  Movement generation, and especially generalisation to unseen situations,
plays an important role in robotics. Different types of movement generation
methods exist such as spline based methods, dynamical system based methods, and
methods based on Gaussian mixture models (GMMs). Using a large, new dataset on
human manipulations, in this paper we provide a highly detailed comparison of
five fundamentally different and widely used movement encoding and generation
frameworks: dynamic movement primitives (DMPs), time based Gaussian mixture
regression (tbGMR), stable estimator of dynamical systems (SEDS), Probabilistic
Movement Primitives (ProMP) and Optimal Control Primitives (OCP). We compare
these frameworks with respect to their movement encoding efficiency,
reconstruction accuracy, and movement generalisation capabilities. The new
dataset consists of nine object manipulation actions performed by 12 humans:
pick and place, put on top/take down, put inside/take out, hide/uncover, and
push/pull with a total of 7,652 movement examples. Our analysis shows that for
movement encoding and reconstruction DMPs and OCPs are the most efficient with
respect to the number of parameters and reconstruction accuracy, if a
sufficient number of kernels is used. In case of movement generalisation to new
start- and end-point situations, DMPs, OCPs and task parameterized GMM (TP-GMM,
movement generalisation framework based on tbGMR) lead to similar performance,
which ProMPs only achieve when using many demonstrations for learning. All
models outperform SEDS, which additionally proves to be difficult to fit.
Furthermore we observe that TP-GMM and SEDS suffer from problems reaching the
end-points of generalizations.These different quantitative results will help
selecting the most appropriate models and designing trajectory representations
in an improved task-dependent way in future robotic applications.
