  This paper describes a computational model, called the Dirichlet process
Gaussian mixture model with latent joints (DPGMM-LJ), that can find latent tree
structure embedded in data distribution in an unsupervised manner. By combining
DPGMM-LJ and a pre-existing body map formation method, we propose a method that
enables an agent having multi-link body structure to discover its kinematic
structure, i.e., body schema, from tactile information alone. The DPGMM-LJ is a
probabilistic model based on Bayesian nonparametrics and an extension of
Dirichlet process Gaussian mixture model (DPGMM). In a simulation experiment,
we used a simple fetus model that had five body parts and performed structured
random movements in a womb-like environment. It was shown that the method could
estimate the number of body parts and kinematic structures without any
pre-existing knowledge in many cases. Another experiment showed that the degree
of motor coordination in random movements affects the result of body schema
formation strongly. It is confirmed that the accuracy rate for body schema
estimation had the highest value 84.6% when the ratio of motor coordination was
0.9 in our setting. These results suggest that kinematic structure can be
estimated from tactile information obtained by a fetus moving randomly in a
womb without any visual information even though its accuracy was not so high.
They also suggest that a certain degree of motor coordination in random
movements and the sufficient dimension of state space that represents the body
map are important to estimate body schema correctly.
