Learning (inverse) kinematics and dynamics models of dexterous robots for the entire action or observation space is challenging and costly. Sampling the entire space is usually intractable in terms of time, tear, and wear. We propose an efficient approach to learn inverse statics models—primarily for gravity compensation—by exploring only a small part of the configuration space and exploiting the symmetry properties of the inverse statics mapping. In particular, there exist symmetric configurations that require the same absolute motor torques to be maintained. We show that those symmetric configurations can be discovered, the functional relations between them can be successfully learned and exploited to generate multiple training samples from one sampled configuration-torque pair. This strategy drastically reduces the number of samples required for learning inverse statics models. Moreover, we demonstrate that exploiting symmetries for learning inverse statics models is a generally applicable strategy for online and offline learning algorithms. We exemplify this by two different learning approaches. First, we modify the Direction Sampling approach for learning inverse statics models online, in a plain exploratory fashion, from scratch and without using a closed-loop controller. Second, we show that inverse statics mappings can be efficiently learned offline utilizing lattice sampling. Results for a 2R planar robot and a 3R simplified human arm demonstrate that their inverse statics mappings can be learned successfully for the entire configuration space. Furthermore, we demonstrate that the number of samples required for learning inverse statics mappings for 2R and 3R manipulators can be reduced at least by factors of approximately 8 and 16, respectively–depending on the number of discovered symmetries.
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