Gaussian Mixture Regression / Task-Parameterized GMM

Summarizing demonstrated trajectories with a handful of Gaussian distributions, then generating a matching motion for a new object position.

These are two classic probabilistic methods for learning from demonstration, systematically laid out in a 2016 tutorial paper by Sylvain Calinon. A Gaussian mixture model (GMM) first fits data points of ‘time plus position’ from several demonstrated trajectories into a set of Gaussian components; GMR then takes a given input (such as time t) and computes its conditional distribution, producing a smooth trajectory along with its variance — a large variance means the demonstrations disagreed a lot at that point, so execution can be looser there. TP-GMM treats coordinate frames such as the start point or the target object as ‘task parameters,’ learning a separate GMM in each frame; for a new scene, these are transformed into the new frame and combined by a product of Gaussians, so just a few demonstrations can adapt to new object positions. It needs little data and is interpretable, but it doesn't capture complex, multimodal motion as well as deep generative methods like diffusion policy.

ExampleDemonstrate placing a cup on a tray 5 times: learn one GMM in the ‘cup frame’ and another in the ‘tray frame’; for a new arrangement, multiply the two together to get a trajectory that passes through the new cup position and lands on the new tray position.

Also called

GMR, TP-GMM, Task-Parameterized Gaussian Mixture Model

Related

Gaussian Mixture Model · Dynamic Movement Primitives · Probabilistic Movement Primitives · Imitation Learning · Demonstration Data · Coordinate Frame

Sources

Calinon, A Tutorial on Task-Parameterized Movement Learning and Retrieval (Intelligent Service Robotics, 2016)