  Tendon-driven musculoskeletal humanoids typically have complex structures
similar to those of human beings, such as ball joints and the scapula, in which
encoders cannot be installed. Therefore, joint angles cannot be directly
obtained and need to be estimated using the changes in muscle lengths. In
previous studies, methods using table-search and extended kalman filter have
been developed. These methods express the joint-muscle mapping, which is the
nonlinear relationship between joint angles and muscle lengths, by using a data
table, polynomials, or a neural network. However, due to computational
complexity, these methods cannot consider the effects of polyarticular muscles.
In this study, considering the limitation of the computational cost, we reduce
unnecessary degrees of freedom, divide joints and muscles into several groups,
and formulate a joint angle estimation method that takes into account
polyarticular muscles. Also, we extend the estimation method to propose a joint
angle estimation method using only the relative changes in muscle lengths. By
this extension, which does not use absolute muscle lengths, we do not need to
execute a difficult calibration of muscle lengths for tendon-driven
musculoskeletal humanoids. Finally, we conduct experiments in simulation and
actual environments, and verify the effectiveness of this study.
