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plot_optimal_solutions.py
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import pickle
import bioviz
import casadi as cas
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
import numpy as np
from pygments.lexers.robotframework import VARIABLE
from DMS_deterministic import prepare_ocp
from DMS_SOCP import prepare_socp
from DMS_SOCP_VARIABLE import prepare_socp_VARIABLE
from DMS_SOCP_FEEDFORWARD import prepare_socp_FEEDFORWARD
from DMS_SOCP_VARIABLE_FEEDFORWARD import prepare_socp_VARIABLE_FEEDFORWARD
from bioptim import (
StochasticBioModel,
Solution,
Shooting,
SolutionIntegrator,
InitialGuessList,
InterpolationType,
)
from utils import (
DMS_sensory_reference,
motor_acuity,
DMS_fb_noised_sensory_input_VARIABLE_no_eyes,
DMS_ff_noised_sensory_input,
DMS_sensory_reference_no_eyes,
DMS_ff_sensory_input,
visual_noise,
vestibular_noise,
DMS_fb_noised_sensory_input_VARIABLE,
)
def box_plot(position, data, axs, color):
axs.plot(np.array([position - 0.1, position - 0.1]), np.array([np.min(data), np.max(data)]), color=color)
axs.plot(np.array([position - 0.15, position - 0.05]), np.array([np.min(data), np.min(data)]), color=color)
axs.plot(np.array([position - 0.15, position - 0.05]), np.array([np.max(data), np.max(data)]), color=color)
axs.plot(position - 0.1, np.mean(data), "s", color=color)
axs.add_patch(
Rectangle((position - 0.15, np.mean(data) - np.std(data)), 0.1, 2 * np.std(data), color=color, alpha=0.3)
)
def plot_CoM(states_integrated, model, n_shooting, save_path, nb_random=30):
nx = states_integrated.shape[0]
nq = int(nx / 2)
time = np.linspace(0, final_time, n_shooting + 1)
fig, axs = plt.subplots(2, 2, figsize=(15, 10))
axs = np.ravel(axs)
CoM = np.zeros((nb_random, n_shooting + 1))
CoMdot = np.zeros((nb_random, n_shooting + 1))
PelvisRot = np.zeros((nb_random, n_shooting + 1))
PelvisVelot = np.zeros((nb_random, n_shooting + 1))
for j in range(nb_random):
for k in range(n_shooting + 1):
CoM[j, k] = model.CoM(states_integrated[:nq, j, k]).to_array()[1]
CoMdot[j, k] = model.CoMdot(states_integrated[:nq, j, k], states_integrated[nq:, j, k]).to_array()[1]
PelvisRot[j, k] = states_integrated[2, j, k]
PelvisVelot[j, k] = states_integrated[nq + 2, j, k]
axs[0].plot(time, CoM[j, :], color="tab:blue", alpha=0.2)
axs[1].plot(time, CoMdot[j, :], color="tab:blue", alpha=0.2)
axs[2].plot(time, PelvisRot[j, :], color="tab:blue", alpha=0.2)
axs[3].plot(time, PelvisVelot[j, :], color="tab:blue", alpha=0.2)
CoM_deterministic = np.zeros((n_shooting + 1))
CoMdot_deterministic = np.zeros((n_shooting + 1))
PelvisRot_deterministic = np.zeros((n_shooting + 1))
PelvisVelot_deterministic = np.zeros((n_shooting + 1))
for k in range(n_shooting + 1):
CoM_deterministic[k] = model.CoM(q_sol[:, k]).to_array()[1]
CoMdot_deterministic[k] = model.CoMdot(q_sol[:, k], qdot_sol[:, k]).to_array()[1]
PelvisRot_deterministic[k] = q_sol[2, k]
PelvisVelot_deterministic[k] = qdot_sol[2, k]
axs[0].plot(time, CoM_deterministic, color="k")
axs[1].plot(time, CoMdot_deterministic, color="k")
axs[2].plot(time, PelvisRot_deterministic, color="k")
axs[3].plot(time, PelvisVelot_deterministic, color="k")
axs[0].set_title("CoM")
axs[1].set_title("CoMdot")
axs[2].set_title("PelvisRot")
axs[3].set_title("PelvisVelot")
plt.suptitle(f"CoM and Pelvis for {save_path}")
plt.savefig(f"{save_path}_CoM.png")
# plt.show()
def bioviz_animate(biorbd_model_path_with_mesh, q, name):
b = bioviz.Viz(
biorbd_model_path_with_mesh,
mesh_opacity=1.0,
background_color=(1, 1, 1),
show_local_ref_frame=False,
show_markers=False,
show_segments_center_of_mass=False,
show_global_center_of_mass=False,
show_global_ref_frame=False,
show_gravity_vector=False,
# show_floor=True,
)
b.set_camera_zoom(0.39)
b.maximize()
b.update()
b.load_movement(q)
b.start_recording(f"videos/{result_folder}/" + name + ".ogv")
for frame in range(q.shape[1] + 1):
b.movement_slider[0].setValue(frame)
b.add_frame()
b.stop_recording()
def noisy_integrate_ocp(
n_q,
n_shooting,
nb_random,
nb_reintegrations,
q_roots_ocp,
q_joints_ocp,
qdot_ocp,
tau_joints_ocp,
time_vector_ocp,
ocp,
forward_dynamics_func,
):
def ocp_dynamics(q_roots, q_joints, qdot_roots, qdot_joints, tau_joints, motor_noise,
nlp, nb_random, forward_dynamics_func):
n_root = 3
n_joints = 4
ddq_roots = None
ddq_joints = None
for i in range(nb_random):
q_this_time = np.hstack((
q_roots[i * n_root: (i + 1) * n_root], q_joints[i * n_joints: (i + 1) * n_joints]
))
qdot_this_time = np.hstack((
qdot_roots[i * n_root: (i + 1) * n_root], qdot_joints[i * n_joints: (i + 1) * n_joints]
))
