def approx_lwr_batch(self):
model = LWR(nb_features=10)
self.make_nonlinear_batch_data()
start = time.process_time()
model.train_lwls(self.x_data, self.y_data)
print("LWR time:", time.process_time() - start)
model.plot(self.x_data, self.y_data)
def perform_new_dmp(given_traj,
initial=None,
end=None,
duration=1.0,
dt=0.001,
use_improved=True):
traj_1d = np.reshape(given_traj, np.size(given_traj))
list_traj = traj_1d.tolist()
if not initial:
initial = list_traj[0]
if not end:
end = list_traj[-1]
while (hasattr(initial, "__getitem__")):
initial = initial[0]
while (hasattr(end, "__getitem__")):
end = end[0]
traj_freq = int(duration / dt)
traj = DiscreteDMP.compute_derivatives(list_traj, traj_freq)
traj = list(traj)
dmp = DiscreteDMP(improved_version=use_improved,
reg_model=LWR(activation=0.1,
exponentially_spaced=True,
n_rfs=20))
dmp.learn_batch(traj, traj_freq)
dmp_adapt = DiscreteDMP(
improved_version=use_improved,
reg_model=dmp.lwr_model) #copy.deepcopy(dmp.lwr_model))
dmp_adapt._is_learned = True
dmp.delta_t = dt
dmp.setup(traj_1d[0], traj_1d[-1], duration)
dmp_adapt.delta_t = dt
dmp_adapt.setup(initial, end, duration)
traj_reproduced = []
traj_adapted = []
for _ in range(int(dmp.tau / dmp.delta_t)):
dmp.run_step()
dmp_adapt.run_step()
traj_reproduced.append(dmp.x)
traj_adapted.append(dmp_adapt.x)
traj_reproduced = np.array(traj_reproduced).reshape(np.size(given_traj))
print(np.size(traj_adapted))
traj_adapted = np.array(traj_adapted).reshape(np.size(given_traj))
print(np.size(traj_adapted))
return [traj_adapted, traj_reproduced]
def main():
# start and goal of the movement (1-dim)
start = 0.5
goal = 1.0
####### generate a trajectory (minimum jerk)
# duration
duration = 1.0
# time steps
delta_t = 0.001
# trajectory is a list of 3-tuples with (pos,vel,acc)
traj = min_jerk_traj(start, goal, 1.0, delta_t)
traj_freq = int(1.0 / delta_t)
####### learn DMP
dmp = DiscreteDMP(
False,
LWR(activation=0.3,
exponentially_spaced=False,
n_rfs=8,
use_offset=True))
dmp.learn_batch(traj, traj_freq)
####### learn DMP
# setup DMP with start and goal
dmp.setup(start + 0.4, goal + 0.2, duration)
# trajectory
reproduced_traj = []
# states of canonical system (plotting)
s = []
s_time = []
# run steps (for each point of the sample trajectory)
for _ in xrange(int(dmp.tau / dmp.delta_t)):
# change goal while execution
#if x == 500:
# dmp.goal = 4.0
# run a single integration step
dmp.run_step()
# remember canonical system values
s.append(dmp.s)
s_time.append(dmp.s_time)
# save reproduced trajectory
reproduced_traj.append([dmp.x, dmp.xd, dmp.xdd])
####### PLOTTING
fig_pos = plt.figure('dmp batch learn from min jerk', figsize=(7, 5))
ax_pos2 = fig_pos.add_subplot(111)
plot_time = np.arange(len(traj)) * delta_t
ax_pos2.plot(plot_time, np.asarray(traj)[:, 0], label='demonstration')
ax_pos2.plot(plot_time,
np.asarray(reproduced_traj)[:, 0],
