-
Notifications
You must be signed in to change notification settings - Fork 17
/
Copy pathanalyze-fa-cartpole.py
269 lines (224 loc) · 9.78 KB
/
analyze-fa-cartpole.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
# Symplectic ODE-Net | 2019
# Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty
# code structure follows the style of HNN by Sam Greydanus
# https://github.com/greydanus/hamiltonian-nn
# This file is a script version of 'analyze-fa-cartpole.ipynb'
# Cells are seperated by the vscode convention '#%%'
#%%
import torch, time, sys
import numpy as np
import matplotlib.pyplot as plt
import scipy.integrate
solve_ivp = scipy.integrate.solve_ivp
EXPERIMENT_DIR = './experiment-fa-cartpole/'
sys.path.append(EXPERIMENT_DIR)
from data import get_dataset, arrange_data
from nn_models import MLP, PSD, MatrixNet
from symoden import SymODEN_R1_T1
from utils import L2_loss, from_pickle
import imageio
#%%
DPI = 600
FORMAT = 'pdf'
LINE_WIDTH = 2
def get_args():
return {'num_angle': 1,
'learn_rate': 1e-3,
'nonlinearity': 'tanh',
'name': 'fa_cart',
'seed': 0,
'save_dir': './{}'.format(EXPERIMENT_DIR),
'fig_dir': './figures',
'num_points': 4,
'gpu': 0,
'solver': 'rk4'}
class ObjectView(object):
def __init__(self, d): self.__dict__ = d
args = ObjectView(get_args())
#%% [markdown]
# ## Load models
#%%
device = torch.device('cuda:' + str(args.gpu) if torch.cuda.is_available() else 'cpu')
def get_model(args, baseline, structure, naive, num_points):
M_net = PSD(3, 400, 2).to(device)
g_net = MatrixNet(3, 300, 4, shape=(2,2)).to(device)
if structure == False:
if naive and baseline:
raise RuntimeError('argument *baseline* and *naive* cannot both be true')
elif naive:
input_dim = 6
output_dim = 5
nn_model = MLP(input_dim, 1000, output_dim, args.nonlinearity).to(device)
model = SymODEN_R1_T1(args.num_angle, H_net=nn_model, device=device, baseline=baseline, naive=naive, u_dim=2)
elif baseline:
input_dim = 6
output_dim = 4
nn_model = MLP(input_dim, 700, output_dim, args.nonlinearity).to(device)
model = SymODEN_R1_T1(args.num_angle, H_net=nn_model, M_net=M_net, device=device, baseline=baseline, naive=naive, u_dim=2)
else:
input_dim = 5
output_dim = 1
nn_model = MLP(input_dim, 500, output_dim, args.nonlinearity).to(device)
model = SymODEN_R1_T1(args.num_angle, H_net=nn_model, M_net=M_net, g_net=g_net, device=device, baseline=baseline, naive=naive, u_dim=2)
elif structure == True and baseline ==False and naive==False:
V_net = MLP(3, 300, 1).to(device)
model = SymODEN_R1_T1(args.num_angle, M_net=M_net, V_net=V_net, g_net=g_net, device=device, baseline=baseline, structure=True, u_dim=2).to(device)
else:
raise RuntimeError('argument *structure* is set to true, no *baseline* or *naive*!')