tau_this_time = tau_joints[:]
# Joint friction
tau_this_time -= nlp.model.friction_coefficients @ qdot_this_time[n_root:]
# Motor noise
tau_this_time += motor_noise[:, i]
ddq = forward_dynamics_func(q_this_time, qdot_this_time, tau_this_time)
ddq_roots = np.vstack((ddq_roots, ddq[:n_root])) if ddq_roots is not None else ddq[:n_root]
ddq_joints = np.vstack((ddq_joints, ddq[n_root:])) if ddq_joints is not None else ddq[n_root:]
return qdot_roots, qdot_joints, ddq_roots.reshape(-1, ), ddq_joints.reshape(-1, )
def integrate(time, q_roots, q_joints, qdot_roots, qdot_joints, tau_joints, motor_noise,
nlp, nb_random, forward_dynamics_func):
dt = time / n_shooting
h = dt / 5
q_roots_integrated = np.zeros((n_root * nb_random, n_shooting + 1))
q_joints_integrated = np.zeros((n_joints * nb_random, n_shooting + 1))
qdot_roots_integrated = np.zeros((n_root * nb_random, n_shooting + 1))
qdot_joints_integrated = np.zeros((n_joints * nb_random, n_shooting + 1))
for i_random in range(nb_random):
q_roots_integrated[n_root*i_random:n_root*(i_random+1), 0] = q_roots[:, i_random]
q_joints_integrated[n_joints*i_random:n_joints*(i_random+1), 0] = q_joints[:, i_random]
qdot_roots_integrated[n_root*i_random:n_root*(i_random+1), 0] = qdot_roots[:, i_random]
qdot_joints_integrated[n_joints*i_random:n_joints*(i_random+1), 0] = qdot_joints[:, i_random]
for i_shooting in range(n_shooting):
q_roots_this_time = q_roots_integrated[:, i_shooting]
q_joints_this_time = q_joints_integrated[:, i_shooting]
qdot_roots_this_time = qdot_roots_integrated[:, i_shooting]
qdot_joints_this_time = qdot_joints_integrated[:, i_shooting]
tau_joints_this_time = tau_joints[:, i_shooting]
motor_noise_this_time = motor_noise[:, :, i_shooting]
for i_step in range(5):
q_roots_dot1, q_joints_dot1, qdot_roots_dot1, qdot_joints_dot1 = ocp_dynamics(q_roots_this_time,
q_joints_this_time,
qdot_roots_this_time,
qdot_joints_this_time,
tau_joints_this_time,
motor_noise_this_time,
nlp,
nb_random,
forward_dynamics_func)
q_roots_dot2, q_joints_dot2, qdot_roots_dot2, qdot_joints_dot2 = ocp_dynamics(
q_roots_this_time + h / 2 * q_roots_dot1, q_joints_this_time + h / 2 * q_joints_dot1,
qdot_roots_this_time + h / 2 * qdot_roots_dot1,
qdot_joints_this_time + h / 2 * qdot_joints_dot1,
tau_joints_this_time,
motor_noise_this_time,
nlp,
nb_random,
forward_dynamics_func)
q_roots_dot3, q_joints_dot3, qdot_roots_dot3, qdot_joints_dot3 = ocp_dynamics(
q_roots_this_time + h / 2 * q_roots_dot2, q_joints_this_time + h / 2 * q_joints_dot2,
qdot_roots_this_time + h / 2 * qdot_roots_dot2,
qdot_joints_this_time + h / 2 * qdot_joints_dot2,
tau_joints_this_time,
motor_noise_this_time,
nlp,
nb_random,
forward_dynamics_func)
q_roots_dot4, q_joints_dot4, qdot_roots_dot4, qdot_joints_dot4 = ocp_dynamics(
q_roots_this_time + h * q_roots_dot3, q_joints_this_time + h * q_joints_dot3,
qdot_roots_this_time + h * qdot_roots_dot3, qdot_joints_this_time + h * qdot_joints_dot3,
tau_joints_this_time,
motor_noise_this_time,
nlp,
nb_random,
forward_dynamics_func)
q_roots_this_time = q_roots_this_time + h / 6 * (
q_roots_dot1 + 2 * q_roots_dot2 + 2 * q_roots_dot3 + q_roots_dot4)
q_joints_this_time = q_joints_this_time + h / 6 * (
q_joints_dot1 + 2 * q_joints_dot2 + 2 * q_joints_dot3 + q_joints_dot4)
qdot_roots_this_time = qdot_roots_this_time + h / 6 * (
qdot_roots_dot1 + 2 * qdot_roots_dot2 + 2 * qdot_roots_dot3 + qdot_roots_dot4)
qdot_joints_this_time = qdot_joints_this_time + h / 6 * (
qdot_joints_dot1 + 2 * qdot_joints_dot2 + 2 * qdot_joints_dot3 + qdot_joints_dot4)
q_roots_integrated[:, i_shooting + 1] = q_roots_this_time
q_joints_integrated[:, i_shooting + 1] = q_joints_this_time
qdot_roots_integrated[:, i_shooting + 1] = qdot_roots_this_time
qdot_joints_integrated[:, i_shooting + 1] = qdot_joints_this_time
return q_roots_integrated, q_joints_integrated, qdot_roots_integrated, qdot_joints_integrated
n_q = ocp.nlp[0].model.nb_q
n_root = ocp.nlp[0].model.nb_root
n_joints = n_q - n_root
q_all_ocp = np.zeros((n_q * (nb_random + 1), n_shooting + 1))
for i_shooting in range(n_shooting + 1):
for i_random in range(nb_random):
q_all_ocp[i_random * n_q : (i_random + 1) * n_q, i_shooting] = np.reshape(
q_ocp[:, i_shooting], (-1,)
)
q_all_ocp[(i_random + 1) * n_q : (i_random + 2) * n_q, i_shooting] = np.reshape(
q_ocp[:, i_shooting], (-1,)
)
q_roots_integrated_ocp = np.zeros((n_root, n_shooting + 1, nb_random * nb_reintegrations))
q_joints_integrated_ocp = np.zeros((n_joints, n_shooting + 1, nb_random * nb_reintegrations))
qdot_roots_integrated_ocp = np.zeros((n_root, n_shooting + 1, nb_random * nb_reintegrations))
