  This study investigates learning from demonstration (LfD) for contact-rich
tasks. The procedure for choosing a task frame to express the learned signals
for the motion and interaction wrench is often omitted or using expert insight.
This article presents a procedure to derive the optimal task frame from motion
and wrench data recorded during the demonstration. The procedure is based on
two principles that are hypothesized to underpin the control configuration
targeted by an expert, and assumes task frame origins and orientations that are
fixed to either the world or the robot tool. It is rooted in screw theory, is
entirely probabilistic and does not involve any hyperparameters. The procedure
was validated by demonstrating several tasks, including surface following and
manipulation of articulated objects, showing good agreement between the
obtained and the assumed expert task frames. To validate the performance of the
learned tasks by a UR10e robot, a constraint-based controller was designed
based on the derived task frames and the learned data expressed therein. These
experiments showed the effectiveness and versatility of the proposed approach.
The task frame derivation approach fills a gap in the state of the art of LfD,
bringing LfD for contact-rich tasks closer to practical application.
