  Learning from Demonstration (LfD) is a popular method of reproducing and
generalizing robot skills from human-provided demonstrations. In this paper, we
propose a novel optimization-based LfD method that encodes demonstrations as
elastic maps. An elastic map is a graph of nodes connected through a mesh of
springs. We build a skill model by fitting an elastic map to the set of
demonstrations. The formulated optimization problem in our approach includes
three objectives with natural and physical interpretations. The main term
rewards the mean squared error in the Cartesian coordinate. The second term
penalizes the non-equidistant distribution of points resulting in the optimum
total length of the trajectory. The third term rewards smoothness while
penalizing nonlinearity. These quadratic objectives form a convex problem that
can be solved efficiently with local optimizers. We examine nine methods for
constructing and weighting the elastic maps and study their performance in
robotic tasks. We also evaluate the proposed method in several simulated and
real-world experiments using a UR5e manipulator arm, and compare it to other
LfD approaches to demonstrate its benefits and flexibility across a variety of
metrics.