if naive:
label = '-naive_ode'
elif baseline:
label = '-baseline_ode'
else:
label = '-hnn_ode'
struct = '-struct' if structure else ''
path = '{}/{}{}{}-{}-p{}.tar'.format(args.save_dir, args.name, label, struct, args.solver, args.num_points)
model.load_state_dict(torch.load(path, map_location=device))
path = '{}/{}{}{}-{}-p{}-stats.pkl'.format(args.save_dir, args.name, label, struct, args.solver, args.num_points)
stats = from_pickle(path)
return model, stats
symoden_ode_struct_model, symoden_ode_struct_stats = get_model(args, baseline=False, structure=True, naive=False, num_points=args.num_points)
#%%
# time info for simualtion
time_step = 400 ; n_eval = 400
t_span = [0,time_step*0.02]
t_linspace_true = np.linspace(t_span[0], time_step, time_step)*0.02
t_linspace_model = np.linspace(t_span[0], t_span[1], n_eval)
# angle info for simuation
q0 = 2
x0 = 1.0
u10 = 0.0 ; u20 = 0.0
# record video
import gym
from gym import wrappers
env = gym.make('My_FA_CartPole-v0')
env = gym.wrappers.Monitor(env, './videos/' + 'cartpole-fa-embed' + '/', force=True) # , video_callable=lambda x: True, force=True
env.reset()
env.env.state = np.array([x0, 0.0, q0, 0.0], dtype=np.float32)
obs = env.env._get_obs()
y = torch.tensor([obs[0], obs[1], obs[2], obs[3], obs[4], u10, u20], requires_grad=True, device=device, dtype=torch.float32).view(1, 7)
t_eval = torch.linspace(t_span[0], t_span[1], n_eval).to(device)
y_traj = []
y_traj.append(y)
frames = []
for i in range(len(t_eval)-1):
frames.append(env.render(mode='rgb_array'))
x_cos_q_sin_q, x_dot_q_dot, u = torch.split(y, [3, 2, 2], dim=1)
M_q_inv = symoden_ode_struct_model.M_net(x_cos_q_sin_q)
x_dot_q_dot_aug = torch.unsqueeze(x_dot_q_dot, dim=2)
p = torch.squeeze(torch.matmul(torch.inverse(M_q_inv), x_dot_q_dot_aug), dim=2)
x_cos_q_sin_q_p = torch.cat((x_cos_q_sin_q, p), dim=1)
x_cos_q_sin_q, p = torch.split(x_cos_q_sin_q_p, [3, 2], dim=1)
M_q_inv = symoden_ode_struct_model.M_net(x_cos_q_sin_q)
_, cos_q, sin_q = torch.chunk(x_cos_q_sin_q, 3,dim=1)
V_q = symoden_ode_struct_model.V_net(x_cos_q_sin_q)
p_aug = torch.unsqueeze(p, dim=2)
H = torch.squeeze(torch.matmul(torch.transpose(p_aug, 1, 2), torch.matmul(M_q_inv, p_aug)))/2.0 + torch.squeeze(V_q)
dH = torch.autograd.grad(H.sum(), x_cos_q_sin_q_p, create_graph=True)[0]
dHdx, dHdcos_q, dHdsin_q, dHdp= torch.split(dH, [1, 1, 1, 2], dim=1)
dV = torch.autograd.grad(V_q, x_cos_q_sin_q)[0]
dVdx, dVdcos_q, dVdsin_q= torch.chunk(dV, 3, dim=1)
dV_q = - dVdcos_q * sin_q + dVdsin_q * cos_q
g_xq = symoden_ode_struct_model.g_net(x_cos_q_sin_q)
g_xq_T = torch.transpose(g_xq, 1, 2)
inv_g_g_T = torch.inverse(torch.matmul(g_xq, g_xq_T))
g_T_inv_g_g_T = torch.matmul(g_xq_T, inv_g_g_T)
# bracket in beta_q
energy_shaping = torch.zeros(2, 1, dtype=torch.float32, device=device)
energy_shaping[0][0] = 2 * dVdx[0][0] - x_cos_q_sin_q[0][0]
energy_shaping[1][0] = 2 * dV_q[0][0]
damping_injection = -2 * p.T
u = torch.matmul(g_T_inv_g_g_T, energy_shaping+damping_injection)
u = u.squeeze().detach().cpu().numpy()
obs, _, _, _ = env.step(u)
y = torch.tensor([obs[0], obs[1], obs[2], obs[3], obs[4], u[0], u[1]], requires_grad=True, device=device, dtype=torch.float32).view(1, 7)
y_traj.append(y)
env.close()
# imageio.mimsave('./videos/cartpole-fa-embed/cartpole-fa-embed.gif', frames, duration=0.02)
y_traj = torch.stack(y_traj).view(-1, 7).detach().cpu().numpy()
# %%
with plt.style.context("seaborn-white"):
