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add new world + add traj. segmentation in GMM

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This commit is contained in:
Brian Delhaisse
2019-07-12 19:42:12 +02:00
parent 557c4620df
commit b7bf9a0d73
13 changed files with 98024 additions and 99 deletions
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pyrobolearn/models/basics/pca.py
+2 -2
View File
@@ -78,11 +78,11 @@ class PCA(object):
##############
@property
def eigenvalues(self): # alias to evals
def eigenvalues(self): # alias to evals
return self.evals
@property
def eigenvectors(self): # alias to evecs
def eigenvectors(self): # alias to evecs
return self.evecs
##################
pyrobolearn/models/gmm/gmm.py
+419 -97
View File
@@ -10,12 +10,16 @@ try:
import cPickle as pickle
except ImportError as e:
import pickle
from scipy import signal
from scipy import interpolate
from sklearn.cluster import KMeans
from sklearn.mixture import GaussianMixture, BayesianGaussianMixture
# from pyrobolearn.models.model import Model
from pyrobolearn.models.gaussian import Gaussian
from pyrobolearn.filters.utils import smooth
__author__ = "Brian Delhaisse"
__copyright__ = "Copyright 2018, PyRoboLearn"
@@ -182,6 +186,9 @@ class GMM(object):
if len(priors) != len(gaussians):
raise ValueError("The number of priors and gaussians are differents")
# Set dimensionality
self._dimensionality = dimensionality if isinstance(dimensionality, int) and dimensionality > 0 else 0
##############
# Properties #
##############
@@ -210,7 +217,7 @@ class GMM(object):
"""Return the dimensionality of the mean"""
if len(self._gaussians) > 0:
return self._gaussians[0].dim
return 0
return self._dimensionality
# alias
dim = dimensionality
@@ -698,15 +705,69 @@ class GMM(object):
"""
return - 2 * self.log_likelihood(x) + self.num_parameters * np.log(self.num_data)
def estimate_num_components_from_trajectory_curvature_segmentation(self, data):
"""
def estimate_num_components_from_trajectory_curvature_segmentation(self, data, interpolation_method='cubic',
smooth_curvature=True):
r"""
Estimate the number of components / Gaussians needed to model a temporal and spatial trajectory based on
trajectory curvature segmentation.
trajectory curvature segmentation. This only works for sequential temporal and spatial data. The first
dimension is assumed to be the time, and the other dimensions have to be spatial data (x [,y [,z]]).
Warnings: this only makes sense with trajectories.
Warnings: this initialization only makes sense with spatial trajectories, and is deterministic. It also
assumes that the trajectories are similar. Currently, we only accept 4D curves (t, x, y, z).
From [1], let's assume a D-dimensional curve :math:`\pmb{x}(t) \in \mathbb{R}^D`, for which we can define a
Frenet frame at each time step :math:`\{\pmb{e}_1(t), ..., \pmb{e}_D(t)\}`. That curve can be the mean
trajectory computed from all the provided trajectories. It might be necessary to align them using dynamic time
wrapping beforehand, The basis vectors are computed using the Gram-Schmidt orthogonalization process, where
the first basis is computed using:
.. math::
\pmb{q}_1(t) &= \frac{\partial \pmb{x}(t)}{\partial t} \\
\pmb{e}_1(t) &= \frac{\pmb{q}_1(t)}{|| \pmb{q}_1(t) ||}
and the subsequent basis are computed recursively using:
.. math::
\pmb{q}_j(t) &= \frac{\partial^j \pmb{x}(t)}{\partial t^j} - \sum_{i=1}^{j-1}
\pmb{e}_i(t)^\top \left( \frac{\partial^j \pmb{x}(t)}{\partial t^j} \right) \pmb{e}_i(t) \\
\pmb{e}_1(t) &= \frac{ \pmb{q}_j(t) }{ ||\pmb{q}_j(t)|| }
Based on these basis vectors, we can compute the generalized curvatures :math:`\{\chi_j(t)\}_{j=1}^{D-1}`,
where:
.. math::
\chi_j(t) = \frac{\pmb{e}_{j+1}(t)^\top \left( \frac{\partial \pmb{e}_j(t)}{\partial t}\right)}
{|| \frac{\partial \pmb{x}(t)}{\partial t} ||}.
Note that, this involves the computation of the jth derivative of the curve wrt to the time for each dimension
:math:`j \in \{1, ..., D\}`. In order to get satisfactory estimations, we can locally approximated the curve by
a D-dimensional polynomial function. "The derivatives can subsequently be analytically computed and are
re-sampled to provide trajectories of T data points" [1]. For instance, for a 3D curve we can use a Hermite
interpolator (a 5th order polynomial) or a 3D polynomial function.
The total norm curvature of a D-dimensional curve is finally defined as:
.. math:: \Sigma(t) = \sqrt{\sum_{i=1}^{D-2} \chi_i(t)^2}
The local maxima of :math:`\Sigma(t)` provide points for segmenting the trajectory, where the data between
two segmentation points represent parts of the trajectory for which directions do not vary much" [1]. The
number of local maxima + 1 provides the number of Gaussian needed.
Args:
data (np.array[T,D]): trajectory data.
data (np.array[N,D], list of np.array[T,D], np.array[N,T,D]): data matrix(ces). For each matrix, we assume
that the first dimension is the time. If only a 2D matrix is provided, the trajectory can be
concatenated but the time has to be relative; that is when you record a trajectory the time
has to between [t0, tf], and when you record another trajectory it has to be between [t0',tf'] where
t0' < tf. We will use that to reshape the matrix.
interpolation_method (str): "Specifies the kind of interpolation as a string ('linear', 'nearest', 'zero',
'slinear', 'quadratic', 'cubic', 'previous', 'next', where 'zero', 'slinear', 'quadratic' and 'cubic'
refer to a spline interpolation of zeroth, first, second or third order; 'previous' and 'next' simply
return the previous or next value of the point) or as an integer specifying the order of the spline
interpolator to use. Default is 'cubic'." from ``scipy.interpolate.interp1d`` documentation.
smooth_curvature (bool): if we should smooth the total norm curvature before looking for the local maxima.