label='adapted reproduction',
linestyle='dashed')
ax_pos2.legend(loc='upper left')
plt.show()
# create figure
fig = plt.figure('dmp batch learn from min jerk', figsize=(16, 4.6))
# create axes
ax_pos = fig.add_subplot(131)
ax_vel = fig.add_subplot(132)
ax_acc = fig.add_subplot(133)
# plot on the axes
plot_pos_vel_acc_trajectory((ax_pos, ax_vel, ax_acc),
traj,
delta_t,
label='demonstration')
plot_pos_vel_acc_trajectory((ax_pos, ax_vel, ax_acc),
reproduced_traj,
dmp.delta_t,
label='reproduction',
linestyle='dashed')
fig.tight_layout()
plt.show()
fig = plt.figure('ftarget', figsize=(16, 4.6))
# plot ftarget (real and predicted)
ax_ft = fig.add_subplot(131)
ax_ft.plot(dmp.target_function_input,
dmp.target_function_ouput,
linewidth=2,
label=r'$f_{target}(s)$')
ax_ft.plot(dmp.target_function_input,
dmp.target_function_predicted,
'--',
linewidth=2,
label=r'$f_{predicted}(s)$') #dashes=(3, 3)
ax_ft.set_xlabel(r'$s$')
ax_ft.set_ylabel(r'$f(s)$')
ax_ft.legend()
# kernels (lwr)
ax_kernel = fig.add_subplot(132)
dmp.lwr_model.plot_kernels(ax_kernel)
ax_kernel.set_xlabel(r'$s$')
ax_kernel.set_ylabel(r'$\psi(s)$')
# canonical system
# ax_cs = fig.add_subplot(236)
# ax_cs.plot(s_time, s)
# ax_cs.set_xlabel('Time [s]')
# ax_cs.set_ylabel(r'$s$')
# weights of kernels (w)
ax_w = fig.add_subplot(133)
ax_w.set_xlabel(r'$s$')
ax_w.set_ylabel(r'$f(s)$')
dmp.lwr_model.plot_linear_models(ax_w)
# lwr_wights = dmp.lwr_model.get_thetas()
# ax_w.bar(range(len(lwr_wights)), lwr_wights, width=0.3)
# ax_w.set_xlabel('$w_i$')
# ax_w.set_ylabel('')
fig.tight_layout()
plt.show()
def __init__(self, transf_system, reg_model=None):
self.ts = transf_system
# state variables
# -----------------------------
self.start = 0.0
self.goal = 1.0
self.tau = 1.0
# Cannonical System
# -----------------------------
# s_min
self.cutoff = 0.001
# alpha (canonical system parameter)
self.alpha = abs(math.log(self.cutoff))
# Canonical System
self.s = 1.0 # canonical system is starting with 1.0
self.s_time = 0.0
# Attractor
# -----------------------------
# spring term
self.K = 50.0
# damping term
self.D = self.K / 4
# time steps (for the run)
self.delta_t = 0.001
# Transformation System
# ----------------------------
# current position, velocity, acceleration
self.x = 0.0
self.xd = 0.0
self.xdd = 0.0
# internal variables
''' xd not scaled by tau aka v'''
self._raw_xd = 0.0
self.f = 0
# target function input (x) and output (y)
self.target_function_input = None
self.Fd = None
# debugging (y values predicted by fitted lwr model)
self.Fp = None
# do not predict f by approximated function,
# use values of ft directly only works if duration is 1.0!!
self.use_ft = False
# create LWR model and set parameters
# -----------------------------
if not reg_model:
# default regression model
self.lwr_model = LWR(activation=0.1,
exponentially_spaced=True,
n_rfs=20)
else:
