Data-Driven Robust Barrier Functions for Safe, Long-Term Operation

Applications that require multi-robot systems to operate independently for extended periods of time in unknown or unstructured environments face a broad set of challenges, such as hardware degradation, changing weather patterns, or unfamiliar terrain. To operate effectively under these changing conditions, algorithms developed for long-term autonomy applications require a stronger focus on robustness. Consequently, this work considers the ability to satisfy the operation-critical constraints of a disturbed system in a modular fashion, which means compatibility with different system objectives and disturbance representations. Toward this end, this paper introduces a controller-synthesis approach to constraint satisfaction for disturbed control-affine dynamical systems by utilizing Control Barrier Functions (CBFs). The aforementioned framework is constructed by modelling the disturbance as a union of convex hulls and leveraging previous work on CBFs for differential inclusions. This method of disturbance modeling grants compatibility with different disturbance-estimation methods. For example, this work demonstrates how a disturbance learned via a Gaussian process may be utilized in the proposed framework. These estimated disturbances are incorporated into the proposed controller-synthesis framework which is then tested on a fleet of robots in different scenarios.

[1]  Paulo Tabuada,et al.  Control Barrier Functions: Theory and Applications , 2019, 2019 18th European Control Conference (ECC).

[2]  Alberto Bemporad,et al.  Robust model predictive control: A survey , 1998, Robustness in Identification and Control.

[3]  Andreas Krause,et al.  Safe Model-based Reinforcement Learning with Stability Guarantees , 2017, NIPS.

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

[5]  Koushil Sreenath,et al.  Torque Saturation in Bipedal Robotic Walking Through Control Lyapunov Function-Based Quadratic Programs , 2013, IEEE Access.

[6]  Seth Hutchinson,et al.  An efficient algorithm for fault-tolerant rendezvous of multi-robot systems with controllable sensing range , 2016, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[7]  Magnus Egerstedt,et al.  Robust Barrier Functions for a Fully Autonomous, Remotely Accessible Swarm-Robotics Testbed , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[8]  Stephen Tyree,et al.  Exact Gaussian Processes on a Million Data Points , 2019, NeurIPS.

[9]  Hiroaki Kitano,et al.  RoboCup Rescue: search and rescue in large-scale disasters as a domain for autonomous agents research , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[10]  Magnus Egerstedt,et al.  Constructive Barrier Certificates with Applications to Fixed-Wing Aircraft Collision Avoidance , 2018, 2018 IEEE Conference on Control Technology and Applications (CCTA).

[11]  Marc Peter Deisenroth,et al.  Distributed Gaussian Processes , 2015, ICML.

[12]  Magnus Egerstedt,et al.  Nonsmooth Barrier Functions With Applications to Multi-Robot Systems , 2017, IEEE Control Systems Letters.

[13]  Li Wang,et al.  The Robotarium: A remotely accessible swarm robotics research testbed , 2016, 2017 IEEE International Conference on Robotics and Automation (ICRA).

[14]  Toshiharu Sugie,et al.  Adaptive model predictive control for a class of constrained linear systems based on the comparison model , 2007, Autom..

[15]  Koushil Sreenath,et al.  Optimal Robust Safety-Critical Control for Dynamic Robotics , 2020, ArXiv.

[16]  Haitao Liu,et al.  When Gaussian Process Meets Big Data: A Review of Scalable GPs , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[17]  R. Freeman,et al.  Robust Nonlinear Control Design: State-Space and Lyapunov Techniques , 1996 .

[18]  Jan Peters,et al.  Model Learning with Local Gaussian Process Regression , 2009, Adv. Robotics.

[19]  J. Cortés Discontinuous dynamical systems , 2008, IEEE Control Systems.

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

[21]  Paulo Tabuada,et al.  Control Barrier Function Based Quadratic Programs with Application to Automotive Safety Systems , 2016, ArXiv.

[22]  Aaron D. Ames,et al.  Safety Barrier Certificates for Collisions-Free Multirobot Systems , 2017, IEEE Transactions on Robotics.

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

[24]  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).

[25]  Aude Billard,et al.  Learning control Lyapunov function to ensure stability of dynamical system-based robot reaching motions , 2014, Robotics Auton. Syst..

[26]  Andreas Krause,et al.  Safe learning of regions of attraction for uncertain, nonlinear systems with Gaussian processes , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[27]  Carl E. Rasmussen,et al.  Gaussian Processes for Data-Efficient Learning in Robotics and Control , 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  Kenji Fujimoto,et al.  Second-order Bounds of Gaussian Kernel-based Functions and its Application to Nonlinear Optimal Control with Stability , 2017 .

[29]  Duy Nguyen-Tuong,et al.  Stability of Controllers for Gaussian Process Forward Models , 2016, ICML.

[30]  Magnus Egerstedt,et al.  Boolean Composability of Constraints and Control Synthesis for Multi-Robot Systems via Nonsmooth Control Barrier Functions , 2018, 2018 IEEE Conference on Control Technology and Applications (CCTA).

[31]  Sriram Sankaranarayanan,et al.  Learning Lyapunov (Potential) Functions from Counterexamples and Demonstrations , 2017, Robotics: Science and Systems.

[32]  Masayuki Fujita,et al.  Passivity-Based Attitude Synchronization in $SE(3)$ , 2009, IEEE Transactions on Control Systems Technology.

[33]  Pratap Tokekar,et al.  Sensor planning for a symbiotic UAV and UGV system for precision agriculture , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[34]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

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

[36]  Aaron D. Ames,et al.  Sufficient conditions for the Lipschitz continuity of QP-based multi-objective control of humanoid robots , 2013, 52nd IEEE Conference on Decision and Control.

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

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

[39]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.