  Several methods exist for teaching robots, with one of the most prominent
being Learning from Demonstration (LfD). Many LfD representations can be
formulated as constrained optimization problems. We propose a novel convex
formulation of the LfD problem represented as elastic maps, which models
reproductions as a series of connected springs. Relying on the properties of
strong duality and perturbation analysis of the constrained optimization
problem, we create a confidence metric. Our method allows the demonstrated
skill to be reproduced with varying confidence level yielding different levels
of smoothness and flexibility. Our confidence-based method provides
reproductions of the skill that perform better for a given set of constraints.
By analyzing the constraints, our method can also remove unnecessary
constraints. We validate our approach using several simulated and real-world
experiments using a Jaco2 7DOF manipulator arm.
