  Dynamic Movement Primitives (DMPs) is a framework for learning a
point-to-point trajectory from a demonstration. Despite being widely used, DMPs
still present some shortcomings that may limit their usage in real robotic
applications. Firstly, at the state of the art, mainly Gaussian basis functions
have been used to perform function approximation. Secondly, the adaptation of
the trajectory generated by the DMP heavily depends on the choice of
hyperparameters and the new desired goal position. Lastly, DMPs are a framework
for `one-shot learning', meaning that they are constrained to learn from a
unique demonstration. In this work, we present and motivate a new set of basis
functions to be used in the learning process, showing their ability to
accurately approximate functions while having both analytical and numerical
advantages w.r.t. Gaussian basis functions. Then, we show how to use the
invariance of DMPs w.r.t. affine transformations to make the generalization of
the trajectory robust against both the choice of hyperparameters and new goal
position, performing both synthetic tests and experiments with real robots to
show this increased robustness. Finally, we propose an algorithm to extract a
common behavior from multiple observations, validating it both on a synthetic
dataset and on a dataset obtained by performing a task on a real robot.
