BarrierNet: A Safety-Guaranteed Layer for Neural Networks

This paper introduces differentiable higher-order control barrier functions (CBF) that are end-toend trainable together with learning systems. CBFs are usually overly conservative, while guaranteeing safety. Here, we address their conservativeness by softening their definitions using environmental dependencies without loosing safety guarantees, and embed them into differentiable quadratic programs. These novel safety layers, termed a BarrierNet, can be used in conjunction with any neural network-based controller, and can be trained by gradient descent. BarrierNet allows the safety constraints of a neural controller be adaptable to changing environments. We evaluate them on a series of control problems such as traffic merging and robot navigations in 2D and 3D space, and demonstrate their effectiveness compared to state-of-the-art approaches.

[1]  Sriram Sankaranarayanan,et al.  Training Neural Network Controllers Using Control Barrier Functions in the Presence of Disturbances , 2020, 2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC).

[2]  Radu Grosu,et al.  On The Verification of Neural ODEs with Stochastic Guarantees , 2020, AAAI.

[3]  Aaron D. Ames,et al.  Episodic Learning for Safe Bipedal Locomotion with Control Barrier Functions and Projection-to-State Safety , 2021, L4DC.

[4]  Zhichao Li,et al.  Comparison between safety methods control barrier function vs. reachability analysis , 2021, ArXiv.

[5]  Dimos V. Dimarogonas,et al.  Learning Control Barrier Functions from Expert Demonstrations , 2020, 2020 59th IEEE Conference on Decision and Control (CDC).

[6]  Sebastian Trimpe,et al.  On exploration requirements for learning safety constraints , 2021, L4DC.

[7]  Paulo Tabuada,et al.  Control barrier function based quadratic programs with application to adaptive cruise control , 2014, 53rd IEEE Conference on Decision and Control.

[8]  Lukasz Kaiser,et al.  Attention is All you Need , 2017, NIPS.

[9]  Jyotirmoy V. Deshmukh,et al.  Learning Deep Neural Network Controllers for Dynamical Systems with Safety Guarantees: Invited Paper , 2019, 2019 IEEE/ACM International Conference on Computer-Aided Design (ICCAD).

[10]  Yisong Yue,et al.  Learning for Safety-Critical Control with Control Barrier Functions , 2019, L4DC.

[11]  Mathias Lechner,et al.  Causal Navigation by Continuous-time Neural Networks , 2021, NeurIPS.

[12]  Paulo Tabuada,et al.  Robustness of Control Barrier Functions for Safety Critical Control , 2016, ADHS.

[13]  Li Wang,et al.  Safe Learning of Quadrotor Dynamics Using Barrier Certificates , 2017, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[14]  Radu Grosu,et al.  Lagrangian Reachtubes: The Next Generation , 2020, 2020 59th IEEE Conference on Decision and Control (CDC).

[15]  Wei Xiao,et al.  Adaptive Control Barrier Functions , 2021, IEEE Transactions on Automatic Control.

[16]  Koushil Sreenath,et al.  Exponential Control Barrier Functions for enforcing high relative-degree safety-critical constraints , 2016, 2016 American Control Conference (ACC).

[17]  Aaron D. Ames,et al.  A Control Barrier Perspective on Episodic Learning via Projection-to-State Safety , 2020, IEEE Control Systems Letters.

[18]  Aaron D. Ames,et al.  Towards a Framework for Realizable Safety Critical Control through Active Set Invariance , 2018, 2018 ACM/IEEE 9th International Conference on Cyber-Physical Systems (ICCPS).

[19]  David Duvenaud,et al.  Neural Ordinary Differential Equations , 2018, NeurIPS.

[20]  Koushil Sreenath,et al.  Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functions , 2020, Robotics: Science and Systems.

[21]  Aaron D. Ames,et al.  Adaptive Safety with Control Barrier Functions , 2019, 2020 American Control Conference (ACC).

[22]  Jean-Jacques E. Slotine,et al.  Robust Adaptive Control Barrier Functions: An Adaptive and Data-Driven Approach to Safety , 2021, IEEE Control Systems Letters.

[23]  Jian Sun,et al.  Deep Residual Learning for Image Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[24]  Christos G. Cassandras,et al.  Bridging the Gap between Optimal Trajectory Planning and Safety-Critical Control with Applications to Autonomous Vehicles , 2020, Autom..

[25]  J. Zico Kolter,et al.  OptNet: Differentiable Optimization as a Layer in Neural Networks , 2017, ICML.

[26]  Evangelos A. Theodorou,et al.  Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs , 2020, ArXiv.

[27]  Guang Yang,et al.  Self-triggered Control for Safety Critical Systems Using Control Barrier Functions , 2019, 2019 American Control Conference (ACC).

[28]  Wei Xiao,et al.  Event-Triggered Safety-Critical Control for Systems with Unknown Dynamics , 2021, 2021 60th IEEE Conference on Decision and Control (CDC).

[29]  P. Olver.  Nonlinear Systems , 2013 .

[30]  Shaoshuai Mou,et al.  Neural Certificates for Safe Control Policies , 2020, ArXiv.

[31]  Thomas A. Henzinger,et al.  Adversarial Training is Not Ready for Robot Learning , 2021, 2021 IEEE International Conference on Robotics and Automation (ICRA).

[32]  Wei Xiao,et al.  High-Order Control Barrier Functions , 2021, IEEE Transactions on Automatic Control.

[33]  Mathias Lechner,et al.  Learning Long-Term Dependencies in Irregularly-Sampled Time Series , 2020, NeurIPS.

[34]  Paulo Tabuada,et al.  Control Barrier Function Based Quadratic Programs for Safety Critical Systems , 2016, IEEE Transactions on Automatic Control.

[35]  Mathias Lechner,et al.  Closed-form Continuous-Depth Models , 2021, ArXiv.

[36]  Radu Grosu,et al.  Gershgorin Loss Stabilizes the Recurrent Neural Network Compartment of an End-to-end Robot Learning Scheme , 2020, 2020 IEEE International Conference on Robotics and Automation (ICRA).

[37]  Samuel Coogan,et al.  Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach , 2020, 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[38]  Thomas A. Henzinger,et al.  GoTube: Scalable Stochastic Verification of Continuous-Depth Models , 2021, ArXiv.

[39]  Ronald,et al.  Learning representations by backpropagating errors , 2004 .

[40]  Wei Xiao,et al.  Decentralized optimal merging control for Connected and Automated Vehicles with safety constraint guarantees , 2021, Autom..

[41]  Jürgen Schmidhuber,et al.  Long Short-Term Memory , 1997, Neural Computation.

[42]  Radu Grosu,et al.  Neural circuit policies enabling auditable autonomy , 2020, Nature Machine Intelligence.

[43]  Yasser Shoukry,et al.  ShieldNN: A Provably Safe NN Filter for Unsafe NN Controllers , 2020, ArXiv.

[44]  Taolue Chen,et al.  Learning safe neural network controllers with barrier certificates , 2020, Formal Aspects of Computing.