Returns:
int: number of components needed
@@ -714,6 +775,215 @@ class GMM(object):
References:
- [1] "Robot Programming by Demonstration: A Probabilistic Approach", Calinon, 2009, Chap 2.8.2
"""
indices = self._get_curvature_segmentation_points(data, interpolation_method=interpolation_method,
smooth_curvature=smooth_curvature)[0]
return len(indices) - 1 # because the indices contain the first and end points
@staticmethod
def _get_curvature_segmentation_points(data, interpolation_method='cubic', smooth_curvature=True):
r"""
Get the trajectory curvature segmentation points. This only works for sequential temporal and
spatial data. The first dimension is assumed to be the time, and the other dimensions have to be spatial data
(x [,y [,z]]).
Warnings: this initialization only makes sense with spatial trajectories, and is deterministic. It also
assumes that the trajectories are similar. Currently, we only accept 4D curves (t, x, y, z).
From [1], let's assume a D-dimensional curve :math:`\pmb{x}(t) \in \mathbb{R}^D`, for which we can define a
Frenet frame at each time step :math:`\{\pmb{e}_1(t), ..., \pmb{e}_D(t)\}`. That curve can be the mean
trajectory computed from all the provided trajectories. It might be necessary to align them using dynamic time
wrapping beforehand, The basis vectors are computed using the Gram-Schmidt orthogonalization process, where
the first basis is computed using:
.. math::
\pmb{q}_1(t) &= \frac{\partial \pmb{x}(t)}{\partial t} \\
\pmb{e}_1(t) &= \frac{\pmb{q}_1(t)}{|| \pmb{q}_1(t) ||}
and the subsequent basis are computed recursively using:
.. math::
\pmb{q}_j(t) &= \frac{\partial^j \pmb{x}(t)}{\partial t^j} - \sum_{i=1}^{j-1}
\pmb{e}_i(t)^\top \left( \frac{\partial^j \pmb{x}(t)}{\partial t^j} \right) \pmb{e}_i(t) \\
\pmb{e}_1(t) &= \frac{ \pmb{q}_j(t) }{ ||\pmb{q}_j(t)|| }
Based on these basis vectors, we can compute the generalized curvatures :math:`\{\chi_j(t)\}_{j=1}^{D-1}`,
where:
.. math::
\chi_j(t) = \frac{\pmb{e}_{j+1}(t)^\top \left( \frac{\partial \pmb{e}_j(t)}{\partial t}\right)}
{|| \frac{\partial \pmb{x}(t)}{\partial t} ||}.
Note that, this involves the computation of the jth derivative of the curve wrt to the time for each dimension
:math:`j \in \{1, ..., D\}`. In order to get satisfactory estimations, we can locally approximated the curve by
a D-dimensional polynomial function. "The derivatives can subsequently be analytically computed and are
re-sampled to provide trajectories of T data points" [1]. For instance, for a 3D curve we can use a Hermite
interpolator (a 5th order polynomial) or a 3D polynomial function.
The total norm curvature of a D-dimensional curve is finally defined as:
.. math:: \Sigma(t) = \sqrt{\sum_{i=1}^{D-2} \chi_i(t)^2}
The local maxima of :math:`\Sigma(t)` provide points for segmenting the trajectory, where the data between
two segmentation points represent parts of the trajectory for which directions do not vary much" [1].
Based on them, we can then compute the mean of each Gaussian by taking the center between two segmentation
points, and compute the covariance matrix by looking at the variation of each trajectory along each dimension
(for the time dimension, we check the distance between the mean of a Gaussian and one of its associated
segmentation point).
Args:
data (np.array[N,D], list of np.array[T,D], np.array[N,T,D]): data matrix(ces). For each matrix, we assume
that the first dimension is the time. If only a 2D matrix is provided, the trajectory can be
concatenated but the time has to be relative; that is when you record a trajectory the time
has to between [t0, tf], and when you record another trajectory it has to be between [t0',tf'] where
t0' < tf. We will use that to reshape the matrix.
interpolation_method (str): "Specifies the kind of interpolation as a string ('linear', 'nearest', 'zero',
'slinear', 'quadratic', 'cubic', 'previous', 'next', where 'zero', 'slinear', 'quadratic' and 'cubic'
refer to a spline interpolation of zeroth, first, second or third order; 'previous' and 'next' simply
return the previous or next value of the point) or as an integer specifying the order of the spline
interpolator to use. Default is 'cubic'." from ``scipy.interpolate.interp1d`` documentation.
smooth_curvature (bool): if we should smooth the total norm curvature before looking for the local maxima.
Returns:
np.array: indices where we have local maxima in the total norm curvature; i.e. segmenting points. The
beginning and end points are also included in the indices. Thus, the number of needed gaussians is
the size of the returned array - 1.
np.array: reshaped trajectories of shape (N, T, D). The trajectories have been reshaped such that they
have the same size (T, D) where T is the maximum time length that was found in the data.
np.array: mean trajectory on the reshaped trajectory. It has a shape (T, D).
