Trajectory Learning From Demonstration With Canal Surfaces: A Parameter-Free Approach

We present a novel geometric framework for intuitively encoding and learning a wide range of trajectory-based skills from human demonstrations. Our approach identifies and extracts the main characteristics of the demonstrated skill, which are spatial correlations across different demonstrations. Using the extracted characteristics, the proposed approach generates a continuous representation of the skill based on the concept of canal surfaces. Canal surfaces are Euclidean surfaces formed as the envelope of a family of regular surfaces (e.g. spheres) whose centers lie on a space curve. The learned skill can be reproduced, as a time-independent trajectory, and generalized to unforeseen situations inside the canal while its main characteristics are preserved. The main advantages of the proposed approach include: (a) requiring no parameter tuning, (b) maintaining the main characteristics and implicit boundaries of the skill, and (c) generalizing the learned skill over the initial condition of the movement, while exploiting the whole demonstration space to reproduce a variety of successful movements. Evaluations using simulated and real-world data exemplify the feasibility and robustness of our approach.