Probabilistic Movement Primitives

A movement primitive that represents a whole family of demonstrated trajectories as a Gaussian distribution, conditionable on via-points or goals.

ProMPs were introduced by Alexandros Paraschos, Christian Daniel, Jan Peters, and Gerhard Neumann at NIPS 2013. Each trajectory is written as y_t = Φ_tᵀw + ε, where Φ_t is a set of time-indexed basis functions (commonly radial basis functions), w is a weight vector, and ε is noise. Each demonstration is fit to its own w, and a Gaussian distribution is then fit over these w vectors: the mean captures the typical motion, and the covariance captures how much the demonstrations vary and how the joints are coupled — so a ProMP represents a whole family of trajectories rather than a single one. Requiring the trajectory to pass through a given point at a given time is handled analytically by Gaussian conditioning, and several ProMPs can be co-activated and blended or switched between. The original paper also derives a stochastic feedback controller that reproduces the resulting trajectory distribution. Compared with dynamic movement primitives (DMPs), which use a differential equation with an attractor to represent a single trajectory, ProMPs model the distribution over trajectories directly, making them better at capturing variation across demonstrations.

ExampleIn the original paper, a 7-DOF KUKA lightweight arm played table hockey using two sets of 10 demonstrations each — one varying only the shot distance, the other only the angle. Combining the two ProMPs produced a shot toward the middle at medium distance; conditioning on a desired angle let it shoot in the specified direction instead.

Also called

ProMP, ProMPs, Probabilistic Movement Primitive

Related

Dynamic Movement Primitives · Motion Primitives · Imitation Learning · Gaussian Mixture Regression / Task-Parameterized GMM · Demonstration Data · Kinesthetic Teaching

Sources

Paraschos et al., Probabilistic Movement Primitives (NIPS 2013) — abstract
Paraschos et al., Probabilistic Movement Primitives (NIPS 2013) — PDF