|Nonlinear dimension reduction techniques from machine learning can be
exploited to determine dynamically optimal motions for high
degree of freedom systems. Using the Gaussian Process Dynamical
Model (GPDM) to learn the low-dimensional embedding,
and a density function that provides a nonlinear mapping from
the low-dimensional latent space to the full-dimensional pose
space, we determine optimal motions by optimizing in the latent
space, and mapping the optimal latent space trajectory to the
pose space. space. The notion of variance tubes are developed to ensure
that kinematic and other constraints are appropriately satisfied
without sacrificing naturalness or richness of the motions.
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