Papers
Topics
Authors
Recent
Search
2000 character limit reached

Rate-Tunable Control Barrier Functions: Methods and Algorithms for Online Adaptation

Published 23 Mar 2023 in math.OC and cs.RO | (2303.12966v2)

Abstract: Control Barrier Functions offer safety certificates by dictating controllers that enforce safety constraints. However, their response depends on the classK function that is used to restrict the rate of change of the value of the barrier function along the system trajectories. This paper introduces the notion of a Rate-Tunable (RT) CBF, which allows for online tuning of the response of CBF-based controllers. In contrast to existing approaches that use a fixed classK function to ensure safety, we parameterize and adapt the classK function parameters online. We show that this helps improve the system's response in terms of the resulting trajectories being closer to a nominal reference while being sufficiently far from the boundary of the safe set. We provide point-wise sufficient conditions to be imposed on any user-given parameter dynamics so that multiple CBF constraints continue to admit a common control input with time. Finally, we introduce RT-CBF parameter dynamics for decentralized noncooperative multi-agent systems, where a trust factor, computed based on the instantaneous ease of constraint satisfaction, is used to update parameters online for a less conservative response.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (41)
  1. A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,” IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3861–3876, 2016.
  2. A. D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K. Sreenath, and P. Tabuada, “Control barrier functions: Theory and applications,” in 2019 18th European control conference (ECC).   IEEE, 2019, pp. 3420–3431.
  3. C. Dawson, S. Gao, and C. Fan, “Safe control with learned certificates: A survey of neural lyapunov, barrier, and contraction methods for robotics and control,” IEEE Transactions on Robotics, 2023.
  4. P. Jagtap, G. J. Pappas, and M. Zamani, “Control barrier functions for unknown nonlinear systems using Gaussian processes.”   IEEE, 2020, pp. 3699–3704.
  5. P. Glotfelter, J. Cortés, and M. Egerstedt, “Nonsmooth barrier functions with applications to multi-robot systems,” IEEE control systems letters, vol. 1, no. 2, pp. 310–315, 2017.
  6. D. M. Stipanović, C. J. Tomlin, and G. Leitmann, “Monotone approximations of minimum and maximum functions and multi-objective problems,” Applied Mathematics & Optimization, vol. 66, no. 3, pp. 455–473, 2012.
  7. D. Panagou, D. M. Stipanovič, and P. G. Voulgaris, “Multi-objective control for multi-agent systems using Lyapunov-like barrier functions,” in 52nd IEEE Conference on Decision and Control.   IEEE, 2013, pp. 1478–1483.
  8. J. Usevitch, K. Garg, and D. Panagou, “Strong invariance using control barrier functions: A clarke tangent cone approach,” in 2020 59th IEEE Conference on Decision and Control.   IEEE, 2020, pp. 2044–2049.
  9. W. Xiao, C. A. Belta, and C. G. Cassandras, “Feasibility-guided learning for constrained optimal control problems,” in 2020 59th IEEE Conference on Decision and Control (CDC).   IEEE, 2020, pp. 1896–1901.
  10. X. Wang, “Ensuring safety of learning-based motion planners using control barrier functions,” IEEE Robotics and Automation Letters, vol. 7, no. 2, pp. 4773–4780, 2022.
  11. Q. Nguyen and K. Sreenath, “Exponential control barrier functions for enforcing high relative-degree safety-critical constraints,” in 2016 American Control Conference (ACC).   IEEE, 2016, pp. 322–328.
  12. W. Xiao and C. Belta, “Control barrier functions for systems with high relative degree,” in 2019 IEEE 58th conference on decision and control (CDC).   IEEE, 2019, pp. 474–479.
  13. A. J. Taylor, P. Ong, T. G. Molnar, and A. D. Ames, “Safe backstepping with control barrier functions,” arXiv preprint arXiv:2204.00653, 2022.
  14. D. R. Agrawal and D. Panagou, “Safe control synthesis via input constrained control barrier functions,” in 2021 60th IEEE Conference on Decision and Control (CDC).   IEEE, 2021, pp. 6113–6118.
  15. A. Robey, H. Hu, L. Lindemann, H. Zhang, D. V. Dimarogonas, S. Tu, and N. Matni, “Learning control barrier functions from expert demonstrations,” in 2020 59th IEEE Conference on Decision and Control (CDC).   IEEE, 2020, pp. 3717–3724.
  16. L. Lindemann, H. Hu, A. Robey, H. Zhang, D. Dimarogonas, S. Tu, and N. Matni, “Learning hybrid control barrier functions from data,” in Conference on Robot Learning.   PMLR, 2021, pp. 1351–1370.
  17. C. Dawson, Z. Qin, S. Gao, and C. Fan, “Safe nonlinear control using robust neural lyapunov-barrier functions,” in Conference on Robot Learning.   PMLR, 2022, pp. 1724–1735.