# custom regression model
self.lwr_model = reg_model
# is the DMP initialized?
self._is_learned = False
def main():
# duration
duration = 1.0
# adaption offset
adapt_offset = +0.02
# time steps
delta_t = 0.001
# load position trajectory
traj_pos = json.load(open("traj_full.json", 'r'))["x"][2000:8000][::6] #[5000:8000][::3]
# rest start and goal position out of trajectory
start = traj_pos[0]
goal = traj_pos[-1]
traj_freq = int(1.0 / delta_t)
# calc it here for easier drawing
traj = DiscreteDMP.compute_derivatives(traj_pos, traj_freq)
print(type(traj))
traj = list(traj)
####### learn DMP
dmp = DiscreteDMP(True, reg_model=LWR(activation=0.1, exponentially_spaced=True, n_rfs=20))
#dmp.use_ft = True
dmp.learn_batch(traj, traj_freq)
dmp_adapt = DiscreteDMP(True, reg_model=dmp.lwr_model) #copy.deepcopy(dmp.lwr_model))
dmp_adapt._is_learned = True
####### learn DMP
# setup DMP with start and goal
dmp.delta_t = delta_t
dmp.setup(start, goal, duration)
dmp_adapt.delta_t = delta_t
dmp_adapt.setup(start, goal + adapt_offset, duration)
# trajectory
traj_reproduced = []
traj_adapted = []
# states of canonical system (plotting)
s = []
s_time = []
# run steps (for each point of the sample trajectory)
for _ in range(int(dmp.tau / dmp.delta_t)):
# change goal while execution
#if x == 500:
# dmp.goal = 4.0
# run a single integration step
dmp.run_step()
dmp_adapt.run_step()
# remember canonical system values
s.append(dmp.s)
s_time.append(dmp.s_time)
# save reproduced trajectory
traj_reproduced.append([dmp.x, dmp.xd, dmp.xdd])
traj_adapted.append([dmp_adapt.x, dmp_adapt.xd, dmp_adapt.xdd])
####### PLOTTING
# create figure
fig = plt.figure('dmp', figsize=(6, 4))
# create axes
ax_pos = fig.add_subplot(111)
# plot on the axes
#ax_pos.plot(np.arange(0,1,0.001), traj_pos)
plot_time = np.arange(len(traj)) * delta_t
ax_pos.plot(plot_time, np.asarray(traj)[:, 0], label='demonstration')
ax_pos.plot(plot_time, np.asarray(traj_reproduced)[:, 0], label='reproduction', linestyle='dashed')
ax_pos.plot(plot_time, np.asarray(traj_adapted)[:, 0], label='adapted (%+0.2f)' % adapt_offset)
ax_pos.legend(loc='lower left')
# plot_pos_vel_acc_trajectory((ax_pos, ax_vel, ax_acc), traj, dmp.delta_t, label='demonstration')
# plot_pos_vel_acc_trajectory((ax_pos, ax_vel, ax_acc), traj_reproduced, dmp.delta_t, label='reproduction', linestyle='dashed')
# plot_pos_vel_acc_trajectory((ax_pos, ax_vel, ax_acc), traj_adapted, dmp.delta_t, label='adapted (+0.02)')
fig.tight_layout()
plt.show()
#
fig2 = plt.figure('lwr', figsize=(6, 4))
#
ax_ft = fig2.add_subplot(211)
ax_ft.plot(dmp.target_function_input, dmp.target_function_ouput, linewidth=2, label=r'$f_{target}(s)$')
ax_ft.plot(dmp.target_function_input, dmp.target_function_predicted, '--', linewidth=2, label=r'$f_{predicted}(s)$') #dashes=(3, 3)
plt.show()
def perform_new_dmp_adapted(given_traj,
initial=None,
end=None,
duration=1.0,
dt=None,
use_improved=True,
k=None,
d=None):
traj_1d = np.reshape(given_traj, np.size(given_traj))
list_traj = traj_1d.tolist()
if not initial:
initial = list_traj[0]
if not end:
end = list_traj[-1]
if (isinstance(initial, (list, np.ndarray))):
print(initial)
initial = initial[0]
if (isinstance(end, (list, np.ndarray))):
end = end[0]
traj_freq = int(np.size(given_traj))
if not dt:
dt = duration / traj_freq
traj = DiscreteDMP.compute_derivatives(list_traj, traj_freq)
traj = list(traj)
dmp = DiscreteDMP(improved_version=use_improved,
reg_model=LWR(activation=0.1,
exponentially_spaced=True,
n_rfs=20),
K=k,
D=d)
dmp.learn_batch(traj, traj_freq)
dmp_adapt = DiscreteDMP(improved_version=use_improved,
reg_model=dmp.lwr_model,
K=k,
D=d) #copy.deepcopy(dmp.lwr_model))
dmp_adapt._is_learned = True
dmp.delta_t = dt
dmp.setup(traj_1d[0], traj_1d[-1], duration)
dmp_adapt.delta_t = dt
dmp_adapt.setup(initial, end, duration)
traj_reproduced = []
traj_adapted = []
for _ in range(int(dmp.tau / dmp.delta_t)):
dmp.run_step()
dmp_adapt.run_step()
traj_reproduced.append(dmp.x)
