movement_primitives.promp.ProMP#

class movement_primitives.promp.ProMP(n_dims, n_weights_per_dim=10)#

Bases: object

Probabilistic Movement Primitive (ProMP).

ProMPs have been proposed first in [1] and have been used later in [2], [3]. The learning algorithm is a specialized form of the one presented in [4].

Note that internally we represented trajectories with the task space dimension as the first axis and the time step as the second axis while the exposed trajectory interface is transposed. In addition, we internally only use a 1d array representation to make handling of the covariance simpler.

Parameters:

n_dimsint: State space dimensions.
n_weights_per_dimint, optional (default: 10): Number of weights of the function approximator per dimension.

Methods

`condition_position`(y_mean[, y_cov, t, t_max])	Condition ProMP on a specific position.
`cov_trajectory`(T)	Get trajectory covariance of ProMP.
`cov_velocities`(T)	Get velocity covariance of ProMP.
`from_weight_distribution`(mean, cov)	Initialize ProMP from mean and covariance in weight space.
`imitate`(Ts, Ys[, n_iter, min_delta, verbose])	Learn ProMP from multiple demonstrations.
`mean_trajectory`(T)	Get mean trajectory of ProMP.
`mean_velocities`(T)	Get mean velocities of ProMP.
`sample_trajectories`(T, n_samples, random_state)	Sample trajectories from ProMP.
`trajectory_from_weights`(T, weights)	Generate trajectory from ProMP weights.
`var_trajectory`(T)	Get trajectory variance of ProMP.
`var_velocities`(T)	Get velocity variance of ProMP.
`weights`(T, Y[, lmbda])	Obtain ProMP weights by linear regression.

References

[1]

Paraschos, A., Daniel, C., Peters, J., Neumann, G. (2013). Probabilistic movement primitives, In C.J. Burges and L. Bottou and M. Welling and Z. Ghahramani and K.Q. Weinberger (Eds.), Advances in Neural Information Processing Systems, 26, https://papers.nips.cc/paper/2013/file/e53a0a2978c28872a4505bdb51db06dc-Paper.pdf

[3]

Maeda, G. J., Neumann, G., Ewerton, M., Lioutikov, R., Kroemer, O., Peters, J. (2017). Probabilistic movement primitives for coordination of multiple human–robot collaborative tasks. Autonomous Robots, 41, 593-612. DOI: 10.1007/s10514-016-9556-2, https://link.springer.com/article/10.1007/s10514-016-9556-2

[2]

Paraschos, A., Daniel, C., Peters, J., Neumann, G. (2018). Using probabilistic movement primitives in robotics. Autonomous Robots, 42, 529-551. DOI: 10.1007/s10514-017-9648-7, https://www.ias.informatik.tu-darmstadt.de/uploads/Team/AlexandrosParaschos/promps_auro.pdf

[4]

Lazaric, A., Ghavamzadeh, M. (2010). Bayesian Multi-Task Reinforcement Learning. In Proceedings of the 27th International Conference on International Conference on Machine Learning (ICML’10) (pp. 599-606). https://hal.inria.fr/inria-00475214/document

condition_position(y_mean, y_cov=None, t=0, t_max=1.0)#

Condition ProMP on a specific position.

For details, see page 4 of [1]

Parameters:

y_meanarray, shape (n_dims,): Position mean.
y_covarray, shape (n_dims, n_dims), optional (default: 0): Covariance of position.
tfloat, optional (default: 0): Time at which the activations of RBFs will be queried. Note that we internally normalize the time so that t_max == 1.
t_maxfloat, optional (default: 1): Duration of the ProMP

Returns:

conditional_prompProMP: New conditional ProMP

References

[1]

cov_trajectory(T)#

Get trajectory covariance of ProMP.

Parameters:

Tarray-like, shape (n_steps,): Time steps

Returns:

covarray, shape (n_dims * n_steps, n_dims * n_steps): Covariance

cov_velocities(T)#

Get velocity covariance of ProMP.

Parameters:

Tarray-like, shape (n_steps,): Time steps

Returns:

covarray, shape (n_dims * n_steps, n_dims * n_steps): Covariance

from_weight_distribution(mean, cov)#

Initialize ProMP from mean and covariance in weight space.

Parameters:

meanarray, shape (n_dims * n_weights_per_dim): Mean of weight distribution
covarray, shape (n_dims * n_weights_per_dim, n_dims * n_weights_per_dim): Covariance of weight distribution

Returns:

selfProMP: This object

imitate(Ts, Ys, n_iter=1000, min_delta=1e-05, verbose=0)#

Learn ProMP from multiple demonstrations.

For details, see Section 3.2 of [1]. We use the parameters \(P = I\) (identity matrix), \(\mu_0 = 0, k_0 = 0, \nu_0 = 0, \Sigma_0 = 0,\alpha_0 = 0,\beta_0 = 0\).

Parameters:

Tsarray, shape (n_demos, n_steps): Time steps of demonstrations
Ysarray, shape (n_demos, n_steps, n_dims): Demonstrations
n_iterint, optional (default: 1000): Maximum number of iterations
min_deltafloat, optional (default: 1e-5): Minimum delta between means to continue iteration
verboseint, optional (default: 0): Verbosity level

References

[1]

mean_trajectory(T)#

Get mean trajectory of ProMP.

Parameters:

Tarray-like, shape (n_steps,): Time steps

Returns:

Yarray, shape (n_steps, n_dims): Mean trajectory

mean_velocities(T)#

Get mean velocities of ProMP.

Parameters:

Tarray-like, shape (n_steps,): Time steps

Returns:

Ydarray, shape (n_steps, n_dims): Mean velocities

sample_trajectories(T, n_samples, random_state)#

Sample trajectories from ProMP.

Parameters:

Tarray-like, shape (n_steps,): Time steps
n_samplesint: Number of trajectories that will be sampled
random_statenp.random.RandomState: State of random number generator

Returns:

samplesarray, shape (n_samples, n_steps, n_dims): Sampled trajectories

trajectory_from_weights(T, weights)#

Generate trajectory from ProMP weights.

Parameters:

Tarray-like, shape (n_steps,): Time steps
weightsarray-like, shape (n_steps * n_weights_per_dim): ProMP weights

Returns:

Yarray, shape (n_steps, n_dims): Trajectory

var_trajectory(T)#

Get trajectory variance of ProMP.

Parameters:

Tarray-like, shape (n_steps,): Time steps

Returns:

vararray, shape (n_steps, n_dims): Variance

var_velocities(T)#

Get velocity variance of ProMP.

Parameters:

Tarray-like, shape (n_steps,): Time steps

Returns:

vararray, shape (n_steps, n_dims): Variance

weights(T, Y, lmbda=1e-12)#

Obtain ProMP weights by linear regression.

Parameters:

Tarray-like, shape (n_steps,): Time steps
Yarray-like, shape (n_steps, n_dims): Demonstrated trajectory
lmbdafloat, optional (default: 1e-12): Regularization coefficient

Returns:

weightsarray, shape (n_steps * n_weights_per_dim): ProMP weights