qdot_joints_integrated_ocp = np.zeros((n_joints, n_shooting + 1, nb_random * nb_reintegrations))
joint_frictions_ocp = np.zeros((n_joints, n_shooting, nb_random * nb_reintegrations))
motor_noises_ocp = np.zeros((n_joints, n_shooting, nb_random * nb_reintegrations))
for i_reintegration in range(nb_reintegrations):
# Prepare the noises
np.random.seed(i_reintegration)
# the last node deos not need motor and sensory noise
motor_noise_numerical_this_time = np.zeros((n_joints, nb_random, n_shooting + 1))
for i_random in range(nb_random):
for i_shooting in range(n_shooting):
motor_noise_numerical_this_time[:, i_random, i_shooting] = np.random.normal(
loc=np.zeros(motor_noise_magnitude.shape[0]),
scale=np.reshape(np.array(motor_noise_magnitude), (n_joints,)),
size=n_joints,
)
initial_cov = np.eye(2 * n_q) * np.hstack((np.ones((n_q,)) * 1e-4, np.ones((n_q,)) * 1e-7)) # P
states_init = np.array(
[-0.0346, 0.1207, 0.2255, 0.0, 3.1, -0.1787, 0.0, # q
0, 2, 2.5 * np.pi, 0, 0, 0, 0] # qdot
)
noised_states = np.random.multivariate_normal(
states_init, initial_cov, nb_random
).T
# initial variability
q_roots_init_this_time = noised_states[:n_root, :]
q_joints_init_this_time = noised_states[n_root: n_q, :]
qdot_roots_init_this_time = noised_states[n_q: n_q + n_root, :]
qdot_joints_init_this_time = noised_states[n_q + n_root:, :]
q_roots_integrated, q_joints_integrated, qdot_roots_integrated, qdot_joints_integrated = integrate(
time_vector_ocp[-1], q_roots_init_this_time, q_joints_init_this_time, qdot_roots_init_this_time,
qdot_joints_init_this_time,
tau_joints_ocp,
motor_noise_numerical_this_time,
ocp.nlp[0],
nb_random,
forward_dynamics_func)
for i_random in range(nb_random):
for i_dof in range(n_joints):
if i_dof < n_root:
q_roots_integrated_ocp[i_dof, :, i_reintegration * nb_random + i_random] = q_roots_integrated[i_dof + n_root*i_random, :]
qdot_roots_integrated_ocp[i_dof, :, i_reintegration * nb_random + i_random] = qdot_roots_integrated[i_dof + n_root*i_random, :]
q_joints_integrated_ocp[i_dof, :, i_reintegration * nb_random + i_random] = q_joints_integrated[i_dof + n_joints*i_random, :]
qdot_joints_integrated_ocp[i_dof, :, i_reintegration * nb_random + i_random] = qdot_joints_integrated[i_dof + n_joints*i_random, :]
# if i_reintegration == 0:
# plt.figure()
# for i_shooting in range(5):
# for i_random in range(nb_random):
# plt.plot(np.ones((3, ))*i_shooting, q_roots_integrated_ocp[:, i_shooting, i_random], '.b')
# plt.plot(np.ones((4, ))*i_shooting, q_joints_integrated_ocp[:, i_shooting, i_random], '.b')
# plt.scatter(np.ones((7, ))*i_shooting, q_ocp[:, i_shooting], color='m')
# plt.savefig("tempo_ocp_0.png")
# # plt.show()
for i_random in range(nb_random):
for i_shooting in range(n_shooting):
if i_shooting < n_shooting:
# Joint friction
joint_frictions_ocp[
:,
i_shooting,
i_reintegration * nb_random
+ (n_q - 3) * i_random : i_reintegration * nb_random
+ (n_q - 3) * (i_random + 1),
] = (
ocp.nlp[0].model.friction_coefficients
@ qdot_joints_integrated_ocp[:, i_shooting, i_reintegration * nb_random + i_random]
)
# Motor noise
motor_noises_ocp[
:,
i_shooting,
i_reintegration * nb_random + i_random,
] = np.reshape(motor_noise_numerical_this_time[:, i_random, i_shooting], (-1, ))
q_ocp_integrated = np.vstack(
(q_roots_integrated_ocp, q_joints_integrated_ocp)
)
qdot_ocp_integrated = np.vstack(
(qdot_roots_integrated_ocp, qdot_joints_integrated_ocp)
)
for i_random in range(nb_random):
q_all_ocp[
n_q * (i_random + 1) : n_q * (i_random + 2), :
] = q_ocp_integrated[:, :, i_random]
return (
q_ocp_integrated,
qdot_ocp_integrated,
q_all_ocp,
joint_frictions_ocp,
motor_noises_ocp,
)
def noisy_integrate_socp(
biorbd_model_path,
time_ocp,
motor_noise_magnitude,
sensory_noise_magnitude,
q_roots_ocp,
q_joints_ocp,
qdot_roots_ocp,
qdot_joints_ocp,
tau_joints_ocp,
n_q,
n_shooting,
nb_random,
nb_reintegrations,
q_roots_socp,
q_joints_socp,
qdot_roots_socp,
qdot_joints_socp,
q_socp,
qdot_socp,
tau_joints_socp,
k_socp,
ref_socp,
time_vector_socp,
q_mean_socp,
DMS_sensory_reference_func,
forward_dynamics_func,
):
def socp_dynamics(q_roots, q_joints, qdot_roots, qdot_joints, tau_joints, k, ref, motor_noise, sensory_noise,
nlp, DMS_sensory_reference_func, forward_dynamics_func):
k_matrix = StochasticBioModel.reshape_to_matrix(k, nlp.model.matrix_shape_k)
n_root = 3
n_joints = 4
ddq_roots = None
ddq_joints = None
for i in range(nlp.model.nb_random):
q_this_time = np.hstack((
q_roots[i * n_root: (i + 1) * n_root], q_joints[i * n_joints: (i + 1) * n_joints]
))
qdot_this_time = np.hstack((
qdot_roots[i * n_root: (i + 1) * n_root], qdot_joints[i * n_joints: (i + 1) * n_joints]
