT(show_online_optim=False)
solver.set_nlp_scaling_method("none")
sol = ocp.solve(solver)
# Check objective function value
f = np.array(sol.cost)
np.testing.assert_equal(f.shape, (1, 1))
np.testing.assert_almost_equal(f[0, 0], 426.8457209111154)
# Check constraints
g = np.array(sol.constraints)
np.testing.assert_equal(g.shape, (442, 1))
# Check some of the results
states, controls, stochastic_variables = (
sol.states,
sol.controls,
sol.stochastic_variables,
)
q, qdot = states["q"], states["qdot"]
tau = controls["tau"]
k, ref, m, cov = (
stochastic_variables["k"],
stochastic_variables["ref"],
stochastic_variables["m"],
stochastic_variables["cov"],
)
# initial and final position
np.testing.assert_almost_equal(q[:, 0], np.array([0.34906585, 2.24586773]))
np.testing.assert_almost_equal(q[:, -1], np.array([0.9256103, 1.29037205]))
np.testing.assert_almost_equal(qdot[:, 0], np.array([0, 0]))
np.testing.assert_almost_equal(qdot[:, -1], np.array([0, 0]))
np.testing.assert_almost_equal(tau[:, 0], np.array([1.72235954, -0.90041542]))
np.testing.assert_almost_equal(tau[:, -2], np.array([-1.64870266, 1.08550928]))
np.testing.assert_almost_equal(ref[:, 0], np.array([2.81907786e-02, 2.84412560e-01, 0, 0]))
np.testing.assert_almost_equal(
m[:, 0],
np.array(
[
1.00000000e00,
1.10362271e-24,
2.22954931e-28,
-1.20515105e-27,
-4.82198156e-25,
1.00000000e00,
-8.11748571e-29,
-1.83751963e-28,
4.94557578e-25,
-1.78093812e-25,
1.00000000e00,
-2.66499977e-27,
-3.86066682e-25,
6.67095096e-26,
-1.34508637e-27,
1.00000000e00,
2.73268581e-01,
8.12760759e-04,
-1.13937433e-01,
-4.80582813e-02,
-6.82535380e-04,
2.92927116e-01,
-4.48357025e-03,
2.46779124e-01,
2.11544998e-02,
-6.30362089e-03,
1.96229280e-01,
-1.11381918e-01,
8.36502545e-04,
1.10428331e-02,
1.30538280e-02,
4.38185419e-02,
4.41297671e-01,
-2.25568192e-03,
-1.30256542e-01,
-1.25440894e-01,
-2.53765683e-04,
4.53128027e-01,
-6.27183235e-03,
2.90336583e-01,
2.03549193e-02,
-4.35582809e-03,
3.68201657e-01,
-1.54792782e-01,
5.56316902e-04,
1.36916324e-02,
1.88617201e-02,
1.49541324e-01,
2.77664470e-01,
-3.70932151e-04,
-2.19982988e-02,
-3.92648307e-02,
-2.51133315e-05,
2.78132403e-01,
-2.01389570e-03,
5.55215545e-02,
3.07424160e-03,
-2.45969266e-04,
2.67004519e-01,
-3.40457592e-02,
3.07722398e-05,
2.73583597e-03,
4.29990529e-03,
2.18202901e-01,
]
),
decimal=2,
)
np.testing.assert_almost_equal(
cov[:, -2],
np.array(
[
-0.57472415,
-0.58086399,
-0.65152237,
-0.20929523,
-0.5808627,
-0.54536228,
-0.42680683,
-0.36921097,
-0.65154088,
-0.42679628,
-0.41733866,
-0.04060819,
-0.20928018,
-0.36921833,
-0.04062543,
-0.37958588,
]
),
decimal=2,
)
def test_obstacle_avoidance_direct_collocation():
from bioptim.examples.stochastic_optimal_control import obstacle_avoidance_direct_collocation as ocp_module
# if platform != "linux":
# return
polynomial_degree = 3
n_shooting = 10
q_init = np.zeros((2, (polynomial_degree + 2) * n_shooting + 1))
zq_init = ocp_module.initialize_circle((polynomial_degree + 1) * n_shooting + 1)
