  Extraction of low-dimensional latent space from high-dimensional observation
data is essential to construct a real-time robot controller with a world model
on the extracted latent space. However, there is no established method for
tuning the dimension size of the latent space automatically, suffering from
finding the necessary and sufficient dimension size, i.e. the minimal
realization of the world model. In this study, we analyze and improve
Tsallis-based variational autoencoder (q-VAE), and reveal that, under an
appropriate configuration, it always facilitates making the latent space
sparse. Even if the dimension size of the pre-specified latent space is
redundant compared to the minimal realization, this sparsification collapses
unnecessary dimensions, allowing for easy removal of them. We experimentally
verified the benefits of the sparsification by the proposed method that it can
easily find the necessary and sufficient six dimensions for a reaching task
with a mobile manipulator that requires a six-dimensional state space.
Moreover, by planning with such a minimal-realization world model learned in
the extracted dimensions, the proposed method was able to exert a more optimal
action sequence in real-time, reducing the reaching accomplishment time by
around 20 %. The attached video is uploaded on youtube:
https://youtu.be/-QjITrnxaRs