))
tau_this_time = tau_joints[:]
# Joint friction
tau_this_time -= nlp.model.friction_coefficients @ qdot_this_time[n_root:]
# Motor noise
tau_this_time += motor_noise[:, i]
# Feedback
tau_this_time += k_matrix @ (
ref - DMS_sensory_reference_func(q_this_time, qdot_this_time) + sensory_noise[:, i]
)
ddq = forward_dynamics_func(q_this_time, qdot_this_time, tau_this_time)
ddq_roots = np.vstack((ddq_roots, ddq[:n_root])) if ddq_roots is not None else ddq[:n_root]
ddq_joints = np.vstack((ddq_joints, ddq[n_root:])) if ddq_joints is not None else ddq[n_root:]
return qdot_roots, qdot_joints, ddq_roots.reshape(-1, ), ddq_joints.reshape(-1, )
def integrate(time, q_roots, q_joints, qdot_roots, qdot_joints, tau_joints, k, ref, motor_noise, sensory_noise,
nlp, DMS_sensory_reference_func, forward_dynamics_func):
dt = time / n_shooting
h = dt / 5
q_roots_integrated = np.zeros((3 * nb_random, n_shooting + 1))
q_joints_integrated = np.zeros((4 * nb_random, n_shooting + 1))
qdot_roots_integrated = np.zeros((3 * nb_random, n_shooting + 1))
qdot_joints_integrated = np.zeros((4 * nb_random, n_shooting + 1))
for i_random in range(nb_random):
q_roots_integrated[3*i_random:3*(i_random+1), 0] = q_roots[:, i_random]
q_joints_integrated[4*i_random:4*(i_random+1), 0] = q_joints[:, i_random]
qdot_roots_integrated[3*i_random:3*(i_random+1), 0] = qdot_roots[:, i_random]
qdot_joints_integrated[4*i_random:4*(i_random+1), 0] = qdot_joints[:, i_random]
for i_shooting in range(n_shooting):
q_roots_this_time = q_roots_integrated[:, i_shooting]
q_joints_this_time = q_joints_integrated[:, i_shooting]
qdot_roots_this_time = qdot_roots_integrated[:, i_shooting]
qdot_joints_this_time = qdot_joints_integrated[:, i_shooting]
tau_joints_this_time = tau_joints[:, i_shooting]
k_this_time = k[:, i_shooting]
ref_this_time = ref[:, i_shooting]
motor_noise_this_time = motor_noise[:, :, i_shooting]
sensory_noise_this_time = sensory_noise[:, :, i_shooting]
for i_step in range(5):
q_roots_dot1, q_joints_dot1, qdot_roots_dot1, qdot_joints_dot1 = socp_dynamics(q_roots_this_time,
q_joints_this_time,
qdot_roots_this_time,
qdot_joints_this_time,
tau_joints_this_time,
k_this_time,
ref_this_time,
motor_noise_this_time,
sensory_noise_this_time,
nlp,
DMS_sensory_reference_func,
forward_dynamics_func)
q_roots_dot2, q_joints_dot2, qdot_roots_dot2, qdot_joints_dot2 = socp_dynamics(
q_roots_this_time + h / 2 * q_roots_dot1, q_joints_this_time + h / 2 * q_joints_dot1,
qdot_roots_this_time + h / 2 * qdot_roots_dot1,
qdot_joints_this_time + h / 2 * qdot_joints_dot1, tau_joints_this_time, k_this_time,
ref_this_time, motor_noise_this_time, sensory_noise_this_time, nlp, DMS_sensory_reference_func,
forward_dynamics_func)
q_roots_dot3, q_joints_dot3, qdot_roots_dot3, qdot_joints_dot3 = socp_dynamics(
q_roots_this_time + h / 2 * q_roots_dot2, q_joints_this_time + h / 2 * q_joints_dot2,
qdot_roots_this_time + h / 2 * qdot_roots_dot2,
qdot_joints_this_time + h / 2 * qdot_joints_dot2, tau_joints_this_time, k_this_time,
ref_this_time, motor_noise_this_time, sensory_noise_this_time, nlp, DMS_sensory_reference_func,
forward_dynamics_func)
q_roots_dot4, q_joints_dot4, qdot_roots_dot4, qdot_joints_dot4 = socp_dynamics(
q_roots_this_time + h * q_roots_dot3, q_joints_this_time + h * q_joints_dot3,
qdot_roots_this_time + h * qdot_roots_dot3, qdot_joints_this_time + h * qdot_joints_dot3,
tau_joints_this_time, k_this_time, ref_this_time, motor_noise_this_time,
sensory_noise_this_time, nlp, DMS_sensory_reference_func, forward_dynamics_func)
q_roots_this_time = q_roots_this_time + h / 6 * (
q_roots_dot1 + 2 * q_roots_dot2 + 2 * q_roots_dot3 + q_roots_dot4)
q_joints_this_time = q_joints_this_time + h / 6 * (
q_joints_dot1 + 2 * q_joints_dot2 + 2 * q_joints_dot3 + q_joints_dot4)
qdot_roots_this_time = qdot_roots_this_time + h / 6 * (
qdot_roots_dot1 + 2 * qdot_roots_dot2 + 2 * qdot_roots_dot3 + qdot_roots_dot4)
qdot_joints_this_time = qdot_joints_this_time + h / 6 * (
qdot_joints_dot1 + 2 * qdot_joints_dot2 + 2 * qdot_joints_dot3 + qdot_joints_dot4)
q_roots_integrated[:, i_shooting + 1] = q_roots_this_time
q_joints_integrated[:, i_shooting + 1] = q_joints_this_time
qdot_roots_integrated[:, i_shooting + 1] = qdot_roots_this_time
qdot_joints_integrated[:, i_shooting + 1] = qdot_joints_this_time
return q_roots_integrated, q_joints_integrated, qdot_roots_integrated, qdot_joints_integrated
n_q = socp.nlp[0].model.nb_q
n_root = socp.nlp[0].model.nb_root
n_joints = n_q - n_root
q_all_socp = np.zeros((n_q * (nb_random + 1), n_shooting + 1))
for i_shooting in range(n_shooting + 1):
