Bridging the Model-Reality Gap with Lipschitz Network Adaptation

TL;DR

This paper introduces a neural network-based adaptation method using Lipschitz networks to align uncertain robot dynamics with a reference model, enabling safer and more effective model-based control in real-world scenarios.

Contribution

It presents a novel Lipschitz neural network architecture for model reference adaptation that guarantees stability and handles highly nonlinear uncertainties.

Findings

Successfully balanced an inverted pendulum on a quadrotor.

Demonstrated robustness to dynamic uncertainties in experiments.

Enabled model-based control despite limited prior knowledge.

Abstract

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.