fig = plt.figure(figsize=(12, 1.3), dpi=DPI)
plt.rcParams["axes.grid"] = False
ax = plt.subplot(1, 10, 1)
ax.imshow(frames[0])
plt.setp(ax.get_xticklabels(), visible=False)
plt.setp(ax.get_yticklabels(), visible=False)
ax = plt.subplot(1, 10, 2)
ax.imshow(frames[15])
plt.setp(ax.get_xticklabels(), visible=False)
plt.setp(ax.get_yticklabels(), visible=False)
ax = plt.subplot(1, 10, 3)
ax.imshow(frames[30])
plt.setp(ax.get_xticklabels(), visible=False)
plt.setp(ax.get_yticklabels(), visible=False)
ax = plt.subplot(1, 10, 4)
ax.imshow(frames[45])
plt.setp(ax.get_xticklabels(), visible=False)
plt.setp(ax.get_yticklabels(), visible=False)
ax = plt.subplot(1, 10, 5)
ax.imshow(frames[60])
plt.setp(ax.get_xticklabels(), visible=False)
plt.setp(ax.get_yticklabels(), visible=False)
ax = plt.subplot(1, 10, 6)
ax.imshow(frames[75])
plt.setp(ax.get_xticklabels(), visible=False)
plt.setp(ax.get_yticklabels(), visible=False)
ax = plt.subplot(1, 10, 7)
ax.imshow(frames[90])
plt.setp(ax.get_xticklabels(), visible=False)
plt.setp(ax.get_yticklabels(), visible=False)
ax = plt.subplot(1, 10, 8)
ax.imshow(frames[105])
plt.setp(ax.get_xticklabels(), visible=False)
plt.setp(ax.get_yticklabels(), visible=False)
ax = plt.subplot(1, 10, 9)
ax.imshow(frames[120])
plt.setp(ax.get_xticklabels(), visible=False)
plt.setp(ax.get_yticklabels(), visible=False)
ax = plt.subplot(1, 10, 10)
ax.imshow(frames[135])
plt.setp(ax.get_xticklabels(), visible=False)
plt.setp(ax.get_yticklabels(), visible=False)
plt.tight_layout()
fig.subplots_adjust(hspace=0, wspace=0)
# fig.savefig('{}/fig-fa-cartpole-frame.{}'.format(args.fig_dir, FORMAT))
# %%
y_traj[0, 5] = y_traj[1, 5]
y_traj[0, 6] = y_traj[1, 6]
fig = plt.figure(figsize=[12, 4], dpi=DPI)
plt.subplot(2, 3, 1)
plt.plot(t_eval.numpy(), 0 * np.ones_like(t_eval.numpy()), color='k', linewidth=0.5)
plt.plot(t_eval.numpy(), y_traj[:, 0], color='b', linewidth=LINE_WIDTH)
plt.title("$r$", fontsize=14)
plt.xlabel('t')
plt.subplot(2, 3, 4)
plt.plot(t_eval.numpy(), 1 * np.ones_like(t_eval.numpy()), 'k--', linewidth=0.5)
plt.plot(t_eval.numpy(), 0 * np.ones_like(t_eval.numpy()), 'k-', linewidth=0.5)
plt.plot(t_eval.numpy(), y_traj[:, 1], 'b--', label=r"$\cos(\phi)$", linewidth=LINE_WIDTH)
plt.plot(t_eval.numpy(), y_traj[:, 2], 'b-', label=r"$\sin(\phi)$", linewidth=LINE_WIDTH)
plt.title("$\phi$", fontsize=14)
plt.xlabel('t')
plt.legend(fontsize=12)
plt.subplot(2, 3, 2)
plt.plot(t_eval.numpy(), 0 * np.ones_like(t_eval.numpy()), 'k-', linewidth=0.5)
plt.plot(t_eval.numpy(), y_traj[:, 3], color='b', linewidth=LINE_WIDTH)
plt.title("$\dot{r}$", fontsize=14)
plt.xlabel('t')
plt.subplot(2, 3, 5)
plt.plot(t_eval.numpy(), 0 * np.ones_like(t_eval.numpy()), 'k-', linewidth=0.5)
plt.plot(t_eval.numpy(), y_traj[:, 4], color='b', linewidth=LINE_WIDTH)
plt.title("$\dot{\phi}$", fontsize=14)
plt.xlabel('t')
plt.subplot(2, 3, 3)
plt.plot(t_eval.numpy(), 0 * np.ones_like(t_eval.numpy()), 'k-', linewidth=0.5)
plt.plot(t_eval.numpy(), y_traj[:, 5], color='b', linewidth=LINE_WIDTH)
plt.title("$u_1$", fontsize=14)
plt.xlabel('t')
plt.subplot(2, 3, 6)
plt.plot(t_eval.numpy(), 0 * np.ones_like(t_eval.numpy()), 'k-', linewidth=0.5)
plt.plot(t_eval.numpy(), y_traj[:, 6], color='b', linewidth=LINE_WIDTH)
plt.title("$u_2$", fontsize=14)
plt.xlabel('t')
plt.tight_layout()
# fig.savefig('{}/fig-fa-cartpole-ctrl.{}'.format(args.fig_dir, FORMAT))