  Online Goal Babbling and Direction Sampling are recently proposed methods for
direct learning of inverse kinematics mappings from scratch even in
high-dimensional sensorimotor spaces following the paradigm of "learning while
behaving". To learn inverse statics mappings - primarily for gravity
compensation - from scratch and without using any closed-loop controller, we
modify and enhance the Online Goal Babbling and Direction Sampling schemes.
Moreover, we exploit symmetries in the inverse statics mappings to drastically
reduce the number of samples required for learning inverse statics models.
Results for a 2R planar robot, a 3R simplified human arm, and a 4R humanoid
robot arm clearly demonstrate that their inverse statics mappings can be
learned successfully with our modified online Goal Babbling scheme.
Furthermore, we show that the number of samples required for the 2R and 3R arms
can be reduced by a factor of at least 8 and 16 resp. -depending on the number
of discovered symmetries.
