Title: Tensor Decompositions for Modeling Inverse Dynamics,
Abstract: Modeling inverse dynamics is crucial for accurate feedforward robot control.
The model computes the necessary joint torques, to perform a desired movement.
The highly non-linear inverse function of the dynamical system can be
approximated using regression techniques. We propose as regression method a
tensor decomposition model that exploits the inherent three-way interaction of
positions x velocities x accelerations. Most work in tensor factorization has
addressed the decomposition of dense tensors. In this paper, we build upon the
decomposition of sparse tensors, with only small amounts of nonzero entries.
The decomposition of sparse tensors has successfully been used in relational
learning, e.g., the modeling of large knowledge graphs. Recently, the approach
has been extended to multi-class classification with discrete input variables.
Representing the data in high dimensional sparse tensors enables the
approximation of complex highly non-linear functions. In this paper we show how
the decomposition of sparse tensors can be applied to regression problems.
Furthermore, we extend the method to continuous inputs, by learning a mapping
from the continuous inputs to the latent representations of the tensor
decomposition, using basis functions. We evaluate our proposed model on a
dataset with trajectories from a seven degrees of freedom SARCOS robot arm. Our
experimental results show superior performance of the proposed functional
tensor model, compared to challenging state-of-the art methods.