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benchmark_lqr_cloth.py
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benchmark_lqr_cloth.py
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'''
Author: Edoardo Caldarelli
Affiliation: Institut de Robòtica i Informàtica Industrial, CSIC-UPC
email: ecaldarelli@iri.upc.edu
January 2024
'''
import pathlib
import random
import matplotlib; matplotlib.use("TkAgg")
import control
import pickle
from sklearn.model_selection import GridSearchCV
from regressors import ThreeDimensionalKernel, KoopmanNystromRegressor, KoopmanRegressor, KoopmanSplineRegressor
from dynamical_systems import *
def validate_dyn_sys(regressor: KoopmanRegressor, true_trajectory, test_controls):
n_samples_traj = true_trajectory.shape[1]
A = regressor.A
B = regressor.B
C = regressor.C
xcurr_true = true_trajectory[:, 0].reshape([-1, 1])
phi_xcurr = regressor.lift(xcurr_true)
xcurr = phi_xcurr
lifted_traj = xcurr
simulated_traj = C @ xcurr
for i in range(0, n_samples_traj - 1):
xcurr = A @ xcurr + B @ test_controls[:, i].reshape([-1, 1])
simulated_traj = np.hstack((simulated_traj, C @ xcurr))
lifted_traj = np.hstack((lifted_traj, xcurr))
# Compute RMSE
rmse = np.sqrt(np.mean(np.square(true_trajectory - simulated_traj)))
return rmse
def learn_hyperparams(X, Y, kapprox):
ls = np.power(10.0, np.arange(0, 3.5))
if kapprox == 'nystrom':
cv_regr = KoopmanNystromRegressor(n_inputs)
elif kapprox == 'splines':
cv_regr = KoopmanSplineRegressor(n_inputs)
if kapprox == 'nystrom':
kernel_candidates = []
max_exp_lth = 3
for i in range(0, max_exp_lth):
for j in range(0, max_exp_lth):
for k in range(0, max_exp_lth):
kernel_candidates.append(ThreeDimensionalKernel(10**i, 10**j, 10**k, Y.shape[0]))
clf = GridSearchCV(cv_regr, {'kernel': kernel_candidates,
'gamma': np.power(10.0, np.arange(-7, -4)),
'm': [500]},
scoring='neg_root_mean_squared_error',
verbose=3,
n_jobs=-1)
else:
clf = GridSearchCV(cv_regr, {
'gamma': np.power(10.0, np.arange(-7, -4)),
'm': [500]},
scoring='neg_root_mean_squared_error',
verbose=3,
n_jobs=-1)
cv_result = clf.fit(X.T, Y.T)
return clf
def lqr_control(num_steps, reference, initial_state, regressor, K):
A = regressor.A
B = regressor.B
C = regressor.C
phi_new = regressor.lift(initial_state)
phi_reference = regressor.lift(reference)
visited_states = np.empty((n_states, 0))
visited_states = np.hstack((initial_state, visited_states))
u_s = np.empty((n_inputs, 0))
u_s = np.hstack((u_s, initial_state[[168, 169, 170, 189, 190, 191], :]))
for i in range(0, num_steps):
u_op = K @ (phi_reference - phi_new)
u_s = np.hstack((u_s, u_s[:, -1].reshape([-1, 1]) + u_op))
new_state = C @ phi_new
visited_states = np.hstack((visited_states, new_state))
phi_new = A @ phi_new + B @ u_op
n_nodes = int(n_states / 3)
x_s = np.zeros((n_nodes, visited_states.shape[1]))
y_s = np.zeros((n_nodes, visited_states.shape[1]))
z_s = np.zeros((n_nodes, visited_states.shape[1]))
for j in range(visited_states.shape[1]):
kx = 0
ky = 0
kz = 0
for i in range(0, n_states):
if i % 3 == 0:
x_s[kx, j] = visited_states[i, j]
kx += 1
if i % 3 == 1:
y_s[ky, j] = visited_states[i, j]
ky += 1
if i % 3 == 2:
z_s[kz, j] = visited_states[i, j]
kz += 1