for i_random in range(nb_random):
q_all_socp[i_random * n_q : (i_random + 1) * n_q, i_shooting] = np.reshape(
q_socp[:, i_shooting, i_random], (-1,)
)
q_all_socp[(i_random + 1) * n_q : (i_random + 2) * n_q, i_shooting] = np.reshape(
q_mean_socp[:, i_shooting], (-1,)
)
q_roots_integrated_socp = np.zeros((3, n_shooting + 1, nb_random * nb_reintegrations))
q_joints_integrated_socp = np.zeros((n_q - 3, n_shooting + 1, nb_random * nb_reintegrations))
qdot_roots_integrated_socp = np.zeros((3, n_shooting + 1, nb_random * nb_reintegrations))
qdot_joints_integrated_socp = np.zeros((n_q - 3, n_shooting + 1, nb_random * nb_reintegrations))
joint_frictions_socp = np.zeros((n_q - 3, n_shooting, nb_random * nb_reintegrations))
motor_noises_socp = np.zeros((n_q - 3, n_shooting, nb_random * nb_reintegrations))
feedbacks_socp = np.zeros((n_q - 3, n_shooting, nb_random * nb_reintegrations))
for i_reintegration in range(nb_reintegrations):
# Prepare the noises
np.random.seed(i_reintegration)
# the last node deos not need motor and sensory noise
motor_noise_numerical_this_time = np.zeros((n_joints, nb_random, n_shooting + 1))
sensory_noise_numerical_this_time = np.zeros((2 * (n_joints + 1), nb_random, n_shooting + 1))
for i_random in range(nb_random):
for i_shooting in range(n_shooting):
motor_noise_numerical_this_time[:, i_random, i_shooting] = np.random.normal(
loc=np.zeros(motor_noise_magnitude.shape[0]),
scale=np.reshape(np.array(motor_noise_magnitude), (n_joints,)),
size=n_joints,
)
sensory_noise_numerical_this_time[:, i_random, i_shooting] = np.random.normal(
loc=np.zeros(sensory_noise_magnitude.shape[0]),
scale=np.reshape(np.array(sensory_noise_magnitude), (2 * (n_joints + 1),)),
size=2 * (n_joints + 1),
)
initial_cov = np.eye(2 * n_q) * np.hstack((np.ones((n_q,)) * 1e-4, np.ones((n_q,)) * 1e-7)) # P
states_init = np.array(
[-0.0346, 0.1207, 0.2255, 0.0, 3.1, -0.1787, 0.0, # q
0, 2, 2.5 * np.pi, 0, 0, 0, 0] # qdot
)
noised_states = np.random.multivariate_normal(
states_init, initial_cov, nb_random
).T
# initial variability
q_roots_init_this_time = noised_states[:n_root, :]
q_joints_init_this_time = noised_states[n_root: n_q, :]
qdot_roots_init_this_time = noised_states[n_q: n_q + n_root, :]
qdot_joints_init_this_time = noised_states[n_q + n_root:, :]
q_roots_integrated, q_joints_integrated, qdot_roots_integrated, qdot_joints_integrated = integrate(
time_vector_socp[-1], q_roots_init_this_time, q_joints_init_this_time, qdot_roots_init_this_time,
qdot_joints_init_this_time, tau_joints_socp,
k_socp, ref_socp, motor_noise_numerical_this_time, sensory_noise_numerical_this_time,
socp.nlp[0],
DMS_sensory_reference_func, forward_dynamics_func)
for i_random in range(nb_random):
for i_dof in range(4):
if i_dof < 3:
q_roots_integrated_socp[i_dof, :, i_reintegration * nb_random + i_random] = q_roots_integrated[i_dof + 3*i_random, :]
qdot_roots_integrated_socp[i_dof, :, i_reintegration * nb_random + i_random] = qdot_roots_integrated[i_dof + 3*i_random, :]
q_joints_integrated_socp[i_dof, :, i_reintegration * nb_random + i_random] = q_joints_integrated[i_dof + 4*i_random, :]
qdot_joints_integrated_socp[i_dof, :, i_reintegration * nb_random + i_random] = qdot_joints_integrated[i_dof + 4*i_random, :]
# if i_reintegration == 0:
# plt.figure()
# for i_shooting in range(5):
# for i_random in range(nb_random):
# plt.plot(np.ones((3, ))*i_shooting, q_roots_integrated_socp[:, i_shooting, i_random], '.b')
# plt.plot(np.ones((4, ))*i_shooting, q_joints_integrated_socp[:, i_shooting, i_random], '.b')
# plt.scatter(np.ones((7, ))*i_shooting, q_socp[:, i_shooting, i_random], color='m')
# plt.savefig("tempo_socp_0.png")
# # plt.show()
for i_random in range(nb_random):
for i_shooting in range(n_shooting):
if i_shooting < n_shooting:
# Joint friction
joint_frictions_socp[
:,
i_shooting,
i_reintegration * nb_random
+ (n_q - 3) * i_random : i_reintegration * nb_random
+ (n_q - 3) * (i_random + 1),
] = (
socp.nlp[0].model.friction_coefficients
@ qdot_joints_integrated_socp[:, i_shooting, i_reintegration * nb_random + i_random]
)
# Motor noise
motor_noises_socp[
:,
i_shooting,
i_reintegration * nb_random + i_random,
] = np.reshape(motor_noise_numerical_this_time[:, i_random, i_shooting], (-1, ))
# Feedback
k_fb_matrix = StochasticBioModel.reshape_to_matrix(
k_socp[:, i_shooting], socp.nlp[0].model.matrix_shape_k
)
feedbacks_socp[
:,
i_shooting,
i_reintegration * nb_random + i_random,
] = np.reshape(
k_fb_matrix
@ (
ref_socp[:, i_shooting]
- DMS_sensory_reference_func(
np.hstack(
(
q_roots_integrated_socp[:, i_shooting, i_reintegration * nb_random + i_random],