References:
- [1] "Robot Programming by Demonstration: A Probabilistic Approach", Calinon, 2009, Chap 2.8.2
"""
# check shape of data
if isinstance(data, list): # if data is a list of np.array[T,D]
for d in data:
if not isinstance(d, np.ndarray):
raise TypeError("Expecting each element in the given data list to be a np.array, instead got: "
"{}".format(type(d)))
if len(d.shape) != 2:
raise ValueError("Expecting each element in the given data list to be a np.array of shape 2, "
"instead got: {}".format(d.shape))
elif isinstance(data, np.ndarray): # if data is a np.array[N,T,D] or np.array[N,D]
if len(data.shape) != 2 and len(data.shape) != 3:
raise ValueError("Expecting the given data array to have a shape of 2 or 3 (i.e. len(shape)), "
"instead got: {}".format(data.shape))
# if 2D matrix, we have to create a list of np.array[T,D]
# we go through each element and when the time associated with an element is smaller than the preceding
# time, we create a trajectory
if len(data.shape) == 2:
d = []
t_prec = data[0][0]
i_prec = 0 # index to cut the data
for i, step in enumerate(data):
t = step[0] # get current time
# if current time is smaller than previous time, we assume it is a new trajectory as we can
# go to the past ;)
if t < t_prec or i == len(data) - 1:
d.append(data[i_prec:i + 1])
i_prec = i
# update precedent time
t_prec = t
# set data
data = d # list of np.array[T,D]
else:
raise TypeError("Expecting the given data to be a list of 2D np.array, a 2D np.array, or 3D np.array, "
"instead got: {}".format(type(data)))
# check if we have enough trajectories to compute the covariances
if len(data) == 0 or len(data) < data[0].shape[1]:
raise ValueError("Expecting to have more trajectories than the dimensionality of each trajectory.")
# fit a polynomial function to each trajectory
data_fcts, num_points, periods, t0s = [], [], [], []
for d in data:
period = (d[-1, 0] - d[0, 0]) # T = (tf - t0)
t = d[:, 0] - d[0, 0] # t = [t0, ..., tf] --> t = [0, ..., tf-t0]
t /= period # t = [0, ..., tf-t0] --> t= [0, ..., 1]
# compute interpolation function
fct = interpolate.interp1d(t, d[:, 1:], kind=interpolation_method, axis=0, assume_sorted=True)
# add useful variables
data_fcts.append(fct)
num_points.append(d.shape[0])
periods.append(period)
t0s.append(d[0, 0])
# sample trajectories (such that they have the same size)
num_max_points = np.max(num_points)
t = np.linspace(0, 1, num_max_points)
trajectories = np.array([fct(t) for fct in data_fcts]) # shape=(N,T,D-1); (D-1) because we removed the time
# compute mean trajectory from which we will compute the Frenet frame
mean_traj = np.mean(trajectories, axis=0) # (T, D-1)
# fit polynomial function to the mean trajectory
# currently, we only consider cubic spline (3D) interpolation
if mean_traj.shape[1] > 3:
raise ValueError("Currently, this method doesn't accept more than 4 dimensions (time, x, y, z), "
"however {} dimensions were given".format(mean_traj.shape[1] + 1))
interpolator = interpolate.CubicSpline(t, mean_traj, axis=0)
# coeffs = np.polyfit(mean_traj[:, 0], mean_traj[:, 1], deg=data.shape[2]-1) # (T,D)
# interpolator = interpolate.KroghInterpolator(t, mean_traj, axis=0)
# derivatives = interpolator.derivatives(t)
# compute basis vectors for the Frenet frame
bases = []
generalized_curvatures = []
norm_first_deriv = 1
for i in range(mean_traj.shape[1]):
derivative = interpolator.derivative(nu=i + 1)
d = derivative(t) # (T, D-1)
# if not first basis vector, compute orthogonal vector using Gram-Schmidt
if i != 0:
d_init = np.array(d)
for basis in bases: # TODO: vectorize this
d -= np.sum(basis * d_init, axis=1) * basis # (T, D-1)
else:
norm_first_deriv = np.linalg.norm(d, axis=1) # (T,)
# normalize basis vector
basis = (d.T / np.linalg.norm(d, axis=1)).T # (T, D-1)
bases.append(basis)
# compute generalized curvature
if i != 0:
# compute first derivative of previous basis
d = interpolate.CubicSpline(t, bases[-1], axis=0).derivative(nu=1)
d = d(t) # (T, D-1)
chi = np.sum(basis * d, axis=1) / norm_first_deriv # (T,)
generalized_curvatures.append(chi)
generalized_curvatures = np.array(generalized_curvatures) # (D-2, T)
# compute total curvature norm
total_curvature_norm = np.linalg.norm(generalized_curvatures, axis=0) # (T,)
# the local maxima of total curvature provide points for segmenting the trajectory (+ start / end points)
if smooth_curvature:
total_curvature_norm = smooth(total_curvature_norm) # smooth the signal
indices = np.diff(np.sign(np.diff(total_curvature_norm))) < 0 # (T-2,)
indices = np.concatenate(([True], indices, [True])) # (T,)
indices = np.where(indices)[0] # (I,)
# peaks_indices = scipy.signal.find_peaks(total_curvature_norm)
# peaks_indices = scipy.signal.find_peaks_cwt(total_curvature_norm, widths=np.arange(1,10))
# extrema = scipy.signal.argrelextrema(total_curvature_norm)
# append time dimension back to trajectories / mean trajectory
trajectories = np.dstack((t.reshape(-1, 1), trajectories)) # (N, T, D)
mean_traj = np.hstack((t.reshape(-1, 1), mean_traj)) # (T, D)
return indices, trajectories, mean_traj
def init_random(self, data, seed=None, reg=1e-8):
r"""
@@ -725,7 +995,11 @@ class GMM(object):
reg (float): regularization term (useful to not have singular covariance matrices)
"""
# initialize random generator
np.random.seed(seed)
if seed is not None:
np.random.seed(seed)
# set dimensionality
self._dimensionality = data.shape[1]
# uniform priors
self._priors = np.ones(self.num_components) / self.num_components
@@ -744,12 +1018,45 @@ class GMM(object):
# create gaussians
self._gaussians = [Gaussian(mean=mu, covariance=cov) for mu, cov in zip(means, covariances)]
def init_kmeans(self, data, seed=None):
r"""
Initialize the GMM using K-means algorithm.