final_us = np.vstack((u_s[0, :], u_s[3, :], u_s[1, :], u_s[4, :], u_s[2, :], u_s[5, :]))
return x_s, y_s, z_s, final_us
def update_scatter(i, traj, ax):
ax.clear()
ax.view_init(elev=12, azim=-6)
# Setting the axes properties
ax.set(xlim3d=(-1, 1), xlabel='X')
ax.set(ylim3d=(0.5, 2.5), ylabel='Y')
ax.set(zlim3d=(-1, 1), zlabel='Z')
ax.scatter(traj[0, :, i].T, traj[1, :, i].T, traj[2, :, i].T)
def create_data_matrices(trajs, controls, indices):
states = np.empty((n_states, 0))
inputs = np.empty((n_inputs, 0))
next_states = np.empty((n_states, 0))
for i in indices:
cloth_trajectory = trajs[i]
cloth_inputs = controls[i]
states = np.hstack((states, cloth_trajectory[:, :-1]))
next_states = np.hstack((next_states, cloth_trajectory[:, 1:]))
inputs = np.hstack((inputs, cloth_inputs[:, :-1]))
augmented_states = np.vstack((states, inputs))
X = augmented_states
Y = next_states
return X, Y
if __name__ == '__main__':
ms = np.logspace(1.0, 2.6, num=20, dtype=int) # np.arange(10, 200, 100)
# ms = np.array([400])
labels = ['nystrom', 'splines']
all_trajs = []
all_controls = []
# swing_angle = 120
path_to_experiment = pathlib.Path(f"./8x8_cloth_swing_xyz")
n_states = 8 * 8 * 3
n_inputs = 6
n_trajs = 50
n_training_trajs = 30
validate_sys_id = False
cross_validate = False
n_val_trajs = 10 # for hyperparameter learning
for i in range(0, n_trajs):
traj = np.loadtxt(f'{path_to_experiment}/state_samples_cloth_swing_{i}.csv', delimiter=',').T
controls = np.loadtxt(f'{path_to_experiment}/input_samples_cloth_swing_{i}.csv', delimiter=',')[:, :n_inputs].T
all_trajs.append(traj)
all_controls.append(controls)
val_trajs = all_trajs[0:n_val_trajs]
val_controls = all_controls[0:n_val_trajs]
all_trajs = all_trajs[n_val_trajs:]
all_controls = all_controls[n_val_trajs:]
if cross_validate:
for kapprox in labels:
Xval, Yval = create_data_matrices(val_trajs, val_controls, range(0, n_val_trajs))
best_clf = learn_hyperparams(Xval, Yval, kapprox)
with open(f"{path_to_experiment}/cross_validated_kern_params_{kapprox}_cloth_swing.npy", 'wb') as f:
pickle.dump(best_clf, f)
if validate_sys_id:
regressor = None
for k, kapprox in enumerate(labels):
all_rmse_across_seeds = np.empty((0, ms.shape[0]))
print(kapprox)
for seed in range(0, 20):
np.random.seed(seed) # Fix seed
random.seed(seed)
trajs_indices = np.arange(0, n_trajs - n_val_trajs)
np.random.shuffle(trajs_indices)
trainings_trajs_indices = trajs_indices[:n_training_trajs]
testing_trajs_indices = trajs_indices[n_training_trajs:]
test_trajs = [all_trajs[i] for i in testing_trajs_indices.tolist()]
test_controlss = [all_controls[i] for i in testing_trajs_indices.tolist()]
X, Y = create_data_matrices(all_trajs, all_controls, trainings_trajs_indices)
with open(f"{path_to_experiment}/cross_validated_kern_params_{kapprox}_cloth_swing.npy", 'rb') as f:
clf = pickle.load(f)
kernel_params = clf.best_params_
# kernel_params = {}
print('----------------K PARAMS----------------', kernel_params)
pathdata = pathlib.Path(f"{path_to_experiment}/sim_results/{kapprox}/data")
pathplots = pathlib.Path(f"{path_to_experiment}/sim_results/{kapprox}/plots")
pathlib.Path.mkdir(pathdata, parents=True, exist_ok=True)
pathlib.Path.mkdir(pathplots, parents=True, exist_ok=True)
