Abstract
Detailed prediction models with robust constraints and small sampling times in Model Predictive Control yield conservative behavior and large computational effort, especially for longer prediction horizons. Here, we extend and combine previous Model Predictive Control methods that account for prediction uncertainty and reduce computational complexity. The proposed method uses robust constraints on a detailed model for short-term predictions, while probabilistic constraints are employed on a simplified model with increased sampling time for long-term predictions. The underlying methods are introduced before presenting the proposed Model Predictive Control approach. The advantages of the proposed method are shown in a mobile robot simulation example.
Zusammenfassung
Detaillierte Prädiktionsmodelle mit robusten Nebenbedingungen in der Modellprädiktiven Regelung führen zu konservativem Verhalten und hohem Rechenaufwand, besonders für lange Prädiktionshorizonte. In dieser Arbeit werden die Vorteile bisheriger Arbeiten zur Modellprädiktiven Regelung erweitert und kombiniert, um Prädiktionsunsicherheit zu berücksichtigen und den Rechenaufwand zu reduzieren. Die vorgeschlagene Methode nutzt robuste Nebenbedingungen und ein detailliertes Modell für kurzfristige Prädiktionen, während probabilistische Nebenbedingungen, ein vereinfachtes Modell und eine größere Abtastzeit für die langfristige Prädiktion genutzt werden. Die Vorteile der neuen Methode werden in einem Simulationsbeispiel analysiert.
About the authors
Tim Brüdigam, M. Sc., is currently a research associate at the Chair of Automatic Control Engineering at the Technical University of Munich. His main research interest lies in advancing Model Predictive Control (MPC), especially stochastic MPC (SMPC), with possible application in automated driving.
Johannes Teutsch, B. Sc., is currently aiming for a Master’s degree in electrical and computer engineering at the Technical University of Munich, with focus on control and machine learning. His research at the Chair of Automatic Control Engineering revolves around Model Predictive Control (MPC).
Dirk Wollherr is Privatdozent at the Institute of Automatic Control Engineering, TU München. From 2001–2004 he was a research assistant at the Control Systems Group, TU Berlin. He was granted a research fellowship at the University of Tokyo in 2004. His research interests include autonomous mobile robots, and human-robot-interaction.
Marion Leibold is Privatdozent at the Institute of Automatic Control Engineering, TU München. From 2003–2004 she was a research assistant at the Control Systems Group, TU Berlin. Her research interests include optimal and nonlinear control in robotics applications.
Martin Buss has been a Full Professor (Chair) in the Chair of Automatic Control Engineering, Faculty of Electrical Engineering and Information Technology, Technical University of Munich since 2003. His research interests include automatic control, mechatronics, multimodal human system interfaces, optimization, nonlinear, and hybrid discrete-continuous systems.
References
1. T. Bäthge, S. Lucia and R. Findeisen. Exploiting models of different granularity in robust predictive control. In 2016 IEEE 55th Conference on Decision and Control (CDC), pages 2763–2768, Las Vegas, USA, Dec 2016.10.1109/CDC.2016.7798680Search in Google Scholar
2. M. J. Tippett, C. K. Tan and J. Bao. Non-constant prediction-step mpc for processes with multi-scale dynamics. IFAC Proceedings Volumes, 47(3):3068–3073, 2014. 19th IFAC World Congress.10.3182/20140824-6-ZA-1003.01093Search in Google Scholar
3. C. K. Tan, M. J. Tippett and J. Bao. Model predictive control with non-uniformly spaced optimization horizon for multi-timescale processes. Computers & Chemical Engineering, 84:162–170, 2016.10.1016/j.compchemeng.2015.08.010Search in Google Scholar
4. R. Cagienard, P. Grieder, E. C. Kerrigan and M. Morari. Move blocking strategies in receding horizon control. In 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No. 04CH37601), volume 2, pages 2023–2028, Dec 2004.10.1109/CDC.2004.1430345Search in Google Scholar
5. R. C. Shekhar and C. Manzie. Optimal move blocking strategies for model predictive control. Automatica, 61:27–34, 2015.10.1016/j.automatica.2015.07.030Search in Google Scholar
6. D. Q. Mayne. Model predictive control: Recent developments and future promise. Automatica, 50(12):2967–2986, 2014.10.1016/j.automatica.2014.10.128Search in Google Scholar
7. A. Mesbah. Stochastic model predictive control: An overview and perspectives for future research. IEEE Control Systems, 36(6):30–44, Dec 2016.10.1109/MCS.2016.2602087Search in Google Scholar
8. A. T. Schwarm and M. Nikolaou. Chance-constrained model predictive control. AIChE Journal, 45(8):1743–1752, 1999.10.1002/aic.690450811Search in Google Scholar
9. B. Kouvaritakis, M. Cannon, S. V. Rakovic and Q. Cheng. Explicit use of probabilistic distributions in linear predictive control. Automatica, 46(10):1719–1724, 2010.10.1049/ic.2010.0343Search in Google Scholar