  18. M. Black and D. Panagou, “Adaptation for validation of a consolidated control barrier function based control synthesis,” arXiv preprint arXiv:2209.08170, 2022.
  19. X. Tan and D. V. Dimarogonas, “Compatibility checking of multiple control barrier functions for input constrained systems,” arXiv preprint arXiv:2209.02284, 2022.
  20. L. Lindemann and D. V. Dimarogonas, “Control barrier functions for multi-agent systems under conflicting local signal temporal logic tasks,” IEEE control systems letters, vol. 3, no. 3, pp. 757–762, 2019.
  21. ——, “Barrier function based collaborative control of multiple robots under signal temporal logic tasks,” IEEE Transactions on Control of Network Systems, vol. 7, no. 4, pp. 1916–1928, 2020.
  22. U. Borrmann, L. Wang, A. D. Ames, and M. Egerstedt, “Control barrier certificates for safe swarm behavior,” IFAC-PapersOnLine, vol. 48, no. 27, pp. 68–73, 2015.
  23. J. Usevitch and D. Panagou, “Adversarial resilience for sampled-data systems using control barrier function methods,” in 2021 American Control Conference (ACC).   IEEE, 2021, pp. 758–763.
  24. A. Mustafa and D. Panagou, “Adversary detection and resilient control for multi-agent systems,” IEEE Transactions on Control of Network Systems, 2022.
  25. J. Zeng, B. Zhang, Z. Li, and K. Sreenath, “Safety-critical control using optimal-decay control barrier function with guaranteed point-wise feasibility,” in 2021 American Control Conference (ACC).   IEEE, 2021, pp. 3856–3863.
  26. K. Garg and D. Panagou, “Control Lyapunov and control barrier functions based quadratic program for spatio-temporal specifications,” in 2019 IEEE 58th Conference on Decision and Control (CDC).   IEEE, 2019, pp. 1422–1429.
  27. J. Seo, J. Lee, E. Baek, R. Horowitz, and J. Choi, “Safety-critical control with nonaffine control inputs via a relaxed control barrier function for an autonomous vehicle,” IEEE Robotics and Automation Letters, vol. 7, no. 2, pp. 1944–1951, 2022.
  28. H. Ma, B. Zhang, M. Tomizuka, and K. Sreenath, “Learning differentiable safety-critical control using control barrier functions for generalization to novel environments,” arXiv preprint arXiv:2201.01347, 2022.
  29. H. Parwana, A. Mustafa, and D. Panagou, “Trust-based rate-tunable control barrier functions for non-cooperative multi-agent systems,” in 2022 IEEE 61st Conference on Decision and Control (CDC).   IEEE, 2022, pp. 2222–2229.
  30. W. Xiao, C. Belta, and C. G. Cassandras, “Adaptive control barrier functions,” IEEE Transactions on Automatic Control, vol. 67, no. 5, pp. 2267–2281, 2021.
  31. L. Lindemann and D. V. Dimarogonas, “Control barrier functions for signal temporal logic tasks,” IEEE control systems letters, vol. 3, no. 1, pp. 96–101, 2018.
  32. X. Tan, W. S. Cortez, and D. V. Dimarogonas, “High-order barrier functions: Robustness, safety, and performance-critical control,” IEEE Transactions on Automatic Control, vol. 67, no. 6, pp. 3021–3028, 2021.
  33. W. Xiao and C. Belta, “High-order control barrier functions,” IEEE Transactions on Automatic Control, vol. 67, no. 7, pp. 3655–3662, 2021.
  34. H. K. Khalil, “Nonlinear systems third edition,” Patience Hall, vol. 115, 2002.
  35. Z. Qin, K. Zhang, Y. Chen, J. Chen, and C. Fan, “Learning safe multi-agent control with decentralized neural barrier certificates,” arXiv preprint arXiv:2101.05436, 2021.
  36. H. Parwana and D. Panagou, “Recursive feasibility guided optimal parameter adaptation of differential convex optimization policies for safety-critical systems,” in 2022 International Conference on Robotics and Automation (ICRA).   IEEE, 2022, pp. 6807–6813.
  37. J. Zeng, Z. Li, and K. Sreenath, “Enhancing feasibility and safety of nonlinear model predictive control with discrete-time control barrier functions,” in 2021 60th IEEE Conference on Decision and Control (CDC).   IEEE, 2021, pp. 6137–6144.
  38. K. Garg, R. G. Sanfelice, and A. A. Cardenas, “Control barrier function-based attack-recovery with provable guarantees,” in 2022 IEEE 61st Conference on Decision and Control (CDC).   IEEE, 2022, pp. 4808–4813.
  39. S. Diamond and S. Boyd, “Cvxpy: A python-embedded modeling language for convex optimization,” The Journal of Machine Learning Research, vol. 17, no. 1, pp. 2909–2913, 2016.
  40. A. Agrawal, S. Barratt, S. Boyd, E. Busseti, and W. M. Moursi, “Differentiating through a cone program,” J. Appl. Numer. Optim, vol. 1, no. 2, pp. 107–115, 2019.
  41. G. Wu and K. Sreenath, “Safety-critical control of a planar quadrotor,” in 2016 American control conference (ACC).   IEEE, 2016, pp. 2252–2258.
Citations (3)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up