Args:
data (np.array[N,D]): data matrix
seed (int, None): seed for random generator
"""
# initialize random generator
if seed is not None:
np.random.seed(seed)
# set dimensionality
self._dimensionality = data.shape[1]
# fit the data using k-means
km = KMeans(n_clusters=self.num_components)
km.fit(data)
# uniform priors
self._priors = np.ones(self.num_components) / self.num_components
# identity covariances
covariances = np.array([np.identity(self.dim)] * self.num_components)
# means = position of the cluster centers
means = km.cluster_centers_
# create gaussians
self._gaussians = [Gaussian(mean=mu, covariance=cov) for mu, cov in zip(means, covariances)]
def init_uniformly(self, data, axis=0):
r"""
Initialize the GMM uniformly in the space with respect to the axis dimension. If the data represents
trajectories, the first dimension is the time and it will distributed uniformly with respect to that one by
default. The covariances of each Gaussian will be a spherical one.
Warnings: this initialization is deterministic (given the same data).
Args:
data (np.array[N,D]): data matrix
axis (int): axis specifying the dimension to distribute the Gaussians uniformly
@@ -780,18 +1087,45 @@ class GMM(object):
# create gaussians
self._gaussians = [Gaussian(mean=mu, covariance=cov) for mu, cov in zip(means, covariances)]
def init_curvature(self, data):
def init_sklearn(self, data, seed=None, max_iter=10, init_params='kmeans', reg=1e-6):
r"""
Initialize the GMM using the curvature of the trajectories. This only works for sequential temporal and
spatial data. The first dimension has to be the time, and the other dimensions have to be spatial data
Initialize the GMM by training a GMM from the sklearn library.
Args:
data (np.array[N,D]): data matrix
seed (int, None): seed for random generator
max_iter (int): the number of EM iterations to perform
init_params (str): {'kmeans', 'random'}, defaults to 'kmeans'. The method used to initialize the
weights, the means and the precisions.
reg (float): regularization term (useful to not have singular covariance matrices)
"""
# check seed
kwargs = {}
if seed is not None:
kwargs['random_state'] = seed
# fit data to gmm
gmm_ = GaussianMixture(n_components=self.num_components, max_iter=max_iter, init_params=init_params,
reg_covar=reg, **kwargs)
gmm_.fit(data)
# create gaussians
self._gaussians = [Gaussian(mean=mu, covariance=cov) for mu, cov in zip(gmm_.means_, gmm_.covariances_)]
def init_curvature(self, data, interpolation_method='cubic', reg=1.e-6, smooth_curvature=True):
r"""
Initialize the GMM using trajectory curvature segmentation. This only works for sequential temporal and
spatial data. The first dimension is assumed to be the time, and the other dimensions have to be spatial data
(x [,y [,z]]).
Warnings: this initialization only makes sense with trajectories.
Warnings: this initialization only makes sense with spatial trajectories, and is deterministic. It also
assumes that the trajectories are similar. Currently, we only accept 4D curves (t, x, y, z).
From [1], let's assume a D-dimensional curve :math:`x(t) \in \mathbb{R}^D`, for which we can define a Frenet
frame at each time step :math:`\{e_1(t), ..., e_D(t)\}`. That curve can be the mean trajectory computed from
all the provided trajectories. The basis vectors are computed using the Gram-Schmidt orthogonalization process,
where the first basis is computed using:
From [1], let's assume a D-dimensional curve :math:`\pmb{x}(t) \in \mathbb{R}^D`, for which we can define a
Frenet frame at each time step :math:`\{\pmb{e}_1(t), ..., \pmb{e}_D(t)\}`. That curve can be the mean
trajectory computed from all the provided trajectories. It might be necessary to align them using dynamic time
wrapping beforehand, The basis vectors are computed using the Gram-Schmidt orthogonalization process, where
the first basis is computed using:
.. math::
@@ -817,10 +1151,10 @@ class GMM(object):
Note that, this involves the computation of the jth derivative of the curve wrt to the time for each dimension
:math:`j \in \{1, ..., D\}`. In order to get satisfactory estimations, we can locally approximated the curve by
a D-dimensional polynomial function. "The derivatives can subsequently be analytically computed and are
resampled to provide trajectories of T datapoints" [1]. For instance, for a 3D curve we can use a Hermite
re-sampled to provide trajectories of T data points" [1]. For instance, for a 3D curve we can use a Hermite
interpolator (a 5th order polynomial) or a 3D polynomial function.
The total curvature of a D-dimensional curve is finally defined as:
The total norm curvature of a D-dimensional curve is finally defined as:
.. math:: \Sigma(t) = \sqrt{\sum_{i=1}^{D-2} \chi_i(t)^2}
@@ -835,105 +1169,73 @@ class GMM(object):
data (np.array[N,D], list of np.array[T,D], np.array[N,T,D]): data matrix(ces). For each matrix, we assume
that the first dimension is the time. If only a 2D matrix is provided, the trajectory can be
concatenated but the time has to be relative; that is when you record a trajectory the time
has to between [t0, tf], and when you record another trajectory it has to be again [t0',tf'] where
has to between [t0, tf], and when you record another trajectory it has to be between [t0',tf'] where
t0' < tf. We will use that to reshape the matrix.
interpolation_method (str): "Specifies the kind of interpolation as a string ('linear', 'nearest', 'zero',
'slinear', 'quadratic', 'cubic', 'previous', 'next', where 'zero', 'slinear', 'quadratic' and 'cubic'
refer to a spline interpolation of zeroth, first, second or third order; 'previous' and 'next' simply
return the previous or next value of the point) or as an integer specifying the order of the spline
interpolator to use. Default is 'cubic'." from ``scipy.interpolate.interp1d`` documentation.
reg (float): regularization term (useful to not have singular covariance matrices)
smooth_curvature (bool): if we should smooth the total norm curvature before looking for the local maxima.
