Tensor Decompositions for Modeling Inverse Dynamics

TL;DR

This paper introduces a tensor decomposition approach for modeling inverse dynamics in robotics, leveraging sparse tensor techniques and basis functions to handle continuous inputs, resulting in improved accuracy over existing methods.

Contribution

The paper presents a novel tensor decomposition regression model for inverse dynamics, extending sparse tensor methods to continuous inputs with basis functions, and demonstrates superior performance on robotic data.

Findings

Outperforms state-of-the-art methods in inverse dynamics prediction

Effectively models complex non-linear functions with sparse tensor representations

Successfully extends tensor decomposition to continuous input variables

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.