traj_adapted.append(dmp_adapt.x)
#print(np.size(traj_adapted))
traj_adapted = np.array(traj_adapted).reshape(np.size(given_traj))
#print(np.size(traj_adapted))
#print(traj_adapted)
return traj_adapted
#def perform_dmp_improved(traj, initial=[], end=[], ay=None, by=None):
# #set up endpoints if none specified
# if not initial:
# initial = traj[0]
# if not end:
# end = traj[max(np.shape(traj)) - 1]
# #transpose if necessary
# if len(np.shape(traj)) > 1:
# if np.shape(traj)[0] > np.shape(traj)[1]:
# traj = np.transpose(traj)
# ntraj = np.reshape(traj, (1, max(np.shape(traj))))
# ## DMP ##
# dmp_traj = perform_dmp(ntraj, [initial, end], alpha_y=ay, beta_y=by)
# dmp_traj = np.reshape(dmp_traj, np.size(traj))
# return dmp_traj
def __init__(self, improved_version=False, reg_model=None):
## time constants choosen for critical damping
# s_min
self.cutoff = 0.001
# alpha (canonical system parameter)
self.alpha = abs(math.log(self.cutoff))
# spring term
self.k_gain = 50.0
# damping term
self.d_gain = self.k_gain / 4
# time steps (for the run)
self.delta_t = 0.001
## state variables
'''start position aka $x_0$'''
self.start = 0.0
'''goal position aka $g$'''
self.goal = 1.0
'''movement duration: temporal scaling factor $\tau$'''
self.tau = 1.0
## Transformation System
# current position, velocity, acceleration
'''$x$ (position)'''
self.x = 0.0
'''$\dot x$ aka v (velocity)'''
self.xd = 0.0
'''$\ddot x$ aka \dot v (acceleration)'''
self.xdd = 0.0
# internal variables
''' xd not scaled by tau aka v'''
self._raw_xd = 0.0
'''current value of function f (perturbation function)'''
self.f = 0.0
# target function input (x) and output (y)
self.target_function_input = None
self.target_function_ouput = None
# debugging (y values predicted by fitted lwr model)
self.target_function_predicted = None
# do not predict f by approximated function, use values of ft directly - only works if duration is 1.0!!
self.use_ft = False
# create LWR model and set parameters
if not reg_model:
# default regression model
self.lwr_model = LWR(activation=0.1, exponentially_spaced=True, n_rfs=20)
else:
# custom regression model
self.lwr_model = reg_model
# Canonical System
self.s = 1.0 # canonical system is starting with 1.0
self.s_time = 0.0
# is the DMP initialized?
self._initialized = False
self._is_learned = False
# set the correct transformation and ftarget functions
if improved_version:
self._transformation_func = self._transformation_func_improved
self._ftarget_func = self._ftarget_func_improved
else:
self._transformation_func = self._transformation_func_original
self._ftarget_func = self._ftarget_func_original
def perform_new_dmp_adapted(given_traj,
initial=None,
end=None,
duration=1.0,
dt=None,
use_improved=True,
k=None,
d=None):
traj_1d = np.reshape(given_traj, np.size(given_traj))
list_traj = traj_1d.tolist()
if not initial:
initial = list_traj[0]
if not end:
end = list_traj[-1]
if (isinstance(initial, (list, np.ndarray))):
print(initial)
initial = initial[0]
if (isinstance(end, (list, np.ndarray))):
end = end[0]
traj_freq = int(np.size(given_traj))
if not dt:
dt = duration / traj_freq
traj = DiscreteDMP.compute_derivatives(list_traj, traj_freq)
traj = list(traj)
dmp = DiscreteDMP(improved_version=use_improved,
reg_model=LWR(activation=0.1,
exponentially_spaced=True,
n_rfs=20),
K=k,
D=d)
dmp.learn_batch(traj, traj_freq)
dmp_adapt = DiscreteDMP(improved_version=use_improved,
reg_model=dmp.lwr_model,
K=k,
D=d) #copy.deepcopy(dmp.lwr_model))
dmp_adapt._is_learned = True
dmp.delta_t = dt
dmp.setup(traj_1d[0], traj_1d[-1], duration)
dmp_adapt.delta_t = dt
dmp_adapt.setup(initial, end, duration)
traj_reproduced = []
traj_adapted = []
for _ in range(int(dmp.tau / dmp.delta_t)):
dmp.run_step()
dmp_adapt.run_step()
traj_reproduced.append(dmp.x)
traj_adapted.append(dmp_adapt.x)
#print(np.size(traj_adapted))
traj_adapted = np.array(traj_adapted).reshape(np.size(given_traj))
#print(np.size(traj_adapted))
#print(traj_adapted)
return traj_adapted