References:
- [1] "Robot Programming by Demonstration: A Probabilistic Approach", Calinon, 2009, Chap 2.8.2
"""
# fit a polynomial function to the trajectories
# get the trajectory curvature segmentation points
ret = self._get_curvature_segmentation_points(data, interpolation_method=interpolation_method,
smooth_curvature=smooth_curvature)
# get the segmentation points (I,), reshaped trajectories (N, T, D), and mean of the reshaped trajectory (T,D)
indices, trajectories, mean_traj = ret
# resample trajectories
# take each couple of segmenting points and compute the mean and covariance of a Gaussian
means, covariances = [], []
for i in range(len(indices) - 1):
idx1, idx2 = indices[i], indices[i+1]
# compute mean trajectory from which we will compute the Frenet frame
# compute the mean
mean = np.mean(mean_traj[idx1:idx2], axis=0) # (D,)
means.append(mean)
# create gaussians
pass
# compute the covariance based on all the trajectories
# 1. center the data
trajs = trajectories[:, idx1:idx2] # (N, dT, D)
trajs -= mean
def init_sklearn(self, data, max_iter=10, init_params='kmeans'):
r"""
Initialize the GMM by training a GMM from the sklearn library.
Args:
data (np.array[N,D]): data matrix
max_iter (int): the number of EM iterations to perform
init_params (str): {'kmeans', 'random'}, defaults to 'kmeans'. The method used to initialize the
weights, the means and the precisions.
"""
# fit data to gmm
gmm_ = GaussianMixture(n_components=self.num_components, max_iter=max_iter, init_params=init_params)
gmm_.fit(data)
# create gaussians
self._gaussians = [Gaussian(mean=mu, covariance=cov) for mu, cov in zip(gmm_.means_, gmm_.covariances_)]
def init_time_warping(self, data):
r"""
Initialize the GMM using Dynamic Time Wrapping [1]. This only works for sequential temporal and spatial data.
The first dimension has to be the time, and the other dimensions have to be spatial data (x [,y [,z]]).
Warnings: this initialization only makes sense with trajectories.
Args:
data (np.array[N,D]): data matrix
References:
- [1] "Robot Programming by Demonstration: A Probabilistic Approach", Calinon, 2009, Chap 2.9.3
"""
pass
def init_kmeans(self, data, seed=None):
r"""
Initialize the GMM using K-means algorithm.
Args:
data (np.array[N,D]): data matrix
seed (int, None): seed for random generator
"""
# initialize random generator
np.random.seed(seed)
# fit the data using k-means
km = KMeans(n_clusters=self.num_components)
km.fit(data)
# uniform priors
self._priors = np.ones(self.num_components) / self.num_components
# identity covariances
covariances = np.array([np.identity(self.dim)] * self.num_components)
# means = position of the cluster centers
means = km.cluster_centers_
# 2. compute the covariance matrix (and add regularization term)
trajs = trajs.reshape(-1, trajs.shape[-1]) # (N*dT, D)
covariance = np.cov(trajs, rowvar=False) # (D, D)
covariance += reg * np.identity(trajs.shape[-1])
covariances.append(covariance)
# create gaussians
self._gaussians = [Gaussian(mean=mu, covariance=cov) for mu, cov in zip(means, covariances)]
def init(self, data, method='k-means', seed=None, reg=1e-8):
def init(self, data, method='k-means', seed=None, reg=1e-6, axis=0):
r"""
Initialize the GMM using the specified method
Args:
data (np.array[N,D]): data matrix
method (str, None): 'k-means', 'random', None. If None, it starts from where the Gaussians are placed.
method (str, None): method to use to initialize the GMM, select between {'random', 'k-means', 'uniform',
'sklearn', 'curvature', None}. If None, it starts from where the Gaussians are placed.
seed (str): seed for random generator
reg (float): regularization term (useful to not have singular covariance matrices)
axis (int): if method axis specifying the dimension to distribute the Gaussians uniformly
"""
if method is None:
return
method = method.lower()
if method == 'random':
if method == 'random': # init the Gaussian randomly
self.init_random(data, seed, reg=reg)
elif method == 'k-means' or method == 'kmeans':
elif method == 'k-means' or method == 'kmeans': # init the Gaussians using K-Means
self.init_kmeans(data, seed)
elif method[:7] == 'uniform':
self.init_uniformly(data)
elif method == 'sklearn' or method[:6] == 'scikit':
self.init_sklearn(data)
elif method == 'curvature':
self.init_curvature(data)
elif method[:4] == 'time' or method[:4] == 'warp':
self.init_time_warping(data)
elif method[:7] == 'uniform': # init the Gaussians uniformly
self.init_uniformly(data, axis=axis)
elif method == 'sklearn' or method[:6] == 'scikit': # init using sklearn
self.init_sklearn(data, seed=seed, reg=reg)
elif method == 'curvature': # init based on the curvature of the trajectories
self.init_curvature(data, reg=reg, smooth_curvature=True)
else:
raise NotImplementedError("The given initialization method has not been implemented")
@@ -1493,10 +1795,10 @@ class GMM(object):
raise ValueError("The given 'wrt' argument is not valid (see documentation)")
def grad_log_likelihood(self, x):
pass
raise NotImplementedError
def hessian(self, x, wrt='x'):
pass
raise NotImplementedError
def update(self, x):
r"""
@@ -1505,7 +1807,7 @@ class GMM(object):
Args:
x (np.array): data vector/matrix
"""
pass
raise NotImplementedError
def approximate_by_single_gaussian(self):
r"""
@@ -1556,7 +1858,7 @@ class GMM(object):
Returns:
float: differential entropy
"""
pass
raise NotImplementedError
def kl_divergence(self, other):
r"""
@@ -1575,7 +1877,26 @@ class GMM(object):
Returns:
float: the divergence between the 2 GMMs.
"""
pass
raise NotImplementedError
def align_trajectories_with_dynamic_time_warping(self, data):
r"""
Align the trajectories using Dynamic Time Wrapping prior to learn a GMM [1]. This only works for sequential
temporal and spatial data. The first dimension is assumed to be the time, and the other dimensions are assumed
to be spatial data (x [,y [,z]]).
