  Model generalization of the underlying dynamics is critical for achieving
data efficiency when learning for robot control. This paper proposes a novel
approach for learning dynamics leveraging the symmetry in the underlying
robotic system, which allows for robust extrapolation from fewer samples.
Existing frameworks that represent all data in vector space fail to consider
the structured information of the robot, such as leg symmetry, rotational
symmetry, and physics invariance. As a result, these schemes require vast
amounts of training data to learn the system's redundant elements because they
are learned independently. Instead, we propose considering the geometric prior
by representing the system in symmetrical object groups and designing neural
network architecture to assess invariance and equivariance between the objects.
Finally, we demonstrate the effectiveness of our approach by comparing the
generalization to unseen data of the proposed model and the existing models. We
also implement a controller of a climbing robot based on learned inverse
dynamics models. The results show that our method generates accurate control
inputs that help the robot reach the desired state while requiring less
training data than existing methods.