all_rmses = [] # Collect RMSEs across all testing trajectories
for i in range(0, len(test_trajs)):
test_traj = test_trajs[i]
test_controls = test_controlss[i]
rmses = []
for m_indx, m in enumerate(ms):
print("Curr seed and number of features: ", seed, " ", m)
kernel_params['m'] = m
regressor = None
if kapprox == 'nystrom':
regressor = KoopmanNystromRegressor(n_inputs, **kernel_params)
elif kapprox == 'splines':
regressor = KoopmanSplineRegressor(n_inputs, state_bounds_params=None, **kernel_params)
regressor.fit(X.T, Y.T) # Careful with transposition (shape required by sklearn estimator API, used for CV)
# Evaluate the prediction accuracy in open loop
curr_rmse = validate_dyn_sys(regressor, test_traj, test_controls)
rmses.append(curr_rmse)
print(rmses)
all_rmses.append(rmses)
all_rmses_array = np.array(all_rmses)
all_rmse_across_seeds = np.vstack((all_rmse_across_seeds, all_rmses_array))
print(np.median(all_rmse_across_seeds, axis=0))
print(np.percentile(all_rmse_across_seeds, axis=0, q=15))
print(np.percentile(all_rmse_across_seeds, axis=0, q=85))
np.savetxt(f"{pathdata}/all_rmses_{kapprox}_cloth_swing_angle.csv", all_rmse_across_seeds)
else:
for seed in range(0, 50):
for k, kapprox in enumerate(labels):
print(kapprox)
np.random.seed(seed) # Fix seed
random.seed(seed)
trajs_indices = np.arange(0, n_trajs)
trainings_trajs_indices = trajs_indices[:n_training_trajs]
X, Y = create_data_matrices(all_trajs, all_controls, trainings_trajs_indices)
with open(f"{path_to_experiment}/cross_validated_kern_params_{kapprox}_cloth_swing.npy", 'rb') as f:
clf = pickle.load(f)
kernel_params = clf.best_params_
m = 100
kernel_params['m'] = m
regressor = None
if kapprox == 'nystrom':
regressor = KoopmanNystromRegressor(n_inputs, **kernel_params)
elif kapprox == 'splines':
regressor = KoopmanSplineRegressor(n_inputs, state_bounds_params=None, **kernel_params)
regressor.fit(X.T, Y.T)
A = regressor.A
B = regressor.B
C = regressor.C
initial_state = all_trajs[0][:, 0].reshape([-1, 1])
R = np.eye(n_inputs)
Q = 0.075e-1 * C.T @ C
Q = (Q + Q.T) / 2
offset = np.zeros((n_states, 1))
alpha = np.pi / 4
z_top = initial_state[-1]
vertical_shift = 0.0
horizontal_shift = 0.0
for i in range(0, n_states):
if i % 3 == 0:
offset[i] = 0
if i % 3 == 1:
r = abs(z_top - initial_state[i + 1])
offset[i] = r * np.sin(alpha) + horizontal_shift
if i % 3 == 2:
r = abs(z_top - initial_state[i])
offset[i] = r - r * np.cos(alpha) + vertical_shift
reference = initial_state + offset
pathdata = pathlib.Path(f"{path_to_experiment}/sim_results/{kapprox}/data")
pathplots = pathlib.Path(f"{path_to_experiment}/sim_results/{kapprox}/plots")
pathdata.mkdir(parents=True, exist_ok=True)
pathplots.mkdir(parents=True, exist_ok=True)
np.savetxt(f"{pathdata}/reference_lqr_m_{m}.csv", reference)
K, _, _ = control.dlqr(A, B, Q, R)
K_SOM = K[[0, 3, 1, 4, 2, 5], :]
# Careful with actual input sequence used by F. Coltraro's simulator in matlab
np.savetxt(f"{pathdata}/REBUTTAL_K_lqr_seed_{seed}_m_{m}.csv", K_SOM)
with open(f"{pathdata}/REBUTTAL_regressor_seed_{seed}_m_{m}.npy", 'wb') as f:
pickle.dump(regressor, f)
end = 60
xs, ys, zs, us = lqr_control(end, reference, initial_state, regressor, K)