Warnings: this initialization only makes sense with trajectories.
Args:
data (np.array[N,T,D], list of np.array[T,D]): trajectories to align.
Returns:
np.array[N,D]: aligned data trajectories
References:
- [1] "Robot Programming by Demonstration: A Probabilistic Approach", Calinon, 2009, Chap 2.9.3
"""
raise NotImplementedError
#############
# Operators #
@@ -1762,8 +2083,9 @@ if __name__ == "__main__":
X = np.hstack((np.array([t] * N).reshape(-1, 1), y.reshape(-1, 1)))
# init GMM
gmm.init(X, method='random') # method='k-means')
plotGMM(gmm, title='GMM after K-Means')
init_method = 'random' # 'k-means'
gmm.init(X, method=init_method)
plotGMM(gmm, title='GMM after ' + init_method.capitalize())
plt.show()
# fit a GMM using EM
pyrobolearn/models/hmm/hmm.py
+2
View File
@@ -1,5 +1,7 @@
# This file describes the Hidden Markov Model
# TODO: implement this model
from gaussian import Gaussian
from model import Model
from hmmlearn.hmm import GaussianHMM
pyrobolearn/worlds/meshes/sports/baseball/BLENDSWAP_LICENSE.txt
+79
View File
@@ -0,0 +1,79 @@
--------------------------------------------------------------------------------
Thank you for downloading "Low Poly Baseball Bat" by laurenceduffy
Released under
Creative Commons Attribution 3.0
Downloaded from http://www.blendswap.com/blends/view/68818
The following is important licensing information, please keep this file for
archival and future reference when working with the file. It's important that
you know, understand and follow any requirements stated in this file regarding
the usage of the materials included.
Some parts of this file are marked with [#], the corresponding numbered note is
at the end of the file.
--------------------------------------------------------------------------------
################################################################################
VERY IMPORTANT LICENSE INFORMATION:
This blend has been released under
Creative Commons Attribution 3.0
This means that you can use it for any purpose you see fit, even commercially,
as long as you respect these requirements:
--You MUST give credit to laurenceduffy.
################################################################################
--------------------------------------------------------------------------------
ABOUT THE BLEND:
Ready for Blender 2.67
Published on: 2013-06-21 17:06:49
--------------------------------------------------------------------------------
HELP US MODERATE THIS BLEND:
If you find anomalies in this blend or any of the contained files such as:
- Missing, unneeded or corrupted files.
- Inaccurate/mismatching preview image on the site.
- Illegal distribution of third party files.
- Ripping from a game or other 3D repository.
- Uncredited or incorrect use of other CC licensed works.
- Some other troubling issues[1].
Please submit a report from http://www.blendswap.com/blends/view/68818
by pressing the red button with the flag, including links and details that serve
as evidence and can help us to solve any conflicts or issues derived from the
contents of this file.
--------------------------------------------------------------------------------
Thank you for using Blend Swap!
Register to get tons of more blends! http://www.blendswap.com/register
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Get answers to your questions and doubts: http://www.blendswap.com/page/faq
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Report website bugs: http://www.blendswap.com/bugs
Consider getting an associate Membership to get some neat features and
enhancements.
--------------------------------------------------------------------------------
NOTES:
[1] Please make sure your problem is not derived from a setting in Blender (like
hidden layers or objects) before submitting a report under the "Other" category.
Issues arising from this type of problem will be ignored.
--------------------------------------------------------------------------------
###################### END OF BLEND SWAP LICENSE.txt #####################
pyrobolearn/worlds/meshes/sports/baseball/CHANGELOG.txt
+2
View File
@@ -0,0 +1,2 @@
Brian Delhaisse: Compared to the original, I rescaled and rotated the baseball bat and ball.
pyrobolearn/worlds/meshes/sports/baseball/INFO.txt
+3
View File
@@ -0,0 +1,3 @@
- The license for the baseball bat is the `BLENDSWAP_LICENSE.txt` file.
- The license for the baseball ball is the `LICENSE.html` file.
pyrobolearn/worlds/meshes/sports/baseball/LICENSE.html
+1
View File
@@ -0,0 +1 @@
