Real-Time Safe Control of Neural Network Dynamic Models with Sound Approximation

TL;DR

This paper introduces a sound approximation method for neural network dynamic models that enables real-time safe control with significantly improved computational efficiency, ensuring safety guarantees in robotics applications.

Contribution

The authors propose Bernstein over-approximated neural dynamics (BOND), a novel sound approximation technique that facilitates real-time safe control of neural network models with safety guarantees.

Findings

BOND achieves 10-100 times faster control computation than MIP-based methods.

The approach guarantees safety while maintaining scalability in large-scale neural dynamic models.

Experiments validate the effectiveness of the worst-case safety index and sound approximation in real-time scenarios.

Abstract

Safe control of neural network dynamic models (NNDMs) is important to robotics and many applications. However, it remains challenging to compute an optimal safe control in real time for NNDM. To enable real-time computation, we propose to use a sound approximation of the NNDM in the control synthesis. In particular, we propose Bernstein over-approximated neural dynamics (BOND) based on the Bernstein polynomial over-approximation (BPO) of ReLU activation functions in NNDM. To mitigate the errors introduced by the approximation and to ensure persistent feasibility of the safe control problems, we synthesize a worst-case safety index using the most unsafe approximated state within the BPO relaxation of NNDM offline. For the online real-time optimization, we formulate the first-order Taylor approximation of the nonlinear worst-case safety constraint as an additional linear layer of NNDM with the l2 bounded bias term for the higher-order remainder. Comprehensive experiments with different neural dynamics and safety constraints show that with safety guaranteed, our NNDMs with sound approximation are 10-100 times faster than the safe control baseline that uses mixed integer programming (MIP), validating the effectiveness of the worst-case safety index and scalability of the proposed BOND in real-time large-scale settings. The code is available at https://github.com/intelligent-control-lab/BOND.