q_joints_integrated_socp[:, i_shooting, i_reintegration * nb_random + i_random],
)
),
np.hstack(
(
qdot_roots_integrated_socp[:, i_shooting, i_reintegration * nb_random + i_random],
qdot_joints_integrated_socp[:, i_shooting, i_reintegration * nb_random + i_random],
)
),
)
+ sensory_noise_numerical_this_time[:, i_random, i_shooting]
),
(-1, ),
)
q_socp_integrated = np.vstack(
(q_roots_integrated_socp, q_joints_integrated_socp)
)
qdot_socp_integrated = np.vstack(
(qdot_roots_integrated_socp, qdot_joints_integrated_socp)
)
return (
q_socp_integrated,
qdot_socp_integrated,
q_all_socp,
joint_frictions_socp,
motor_noises_socp,
feedbacks_socp,
)
def noisy_integrate_socp_variable(
biorbd_model_path,
time,
motor_noise_magnitude,
sensory_noise_magnitude,
q_roots_ocp,
q_joints_ocp,
qdot_roots_ocp,
qdot_joints_ocp,
tau_joints_ocp,
n_q,
n_shooting,
nb_random,
nb_reintegrations,
q_roots_socp_variable,
q_joints_socp_variable,
qdot_roots_socp_variable,
qdot_joints_socp_variable,
q_socp_variable,
qdot_socp_variable,
tau_joints_socp_variable,
k_socp_variable,
ref_socp_variable,
time_vector_socp_variable,
q_mean_socp_variable,
DMS_fb_noised_sensory_input_VARIABLE_func,
forward_dynamics_func,
):
def socp_variable_dynamics(q_roots, q_joints, qdot_roots, qdot_joints, tau_joints, k, ref_fb, motor_noise, sensory_noise,
nlp, DMS_fb_noised_sensory_input_VARIABLE_func, forward_dynamics_func):
k_matrix = StochasticBioModel.reshape_to_matrix(k, nlp.model.matrix_shape_k)
n_root = 3
n_joints = 4
ddq_roots = None
ddq_joints = None
for i in range(nlp.model.nb_random):
q_this_time = np.hstack((
q_roots[i * n_root: (i + 1) * n_root], q_joints[i * n_joints: (i + 1) * n_joints]
))
qdot_this_time = np.hstack((
qdot_roots[i * n_root: (i + 1) * n_root], qdot_joints[i * n_joints: (i + 1) * n_joints]
))
tau_this_time = tau_joints[:]
# Joint friction
tau_this_time -= nlp.model.friction_coefficients @ qdot_this_time[n_root:]
# Motor noise
motor_noise_computed = motor_acuity(motor_noise[:, i], tau_joints)
tau_this_time += motor_noise_computed
# Feedback
tau_this_time += k_matrix @ (
ref_fb - DMS_fb_noised_sensory_input_VARIABLE_func(q_this_time, qdot_this_time, sensory_noise[:, i])
)
ddq = forward_dynamics_func(q_this_time, qdot_this_time, tau_this_time)
ddq_roots = np.vstack((ddq_roots, ddq[:n_root])) if ddq_roots is not None else ddq[:n_root]
ddq_joints = np.vstack((ddq_joints, ddq[n_root:])) if ddq_joints is not None else ddq[n_root:]
return qdot_roots, qdot_joints, ddq_roots.reshape(-1, ), ddq_joints.reshape(-1, )
def integrate(tf, q_roots, q_joints, qdot_roots, qdot_joints, tau_joints, k, ref, motor_noise, sensory_noise,
nlp, DMS_fb_noised_sensory_input_VARIABLE_func, forward_dynamics_func):
dt = tf / n_shooting
h = dt / 5
q_roots_integrated = np.zeros((n_root * nb_random, n_shooting + 1))
q_joints_integrated = np.zeros((n_joints * nb_random, n_shooting + 1))
qdot_roots_integrated = np.zeros((n_root * nb_random, n_shooting + 1))
qdot_joints_integrated = np.zeros((n_joints * nb_random, n_shooting + 1))
for i_random in range(nb_random):
q_roots_integrated[n_root*i_random:n_root*(i_random+1), 0] = q_roots[:, i_random]
q_joints_integrated[n_joints*i_random:n_joints*(i_random+1), 0] = q_joints[:, i_random]
qdot_roots_integrated[n_root*i_random:n_root*(i_random+1), 0] = qdot_roots[:, i_random]
qdot_joints_integrated[n_joints*i_random:n_joints*(i_random+1), 0] = qdot_joints[:, i_random]
for i_shooting in range(n_shooting):
q_roots_this_time = q_roots_integrated[:, i_shooting]
q_joints_this_time = q_joints_integrated[:, i_shooting]
qdot_roots_this_time = qdot_roots_integrated[:, i_shooting]
qdot_joints_this_time = qdot_joints_integrated[:, i_shooting]
tau_joints_this_time = tau_joints[:, i_shooting]
k_this_time = k[:, i_shooting]
ref_this_time = ref[:, i_shooting]
motor_noise_this_time = motor_noise[:, :, i_shooting]
sensory_noise_this_time = sensory_noise[:, :, i_shooting]
for i_step in range(5):
q_roots_dot1, q_joints_dot1, qdot_roots_dot1, qdot_joints_dot1 = socp_variable_dynamics(q_roots_this_time,
q_joints_this_time,
qdot_roots_this_time,
qdot_joints_this_time,
tau_joints_this_time,
k_this_time,
ref_this_time,
motor_noise_this_time,
sensory_noise_this_time,
nlp,
DMS_fb_noised_sensory_input_VARIABLE_func,
forward_dynamics_func)
q_roots_dot2, q_joints_dot2, qdot_roots_dot2, qdot_joints_dot2 = socp_variable_dynamics(
q_roots_this_time + h / 2 * q_roots_dot1,
q_joints_this_time + h / 2 * q_joints_dot1,
qdot_roots_this_time + h / 2 * qdot_roots_dot1,
qdot_joints_this_time + h / 2 * qdot_joints_dot1,
tau_joints_this_time,