<!DOCTYPE html><html lang="en"><head> <meta charset="UTF-8"> <title>67352 - Baseball - Downloaded from Blend Swap</title> <meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1"> <style> body {background: #f0f0f0; color: #666; max-width: 960px; width: 100%; margin: auto; font-family: sans-serif; } a {color: #f80; text-decoration: none; } a:hover {color: #f50; } a:active {color: #f00; } article {background: #fff; padding: 32px; margin: 16px; } footer {margin: 16px; padding: 32px; } </style></head><body> <article class="license"> <h1><a href="http://www.blendswap.com/blends/view/67352">Blend #67352: Baseball</a></h1><h3>Released under <a href="https://creativecommons.org/licenses/by/3.0/">Creative Commons Attribution 3.0</a></h3><hr /><p>You are free to use this asset privately for any use you see fit. If you choose to distribute copies or modified versions of this asset you must do so under the following requirements:</p><ul><li>You must mention the author of this blend in your copies and derivative works.</li></ul><p>Failure to comply with these requirements, if any, is considered a severe violation of the License and the Blend Swap Terms of Use, Upload Rules and Code of Conduct.</p><hr /><h2>About "Baseball":</h2><ul><li>Blender: 2.66</li><li>Render Engine: Cycles</li><li>Uploaded on: 2013-03-29 15:13:48</li></ul><blockquote>Just a simple Baseball- model.Have fun and please visit my Homepage. </blockquote><hr /><h3>Help us moderate this file</h3><p>Blend Swap is a place to share and get awesome 3D work, if you think this blend falls into one of the following issues please file a report from <a href="http://www.blendswap.com/blends/view/67352">http://www.blendswap.com/blends/view/67352</a> by clicking on the <strong>Manage</strong> panel to the left of the blend and then on <strong>Report/Flag</strong>:</p><ul><li>The blend author didn't make this blend and posted it as their own.</li><li>The blend author is violating a Creative Commons License or copyright.</li><li>The blend is incomplete, work in progress, or has missing textures.</li><li>The blend contains simulation cache files and other unneeded media.</li><li>The preview image has nothing to do with the blend's contents.</li></ul><p>Your help allows the site to stay clear of broken and stolen work.</p><hr /><h4>Notes:</h4><ul><li>Do NOT report this blend if you dont' know how to use a feature on Blender, instead use the <a href="http://www.blendswap.com/questions">questions section</a> of the site.</li></ul> </article> <footer> Original file hosted by <a href="https://www.blendswap.com">Blend Swap, LLC</a>. </footer></body></html>
pyrobolearn/worlds/meshes/sports/baseball/ball.mtl
+34
View File
@@ -0,0 +1,34 @@
# Blender MTL File: 'Baseball_by_www_up3d_de.blend'
# Material Count: 3
newmtl Leder_1
Ns 96.078431
Ka 1.000000 1.000000 1.000000
Kd 0.640000 0.640000 0.640000
Ks 0.500000 0.500000 0.500000
Ke 0.000000 0.000000 0.000000
Ni 1.000000
d 1.000000
illum 2
map_Kd C:/Users/Thomas/Desktop/Loecher_Baseball.png
newmtl Leder_2
Ns 96.078431
Ka 1.000000 1.000000 1.000000
Kd 0.640000 0.640000 0.640000
Ks 0.500000 0.500000 0.500000
Ke 0.000000 0.000000 0.000000
Ni 1.000000
d 1.000000
illum 2
map_Kd C:/Users/Thomas/Desktop/Loecher_Baseball.png
newmtl Naht
Ns 96.078431
Ka 1.000000 1.000000 1.000000
Kd 0.640000 0.640000 0.640000
Ks 0.500000 0.500000 0.500000
Ke 0.000000 0.000000 0.000000
Ni 1.000000
d 1.000000
illum 2
pyrobolearn/worlds/meshes/sports/baseball/ball.obj
+96596
View File
File diff suppressed because it is too large Load Diff
pyrobolearn/worlds/meshes/sports/baseball/bat.mtl
+11
View File
@@ -0,0 +1,11 @@
# Blender MTL File: 'Model.blend'
# Material Count: 1
newmtl None
Ns 0
Ka 0.000000 0.000000 0.000000
Kd 0.8 0.8 0.8
Ks 0.8 0.8 0.8
d 1
illum 2
map_Kd texture.png
pyrobolearn/worlds/meshes/sports/baseball/bat.obj
+795
View File
@@ -0,0 +1,795 @@
# Blender v2.76 (sub 0) OBJ File: 'Model.blend'
# www.blender.org
mtllib bat.mtl
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usemtl None
s 1
f 1/1/1 50/2/2 143/3/3 47/4/4
f 1/1/1 47/4/4 144/5/5 48/6/6
f 1/1/1 48/6/6 140/7/7 49/8/8
f 1/1/1 49/8/8 139/9/9 50/2/2
f 2/10/10 111/11/11 171/12/12 51/13/13
f 2/10/10 51/13/13 145/14/14 52/15/15
f 2/10/10 52/15/15 141/16/16 60/17/17
f 2/10/10 60/17/17 173/18/18 111/11/11
f 3/19/19 52/20/15 145/21/14 54/22/20
f 3/19/19 54/22/20 146/23/21 55/24/22
f 3/19/19 55/24/22 142/25/23 56/26/24
f 3/19/19 56/26/24 141/27/16 52/20/15
f 4/28/25 103/29/26 168/30/27 57/31/28
f 4/28/25 57/31/28 143/32/3 50/33/2
f 4/28/25 50/33/2 139/34/9 62/35/29
f 4/28/25 62/35/29 170/36/30 103/29/26
f 5/37/31 58/38/32 172/39/33 112/40/34
f 5/37/31 112/40/34 173/18/18 60/41/17
f 5/37/31 60/41/17 141/42/16 56/43/24
f 5/37/31 56/43/24 142/44/23 58/38/32
f 6/45/35 57/46/28 168/47/27 104/48/36
f 6/45/35 104/48/36 169/49/37 59/50/38
f 6/45/35 59/50/38 144/51/5 47/52/4
f 6/45/35 47/52/4 143/53/3 57/46/28
f 7/54/39 82/55/40 163/56/41 70/57/41
f 7/54/39 70/57/41 147/58/42 63/59/43
f 7/54/39 63/59/43 148/60/44 69/61/45
f 7/54/39 69/61/45 164/62/45 82/55/40
f 8/63/46 137/64/47 183/65/48 110/66/49
f 8/63/46 110/66/49 149/67/50 64/68/51
f 8/63/46 64/68/51 150/69/52 108/70/53
f 8/63/46 108/70/53 185/71/54 137/64/47
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f 9/72/55 80/75/57 164/62/45 69/61/45
f 9/72/55 69/61/45 148/60/44 65/76/58
f 9/72/55 65/76/58 150/69/52 67/73/56
f 10/77/59 110/78/49 183/79/48 136/80/60
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f 10/77/59 107/82/62 147/58/42 66/83/63
f 10/77/59 66/83/63 149/84/50 110/78/49
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f 11/85/64 93/92/71 166/74/56 79/86/65
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f 15/119/98 81/121/99 165/122/66 68/120/66
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f 16/123/100 67/73/56 150/69/52 64/68/51