for i in range(n_shooting + 1):
j = i * (polynomial_degree + 1)
k = i * (polynomial_degree + 2)
q_init[:, k] = zq_init[:, j]
q_init[:, k + 1 : k + 1 + (polynomial_degree + 1)] = zq_init[:, j : j + (polynomial_degree + 1)]
ocp = ocp_module.prepare_socp(
final_time=4,
n_shooting=n_shooting,
polynomial_degree=polynomial_degree,
motor_noise_magnitude=np.array([1, 1]),
q_init=q_init,
is_sotchastic=True,
is_robustified=True,
socp_type=SocpType.COLLOCATION(polynomial_degree=polynomial_degree, method="legendre"),
)
# Solver parameters
solver = Solver.IPOPT(show_online_optim=False)
solver.set_maximum_iterations(4)
sol = ocp.solve(solver)
# Check objective function value
f = np.array(sol.cost)
np.testing.assert_equal(f.shape, (1, 1))
np.testing.assert_almost_equal(f[0, 0], 4.099146411209181)
# Check constraints
g = np.array(sol.constraints)
np.testing.assert_equal(g.shape, (1043, 1))
# Check some of the results
states, controls, stochastic_variables = (
sol.states,
sol.controls,
sol.stochastic_variables,
)
q, qdot = states["q"], states["qdot"]
u = controls["u"]
m, cov = (
stochastic_variables["m"],
stochastic_variables["cov"],
)
# initial and final position
np.testing.assert_almost_equal(q[:, 0], np.array([0.0, 2.97814416e00]))
np.testing.assert_almost_equal(q[:, -1], np.array([0.0, 2.97814416e00]))
np.testing.assert_almost_equal(qdot[:, 0], np.array([4.28153262, 0.36568711]))
np.testing.assert_almost_equal(qdot[:, -1], np.array([4.28153262, 0.36568711]))
np.testing.assert_almost_equal(u[:, 0], np.array([2.62449641, 1.42518093]))
np.testing.assert_almost_equal(u[:, -2], np.array([0.98869976, 2.83323732]))
np.testing.assert_almost_equal(
m[:, 0],
np.array(
[
1.00000000e+00, 4.18671255e-23, 4.28371222e-21, -2.09918267e-19,
3.44229928e-22, 1.00000000e+00, -4.66804386e-20, -5.14324329e-20,
-2.06675909e-23, -1.61247050e-22, 1.00000000e+00, -7.04413401e-20,
-3.27139223e-22, -2.61268483e-22, 4.41399057e-20, 1.00000000e+00,
2.11891384e-01, -1.58680379e-02, -3.07585749e-01, -9.08757981e-02,
-1.72161795e-02, 1.95250052e-01, -9.69940564e-02, -3.86911301e-01,
2.81495095e-02, 4.94627743e-03, -1.06536334e-02, -3.39095322e-03,
6.01146660e-03, 4.34835191e-02, -2.32542690e-03, -7.95425413e-03,
4.08499325e-01, -9.64710094e-03, -4.26676607e-01, -9.74461605e-02,
-9.88390650e-03, 4.05552654e-01, -1.00910193e-01, -4.92316087e-01,
4.39486929e-02, 8.74347038e-03, 4.72289379e-02, 3.98745524e-02,
9.07610650e-03, 5.27435499e-02, 4.32026417e-02, 8.63948277e-02,
2.77396392e-01, 3.38212145e-05, -9.93589312e-02, -1.01929042e-02,
-8.60843770e-06, 2.77166036e-01, -9.77442621e-03, -1.02836238e-01,
9.71202833e-03, 1.00344034e-03, 1.90048454e-01, 2.17086631e-02,
1.03402088e-03, 9.94432755e-03, 2.14855478e-02, 2.02784050e-01,
]
),
decimal=6,
)
np.testing.assert_almost_equal(
cov[:, -2],
np.array(
[
0.00373282, 0.00024041, 0.00319094, -0.00109769, 0.00024041,
0.00075171, -0.00102995, 0.00112714, 0.00319094, -0.00102995,
0.03139494, -0.01650263, -0.00109769, 0.00112714, -0.01650263,
0.01354738,
]
),
decimal=6,
)