k_this_time,
ref_this_time,
motor_noise_this_time,
sensory_noise_this_time,
nlp,
DMS_fb_noised_sensory_input_VARIABLE_func,
forward_dynamics_func)
q_roots_dot3, q_joints_dot3, qdot_roots_dot3, qdot_joints_dot3 = socp_variable_dynamics(
q_roots_this_time + h / 2 * q_roots_dot2,
q_joints_this_time + h / 2 * q_joints_dot2,
qdot_roots_this_time + h / 2 * qdot_roots_dot2,
qdot_joints_this_time + h / 2 * qdot_joints_dot2,
tau_joints_this_time,
k_this_time,
ref_this_time,
motor_noise_this_time,
sensory_noise_this_time,
nlp,
DMS_fb_noised_sensory_input_VARIABLE_func,
forward_dynamics_func)
q_roots_dot4, q_joints_dot4, qdot_roots_dot4, qdot_joints_dot4 = socp_variable_dynamics(
q_roots_this_time + h * q_roots_dot3,
q_joints_this_time + h * q_joints_dot3,
qdot_roots_this_time + h * qdot_roots_dot3,
qdot_joints_this_time + h * qdot_joints_dot3,
tau_joints_this_time,
k_this_time,
ref_this_time,
motor_noise_this_time,
sensory_noise_this_time,
nlp,
DMS_fb_noised_sensory_input_VARIABLE_func,
forward_dynamics_func)
q_roots_this_time = q_roots_this_time + h / 6 * (
q_roots_dot1 + 2 * q_roots_dot2 + 2 * q_roots_dot3 + q_roots_dot4)
q_joints_this_time = q_joints_this_time + h / 6 * (
q_joints_dot1 + 2 * q_joints_dot2 + 2 * q_joints_dot3 + q_joints_dot4)
qdot_roots_this_time = qdot_roots_this_time + h / 6 * (
qdot_roots_dot1 + 2 * qdot_roots_dot2 + 2 * qdot_roots_dot3 + qdot_roots_dot4)
qdot_joints_this_time = qdot_joints_this_time + h / 6 * (
qdot_joints_dot1 + 2 * qdot_joints_dot2 + 2 * qdot_joints_dot3 + qdot_joints_dot4)
q_roots_integrated[:, i_shooting + 1] = q_roots_this_time
q_joints_integrated[:, i_shooting + 1] = q_joints_this_time
qdot_roots_integrated[:, i_shooting + 1] = qdot_roots_this_time
qdot_joints_integrated[:, i_shooting + 1] = qdot_joints_this_time
return q_roots_integrated, q_joints_integrated, qdot_roots_integrated, qdot_joints_integrated
n_q = socp_variable.nlp[0].model.nb_q
n_root = socp_variable.nlp[0].model.nb_root
n_joints = n_q - n_root
q_all_socp_variable = np.zeros((n_q * (nb_random + 1), n_shooting + 1))
for i_shooting in range(n_shooting + 1):
for i_random in range(nb_random):
q_all_socp_variable[i_random * n_q : (i_random + 1) * n_q, i_shooting] = np.reshape(
q_socp_variable[:, i_shooting, i_random], (-1,)
)
q_all_socp_variable[(i_random + 1) * n_q : (i_random + 2) * n_q, i_shooting] = np.reshape(
q_mean_socp_variable[:, i_shooting], (-1,)
)
q_roots_integrated_socp_variable = np.zeros((3, n_shooting + 1, nb_random * nb_reintegrations))
q_joints_integrated_socp_variable = np.zeros((n_q - 3, n_shooting + 1, nb_random * nb_reintegrations))
qdot_roots_integrated_socp_variable = np.zeros((3, n_shooting + 1, nb_random * nb_reintegrations))
qdot_joints_integrated_socp_variable = np.zeros((n_q - 3, n_shooting + 1, nb_random * nb_reintegrations))
joint_frictions_socp_variable = np.zeros((n_q - 3, n_shooting, nb_random * nb_reintegrations))
motor_noises_socp_variable = np.zeros((n_q - 3, n_shooting, nb_random * nb_reintegrations))
feedbacks_socp_variable = np.zeros((n_q - 3, n_shooting, nb_random * nb_reintegrations))
for i_reintegration in range(nb_reintegrations):
# Prepare the noises
np.random.seed(i_reintegration)
motor_noise_numerical = np.zeros((n_joints, nb_random, n_shooting + 1))
sensory_noise_numerical = np.zeros((2 * (n_joints + 1), nb_random, n_shooting + 1))
for i_random in range(nb_random):
for i_shooting in range(n_shooting):
motor_noise_numerical[:, i_random, i_shooting] = np.random.normal(
loc=np.zeros(motor_noise_magnitude.shape[0]),
scale=np.reshape(np.array(motor_noise_magnitude), (n_joints,)),
size=n_joints,
)
sensory_noise_numerical[:, i_random, i_shooting] = np.random.normal(
loc=np.zeros(sensory_noise_magnitude.shape[0]),
scale=np.reshape(np.array(sensory_noise_magnitude), (2 * (n_joints + 1),)),
size=2 * (n_joints + 1),
)
initial_cov = np.eye(2 * n_q) * np.hstack((np.ones((n_q,)) * 1e-4, np.ones((n_q,)) * 1e-7)) # P
states_init = np.random.multivariate_normal(
np.array([-0.0346, 0.1207, 0.2255, 0.0, 3.1, -0.1787, 0, 0, 2, 2.5 * np.pi, 0, 0, 0, 0]), initial_cov, nb_random
).T
# initial variability
q_roots_init_this_time = states_init[:n_root, :]
q_joints_init_this_time = states_init[n_root: n_q, :]
qdot_roots_init_this_time = states_init[n_q: n_q + n_root, :]
qdot_joints_init_this_time = states_init[n_q + n_root:, :]
q_roots_integrated, q_joints_integrated, qdot_roots_integrated, qdot_joints_integrated = integrate(
time_vector_socp[-1],
q_roots_init_this_time,
q_joints_init_this_time,
qdot_roots_init_this_time,
qdot_joints_init_this_time,
tau_joints_socp_variable,
k_socp_variable,