10. M. Farina, L. Giulioni and R. Scattolini. Stochastic linear model predictive control with chance constraints – a review. Journal of Process Control, 44(Supplement C):53–67, 2016.10.1016/j.jprocont.2016.03.005Search in Google Scholar
11. M. Lorenzen, F. Dabbene, R. Tempo and F. Allgoewer. Constraint-tightening and stability in stochastic model predictive control. IEEE Transactions on Automatic Control, 62(7):3165–3177, July 2017.10.1109/TAC.2016.2625048Search in Google Scholar
12. L. Blackmore, M. Ono, A. Bektassov and B. C. Williams. A probabilistic particle-control approximation of chance-constrained stochastic predictive control. Trans. Rob., 26(3):502–517, June 2010.10.1109/TRO.2010.2044948Search in Google Scholar
13. G. Schildbach, L. Fagiano, C. Frei and M. Morari. The scenario approach for stochastic model predictive control with bounds on closed-loop constraint violations. Automatica, 50(12):3009–3018, 2014.10.1016/j.automatica.2014.10.035Search in Google Scholar
14. T. Brüdigam, J. Teutsch, D. Wollherr and M. Leibold. Combined robust and stochastic model predictive control for models of different granularity. In 21st IFAC World Congress, Berlin, Germany, 2020.10.1016/j.ifacol.2020.12.515Search in Google Scholar
15. T. Brüdigam, D. Prader, D. Wollherr and M. Leibold. Model predictive control with models of different granularity and a non-uniformly spaced prediction horizon. In 2021 American Control Conference, 2021.10.23919/ACC50511.2021.9482617Search in Google Scholar
16. S. Gugercin and A. C. Antoulas. A survey of model reduction by balanced truncation and some new results. International Journal of Control, 77(8):748–766, 2004.10.1080/00207170410001713448Search in Google Scholar
17. J. B. Rawlings, D. Q. Mayne and M. Diehl. Model Predictive Control: Theory, Computation, and Design. Nob Hill Publishing, 2017.Search in Google Scholar
18. D. Q. Mayne, M. M. Seron and S. V. Raković. Robust model predictive control of constrained linear systems with bounded disturbances. Automatica, 41(2):219–224, 2005.10.1016/j.automatica.2004.08.019Search in Google Scholar
19. A. V. Raković, E. Kerrigan, K. Kouramas and D. Q. Mayne. Invariant approximations of robustly positively invariant sets for constrained linear discrete-time systems subject to bounded disturbances. Technical report, Department of Engineering, University of Cambridge, UK, 2004.10.3182/20050703-6-CZ-1902.01038Search in Google Scholar
20. M. Lorenzen, F. Dabbene, R. Tempo and F. Allgöwer. Stochastic mpc with offline uncertainty sampling. Automatica, 81:176–183, 2017.10.1016/j.automatica.2017.03.031Search in Google Scholar
21. M. C. Campi and S. Garatti. A sampling-and-discarding approach to chance-constrained optimization: Feasibility and optimality. Journal of Optimization Theory and Applications, 148(2):257–280, Feb 2011.10.1007/s10957-010-9754-6Search in Google Scholar
22. B. Brito, B. Floor, L. Ferranti and J. Alonso-Mora. Model predictive contouring control for collision avoidance in unstructured dynamic environments. IEEE Robotics and Automation Letters, 4(4):4459–4466, 2019.10.1109/LRA.2019.2929976Search in Google Scholar
23. C. Jewison, R. S. Erwin and A. Saenz-Otero. Model predictive control with ellipsoid obstacle constraints for spacecraft rendezvous. IFAC-PapersOnLine, 48(9):257–262, 2015. 1st IFAC Workshop on Advanced Control and Navigation for Autonomous Aerospace Vehicles ACNAAV’15.10.1016/j.ifacol.2015.08.093Search in Google Scholar
24. A. Schimpe and F. Diermeyer. Steer with me: A predictive, potential field-based control approach for semi-autonomous, teleoperated road vehicles. In 2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC), pages 1–6, 2020.10.1109/ITSC45102.2020.9294702Search in Google Scholar
25. T. Brüdigam, J. Zhan, D. Wollherr and M. Leibold. Collision avoidance with stochastic model predictive control for systems with a twofold uncertainty structure, 2021. arXiv:2106.08463.10.1109/ITSC48978.2021.9564589Search in Google Scholar
26. T. Brüdigam, M. Olbrich, M. Leibold and D. Wollherr. Combining stochastic and scenario model predictive control to handle target vehicle uncertainty in autonomous driving. In 2018 IEEE 21st International Conference on Intelligent Transportation Systems (ITSC), Maui, USA, 2018.10.1109/ITSC.2018.8569909Search in Google Scholar
27. M. Herceg, M. Kvasnica, C. N. Jones and M. Morari. Multi-Parametric Toolbox 3.0. In Proc. of the European Control Conference, pages 502–510, Zürich, Switzerland, July 17–19, 2013.10.23919/ECC.2013.6669862Search in Google Scholar
28. A. Domahidi and J. Jerez. Forces professional. Embotech AG, https://embotech.com/FORCES-Pro, 2014–2019.Search in Google Scholar
29. A. Zanelli, A. Domahidi, J. Jerez and M. Morari. Forces nlp: an efficient implementation of interior-point methods for multistage nonlinear nonconvex programs. International Journal of Control, pages 1–17, 2017.10.1080/00207179.2017.1316017Search in Google Scholar
30. T. Brüdigam, M. Olbrich, D. Wollherr and M. Leibold. Stochastic model predictive control with a safety guarantee for automated driving. IEEE Transactions on Intelligent Vehicles, 2021.10.1109/TIV.2021.3074645Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
