Using Dynamic Safety Margins as Control Barrier Functions
Abstract: This paper provides a systematic approach to design control barrier functions (CBFs) for arbitrary state and input constraints using tools from the reference governor literature. In particular, it is shown that dynamic safety margins (DSMs) are CBFs for an augmented system obtained by concatenating the state and a virtual reference. The proposed approach is agnostic to the relative degree and can handle multiple state and input constraints using the control-sharing property of CBFs. The construction of CBFs using Lyapunov-based DSMs is then investigated in further detail. Numerical simulations show that the method outperforms existing DSM-based approaches, while also guaranteeing safety and persistent feasibility of the associated optimization program.
- A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,” IEEE Trans. Autom. Control, vol. 62, no. 8, pp. 3861–3876, Aug. 2017.
- M. Rauscher, M. Kimmel, and S. Hirche, “Constrained robot control using control barrier functions,” in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS), Oct. 2016, pp. 279–285.
- V. Freire and X. Xu, “Flatness-based quadcopter trajectory planning and tracking with continuous-time safety guarantees,” IEEE Trans. Control Syst. Technol., vol. 31, no. 6, pp. 2319–2334, Mar. 2023.
- T. G. Molnar, G. Orosz, and A. D. Ames, “On the safety of connected cruise control: analysis and synthesis with control barrier functions,” in Proc. IEEE 62nd Conf. Decis. Control (CDC), Dec. 2023, pp. 1106–1111.
- J. Zeng, B. Zhang, Z. Li, and K. Sreenath, “Safety-critical control using optimal-decay control barrier function with guaranteed point-wise feasibility,” in Proc. IEEE Amer. Control Conf. (ACC), May 2021, pp. 3856–3863.
- W. S. Cortez and D. V. Dimarogonas, “Safe-by-design control for Euler–Lagrange systems,” Automatica, vol. 146, p. 110620, Dec. 2022.
- Y. Chen, M. Jankovic, M. Santillo, and A. D. Ames, “Backup control barrier functions: Formulation and comparative study,” in Proc. IEEE 60th Conf. Decis. Control (CDC), Dec. 2021, pp. 6835–6841.
- V. Freire and M. M. Nicotra, “Systematic design of discrete-time control barrier functions using maximal output admissible sets,” IEEE Control Syst. Lett., vol. 7, pp. 1891–1896, Jun. 2023.
- M. M. Nicotra and E. Garone, “The explicit reference governor: A general framework for the closed-form control of constrained nonlinear systems,” IEEE Control Syst. Mag., vol. 38, no. 4, pp. 89–107, Aug. 2018.
- X. Xu, “Constrained control of input–output linearizable systems using control sharing barrier functions,” Automatica, vol. 87, pp. 195–201, Jan. 2018.
- M. M. Nicotra and E. Garone, “Control of Euler-Lagrange systems subject to constraints: An explicit reference governor approach,” in Proc. IEEE 54th Conf. Decis. Control (CDC). IEEE, Dec. 2015, pp. 1154–1159.
- E. Garone, M. Nicotra, and L. Ntogramatzidis, “Explicit reference governor for linear systems,” Int. J. Control, vol. 91, no. 6, pp. 1415–1430, 2018.
- M. M. Nicotra, T. W. Nguyen, E. Garone, and I. V. Kolmanovsky, “Explicit reference governor for the constrained control of linear time-delay systems,” IEEE Trans. Autom. Control, vol. 64, no. 7, pp. 2883–2889, Jul. 2019.
- F. Blanchini, “Set invariance in control,” Automatica, vol. 35, no. 11, pp. 1747–1767, 1999.
- E. Rimon and D. E. Koditschek, “The construction of analytic diffeomorphisms for exact robot navigation on star worlds,” in Proc. IEEE Int. Conf. Robot. Autom. (ICRA), May 1989, pp. 21–26.
- Y. Fang, E. Zergeroglu, W. Dixon, and D. Dawson, “Nonlinear coupling control laws for an overhead crane system,” in Proc. IEEE Int. Conf. Control Appl. (CCA), Sep. 2001, pp. 639–644.
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