# End-to-End Learning of Hybrid Inverse Dynamics Models for Precise and Compliant Impedance Control

arXiv: https://arxiv.org/abs/2205.13804 · HTML: https://mlsanity.com/paper/2205.13804/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 27 May 2022.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems](https://mlsanity.com/paper/1907.04489/) (2019)
- [Encoding Physical Constraints in Differentiable Newton-Euler Algorithm](https://mlsanity.com/paper/2001.08861/) (2020)
- [Structured Mechanical Models for Robot Learning and Control](https://mlsanity.com/paper/2004.10301/) (2020)
- [Action-Conditional Recurrent Kalman Networks For Forward and Inverse Dynamics Learning](https://mlsanity.com/paper/2010.10201/) (2020)
- [Linear Matrix Inequalities for Physically-Consistent Inertial Parameter Identification: A Statistical Perspective on the Mass Distribution](https://mlsanity.com/paper/1701.04395/) (2017)
- [Identification of Fully Physical Consistent Inertial Parameters using Optimization on Manifolds](https://mlsanity.com/paper/1610.08703/) (2016)
- [Structured learning of rigid-body dynamics: A survey and unified view from a robotics perspective](https://mlsanity.com/paper/2012.06250/) (2020)
- [A Differentiable Newton-Euler Algorithm for Real-World Robotics](https://mlsanity.com/paper/2110.12422/) (2021)
- [A New Data Source for Inverse Dynamics Learning](https://mlsanity.com/paper/1710.02513/) (2017)

## Built on by (most cited first, 2 of 2)

- [FACTR 2: Learning External Force Sensing for Commodity Robot Arms Improves Policy Learning](https://mlsanity.com/paper/2606.12406/) (2026)
- [Learning World Models With Hierarchical Temporal Abstractions: A Probabilistic Perspective](https://mlsanity.com/paper/2404.16078/) (2024)

## Abstract (arXiv)

It is well-known that inverse dynamics models can improve tracking performance in robot control. These models need to precisely capture the robot dynamics, which consist of well-understood components, e.g., rigid body dynamics, and effects that remain challenging to capture, e.g., stick-slip friction and mechanical flexibilities. Such effects exhibit hysteresis and partial observability, rendering them, particularly challenging to model. Hence, hybrid models, which combine a physical prior with data-driven approaches are especially well-suited in this setting. We present a novel hybrid model formulation that enables us to identify fully physically consistent inertial parameters of a rigid body dynamics model which is paired with a recurrent neural network architecture, allowing us to capture unmodeled partially observable effects using the network memory. We compare our approach against state-of-the-art inverse dynamics models on a 7 degree of freedom manipulator. Using data sets obtained through an optimal experiment design approach, we study the accuracy of offline torque prediction and generalization capabilities of joint learning methods. In control experiments on the real system, we evaluate the model as a feed-forward term for impedance control and show the feedback gains can be drastically reduced to achieve a given tracking accuracy.