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f 20/137/111 75/142/116 159/143/117 126/144/118
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f 21/145/119 91/132/107 163/56/41 82/55/40
f 21/145/119 82/55/40 164/62/45 94/136/110
f 21/145/119 94/136/110 154/108/87 86/107/86
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f 22/146/120 130/149/121 181/104/83 125/150/122
f 22/146/120 125/150/122 160/97/76 76/151/123
f 22/146/120 76/151/123 161/152/115 124/147/114
f 23/153/124 120/154/125 176/155/126 116/156/127
f 23/153/124 116/156/127 156/157/128 87/158/129
f 23/153/124 87/158/129 158/118/97 117/159/130
f 23/153/124 117/159/130 177/160/131 120/154/125
f 24/161/132 97/162/133 177/160/131 121/163/134
f 24/161/132 121/163/134 178/101/80 98/100/79
f 24/161/132 98/100/79 162/99/78 78/164/135
f 24/161/132 78/164/135 159/143/117 97/162/133
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f 25/165/136 88/171/140 156/172/128 116/166/127
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f 26/173/141 101/175/143 157/170/139 89/176/144
f 26/173/141 89/176/144 155/116/95 99/115/94
f 26/173/141 99/115/94 167/114/93 106/174/142
f 27/177/145 87/158/129 156/157/128 100/178/146
f 27/177/145 100/178/146 168/30/27 103/29/26
f 27/177/145 103/29/26 170/36/30 102/112/91
f 27/177/145 102/112/91 158/118/97 87/158/129
f 28/179/147 100/180/146 156/172/128 88/171/140
f 28/179/147 88/171/140 157/170/139 101/175/143
f 28/179/147 101/175/143 169/49/37 104/48/36
f 28/179/147 104/48/36 168/47/27 100/180/146
f 29/181/148 62/182/29 139/183/9 49/184/8
f 29/181/148 49/184/8 140/185/7 53/186/149
f 29/181/148 53/186/149 167/114/93 105/113/92
f 29/181/148 105/113/92 170/36/30 62/182/29
f 30/187/150 48/188/6 144/189/5 59/190/38
f 30/187/150 59/190/38 169/49/37 106/174/142
f 30/187/150 106/174/142 167/114/93 53/191/149
f 30/187/150 53/191/149 140/192/7 48/188/6
f 31/193/151 138/194/152 186/81/61 133/195/153
f 31/193/151 133/195/153 171/12/12 111/11/11
f 31/193/151 111/11/11 173/18/18 134/196/154
f 31/193/151 134/196/154 184/197/155 138/194/152
f 32/198/156 132/199/157 185/71/54 135/200/158
f 32/198/156 135/200/158 184/197/155 134/196/154
f 32/198/156 134/196/154 173/18/18 112/40/34
f 32/198/156 112/40/34 172/39/33 132/199/157
f 33/201/159 55/202/22 146/203/21 61/204/160
f 33/201/159 61/204/160 174/205/161 113/206/162
f 33/201/159 113/206/162 172/39/33 58/207/32
f 33/201/159 58/207/32 142/208/23 55/202/22
f 34/209/163 61/210/160 146/211/21 54/212/20
f 34/209/163 54/212/20 145/213/14 51/214/13
f 34/209/163 51/214/13 171/12/12 114/215/164
f 34/209/163 114/215/164 174/216/161 61/210/160
f 35/217/165 89/176/144 157/170/139 115/169/138
f 35/217/165 115/169/138 175/95/74 119/94/73
f 35/217/165 119/94/73 178/101/80 118/218/166
f 35/217/165 118/218/166 155/116/95 89/176/144
f 36/219/167 75/142/116 161/141/115 96/220/168
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pyrobolearn/worlds/samples/sports/baseball.py
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#!/usr/bin/env python
r"""Provide the baseball world.
"""
import os
import numpy as np
from pyrobolearn.worlds import BasicWorld
__author__ = "Brian Delhaisse"
__copyright__ = "Copyright 2019, PyRoboLearn"
__credits__ = ["Brian Delhaisse"]
__license__ = "GNU GPLv3"
__version__ = "1.0.0"
__maintainer__ = "Brian Delhaisse"
__email__ = "briandelhaisse@gmail.com"
__status__ = "Development"
# TODO: finish to implement the world, create corresponding environment (in `envs` folder) with state and reward.
class BaseballWorld(BasicWorld):
r"""Baseball world
"""
def __init__(self, simulator, position=(0., 0., 1.5), scale=(1., 1., 1.)):
"""
Initialize the baseball world.
Args:
simulator (Simulator): the simulator instance.
position (tuple/list of 3 float, np.array[3]): position of the baseball bat.
scale (tuple/list of 3 float): scale of the bat.
"""
super(BaseballWorld, self).__init__(simulator)
mesh_path = os.path.dirname(os.path.abspath(__file__)) + '/../../meshes/sports/baseball/'
position = np.asarray(position)
# load bat
self.bat = self.load_mesh(mesh_path + 'bat.obj', position=[0., 0., 2.], scale=scale, mass=0.94, flags=0)
self.bat_grip_radius = 0.035
# load ball
self.ball = self.load_mesh(mesh_path + 'ball.obj', position=[0.2, -0.4, 2.], scale=scale, mass=0.145, flags=0)
self.ball_radius = 0.0375
def reset(self, world_state=None):
super(BaseballWorld, self).reset(world_state)
def step(self, sleep_dt=None):
super(BaseballWorld, self).step(sleep_dt)
# Test
if __name__ == '__main__':
from itertools import count
import pyrobolearn as prl
# create simulator
sim = prl.simulators.Bullet()
# create world
world = BaseballWorld(sim)
# create manipulator
robot = world.load_robot('kuka_iiwa')
# attach bat to robot end effector
world.attach(body1=robot, body2=world.bat, link1=robot.end_effectors[0], link2=-1, joint_axis=[0., 0., 0.],
parent_frame_position=[0., 0., world.bat_grip_radius], child_frame_position=[0., 0.3, 0.],
parent_frame_orientation=[0, 0., 0., 1.])
# apply force to ball to throw it; f=dp/dt thus dp = f dt (change of momentum)
# run simulation
for t in count():
world.step(sim.dt)