  In the field of Learning from Demonstration (LfD), Dynamical Systems (DSs)
have gained significant attention due to their ability to generate real-time
motions and reach predefined targets. However, the conventional
convergence-centric behavior exhibited by DSs may fall short in safety-critical
tasks, specifically, those requiring precise replication of demonstrated
trajectories or strict adherence to constrained regions even in the presence of
perturbations or human intervention. Moreover, existing DS research often
assumes demonstrations solely in Euclidean space, overlooking the crucial
aspect of orientation in various applications. To alleviate these shortcomings,
we present an innovative approach geared toward ensuring the safe execution of
learned orientation skills within constrained regions surrounding a reference
trajectory. This involves learning a stable DS on SO(3), extracting
time-varying conic constraints from the variability observed in expert
demonstrations, and bounding the evolution of the DS with Conic Control Barrier
Function (CCBF) to fulfill the constraints. We validated our approach through
extensive evaluation in simulation and showcased its effectiveness for a
cutting skill in the context of assisted teleoperation.
