Generalizing Robot Trajectories from Single-Context Human Demonstrations: A Probabilistic Approach

TL;DR

This paper tackles the challenge of generalizing robot trajectories from single-context human demonstrations in Learning from Demonstration (LfD). It introduces a Gaussian Mixture Model (GMM) framework with component-level reparameterization and Gaussian Mixture Regression (GMR) to extrapolate to unseen start and goal configurations while preserving the demonstrated motion structure. The key contributions are (1) a two-stage parameter adaptation (means and covariances) conditioned on new task endpoints, (2) guaranteed convergence at task boundaries, and (3) preservation of the intrinsic spatiotemporal patterns of the demonstrated skills. The approach demonstrates superior trajectory fidelity and boundary convergence compared to TP-GMM, DMP, and ProMP, including successful deployment on a real dual-arm robot, highlighting its practicality for data-efficient, boundary-aware generalization in manipulation tasks.

Abstract

Generalizing robot trajectories from human demonstrations to new contexts remains a key challenge in Learning from Demonstration (LfD), particularly when only single-context demonstrations are available. We present a novel Gaussian Mixture Model (GMM)-based approach that enables systematic generalization from single-context demonstrations to a wide range of unseen start and goal configurations. Our method performs component-level reparameterization of the GMM, adapting both mean vectors and covariance matrices, followed by Gaussian Mixture Regression (GMR) to generate smooth trajectories. We evaluate the approach on a dual-arm pick-and-place task with varying box placements, comparing against several baselines. Results show that our method significantly outperforms baselines in trajectory success and fidelity, maintaining accuracy even under combined translational and rotational variations of task configurations. These results demonstrate that our method generalizes effectively while ensuring boundary convergence and preserving the intrinsic structure of demonstrated motions.

Figures (9)

• Figure 1: Gaussian components capturing spatiotemporal correlations (single dimension): (a) original hyper=false]GMM trained on demonstration data, (b) after mean vectors reparameterization, and (c) after covariance matrices reparameterization.
• Figure 2: (a) Single-context demonstrations of grasp, transport, and release phases, where a box is transported from location A to location B. (b) The goal is to leverage these demonstrations to generate trajectories for any novel start and goal poses (A' and B'). Example pairs are shown, with one generated trajectory illustrated.
• Figure 3: Sequential stages of human demonstration for the box pick-and-place task: (a) grasping, (b) transporting, and (c) releasing.
• Figure 4: Demonstration trajectories (grey dotted) are shown alongside colored axes representing the orientation of the object during motion. The Gaussian components are visualized as blue ellipsoids.
• Figure 5: Control architecture of the dual-arm robotic system.