# Bridging the Model-Reality Gap with Lipschitz Network Adaptation

arXiv: https://arxiv.org/abs/2112.03756 · HTML: https://mlsanity.com/paper/2112.03756/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 7 Dec 2021.

## Builds on (most cited first, 10 of 10)

- [Sim-to-Real Transfer of Robotic Control with Dynamics Randomization](https://mlsanity.com/paper/1710.06537/) (2017)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [Deep Reinforcement Learning amidst Lifelong Non-Stationarity](https://mlsanity.com/paper/2006.10701/) (2020)
- [Deep Model Reference Adaptive Control](https://mlsanity.com/paper/1909.08602/) (2019)
- [Learn Fast, Forget Slow: Safe Predictive Learning Control for Systems with Unknown and Changing Dynamics Performing Repetitive Tasks](https://mlsanity.com/paper/1810.06681/) (2018)
- [Experience Selection Using Dynamics Similarity for Efficient Multi-Source Transfer Learning Between Robots](https://mlsanity.com/paper/2003.13150/) (2020)
- [Knowledge Transfer Between Robots with Similar Dynamics for High-Accuracy Impromptu Trajectory Tracking](https://mlsanity.com/paper/1904.00249/) (2019)

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

- [Automatic Optimisation of Normalised Neural Networks](https://mlsanity.com/paper/2312.10672/) (2023)
- [Efficient Deep Learning of Robust, Adaptive Policies using Tube MPC-Guided Data Augmentation](https://mlsanity.com/paper/2303.15688/) (2023)

## Abstract (arXiv)

As robots venture into the real world, they are subject to unmodeled dynamics and disturbances. Traditional model-based control approaches have been proven successful in relatively static and known operating environments. However, when an accurate model of the robot is not available, model-based design can lead to suboptimal and even unsafe behaviour. In this work, we propose a method that bridges the model-reality gap and enables the application of model-based approaches even if dynamic uncertainties are present. In particular, we present a learning-based model reference adaptation approach that makes a robot system, with possibly uncertain dynamics, behave as a predefined reference model. In turn, the reference model can be used for model-based controller design. In contrast to typical model reference adaptation control approaches, we leverage the representative power of neural networks to capture highly nonlinear dynamics uncertainties and guarantee stability by encoding a certifying Lipschitz condition in the architectural design of a special type of neural network called the Lipschitz network. Our approach applies to a general class of nonlinear control-affine systems even when our prior knowledge about the true robot system is limited. We demonstrate our approach in flying inverted pendulum experiments, where an off-the-shelf quadrotor is challenged to balance an inverted pendulum while hovering or tracking circular trajectories.