ref_socp_variable,
motor_noise_numerical,
sensory_noise_numerical,
socp_variable.nlp[0],
DMS_fb_noised_sensory_input_VARIABLE_func,
forward_dynamics_func)
for i_random in range(nb_random):
for i_dof in range(n_joints):
if i_dof < 3:
q_roots_integrated_socp_variable[i_dof, :, i_reintegration * nb_random + i_random] = q_roots_integrated[i_dof + n_root*i_random, :]
qdot_roots_integrated_socp_variable[i_dof, :, i_reintegration * nb_random + i_random] = qdot_roots_integrated[i_dof + n_root*i_random, :]
q_joints_integrated_socp_variable[i_dof, :, i_reintegration * nb_random + i_random] = q_joints_integrated[i_dof + n_joints*i_random, :]
qdot_joints_integrated_socp_variable[i_dof, :, i_reintegration * nb_random + i_random] = qdot_joints_integrated[i_dof + n_joints*i_random, :]
# if i_reintegration == 0:
# plt.figure()
# for i_shooting in range(5):
# for i_random in range(nb_random):
# plt.plot(np.ones((n_root, ))*i_shooting, q_roots_integrated_socp_variable[:, i_shooting, i_random], '.b')
# plt.plot(np.ones((n_joints, ))*i_shooting, q_joints_integrated_socp_variable[:, i_shooting, i_random], '.b')
# plt.scatter(np.ones((n_root + n_joints, ))*i_shooting, q_socp_variable[:, i_shooting, i_random], color='m')
# plt.savefig("tempo_socp_variable_0.png")
# # plt.show()
for i_random in range(nb_random):
for i_shooting in range(n_shooting):
if i_shooting < n_shooting:
k_matrix = StochasticBioModel.reshape_to_matrix(
k_socp_variable[:, i_shooting], socp_variable.nlp[0].model.matrix_shape_k
)
# Joint friction
joint_frictions_socp_variable[
:,
i_shooting,
i_reintegration * nb_random
+ n_joints * i_random : i_reintegration * nb_random
+ n_joints * (i_random + 1),
] = (
socp_variable.nlp[0].model.friction_coefficients
@ qdot_joints_integrated_socp_variable[:, i_shooting, i_reintegration * nb_random + i_random]
)
# Motor noise
motor_noise_computed = motor_acuity(motor_noise_numerical[:, i_random, i_shooting], tau_joints_socp_variable[:, i_shooting])
motor_noise_computed[1] = 0 # No noise on the eyes
motor_noises_socp_variable[
:,
i_shooting,
i_reintegration * nb_random + i_random,
] = np.array(motor_noise_computed).reshape(-1, )
# Feedback
feedbacks_socp_variable[
:,
i_shooting,
i_reintegration * nb_random + i_random,
] = np.reshape(
k_matrix
@ (
ref_socp_variable[:, i_shooting]
- DMS_fb_noised_sensory_input_VARIABLE_func(
np.hstack(
(
q_roots_integrated_socp_variable[:, i_shooting, i_reintegration * nb_random + i_random],
q_joints_integrated_socp_variable[:, i_shooting, i_reintegration * nb_random + i_random],
)
),
np.hstack(
(
qdot_roots_integrated_socp_variable[:, i_shooting, i_reintegration * nb_random + i_random],
qdot_joints_integrated_socp_variable[:, i_shooting, i_reintegration * nb_random + i_random],
)
),
sensory_noise_numerical[:, i_random, i_shooting]
)
),
(-1, ),
)
q_socp_variable_integrated = np.vstack(
(q_roots_integrated_socp_variable, q_joints_integrated_socp_variable)
)
qdot_socp_variable_integrated = np.vstack(
(qdot_roots_integrated_socp_variable, qdot_joints_integrated_socp_variable)
)
return (
q_socp_variable_integrated,
qdot_socp_variable_integrated,
q_all_socp_variable,
joint_frictions_socp_variable,
motor_noises_socp_variable,
feedbacks_socp_variable,
)
def noisy_integrate_socp_feedforward(
biorbd_model_path,
time,
motor_noise_magnitude,
sensory_noise_magnitude,
q_roots_ocp,
q_joints_ocp,
qdot_roots_ocp,
qdot_joints_ocp,
tau_joints_ocp,
n_q,
n_shooting,
nb_random,
nb_reintegrations,
q_roots_socp_feedforward,
q_joints_socp_feedforward,
qdot_roots_socp_feedforward,
qdot_joints_socp_feedforward,
q_socp_feedforward,
qdot_socp_feedforward,
tau_joints_socp_feedforward,
k_socp_feedforward,
ref_fb_socp_feedforward,
ref_ff_socp_feedforward,
time_vector_socp_feedforward,
q_mean_socp_feedforward,
DMS_sensory_reference_no_eyes_func,
DMS_ff_sensory_input_func,
forward_dynamics_func,
):
def socp_feedforward_dynamics(q_roots, q_joints, qdot_roots, qdot_joints, tau_joints, k, ref_fb, ref_ff, motor_noise, sensory_noise,
current_time, tf, nlp, DMS_sensory_reference_no_eyes_func, DMS_ff_sensory_input_func, forward_dynamics_func):
k_matrix = StochasticBioModel.reshape_to_matrix(k, nlp.model.matrix_shape_k)
k_matrix_fb = k_matrix[:, :-1]
k_matrix_ff = k_matrix[:, -1]
n_root = 3
n_joints = 5
ddq_roots = None
ddq_joints = None
for i in range(nlp.model.nb_random):
q_this_time = np.hstack((
q_roots[i * n_root: (i + 1) * n_root], q_joints[i * n_joints: (i + 1) * n_joints]
))
qdot_this_time = np.hstack((
qdot_roots[i * n_root: (i + 1) * n_root], qdot_joints[i * n_joints: (i + 1) * n_joints]
))
tau_this_time = tau_joints[:]