Mobility
Triggered by technological advances, automated driving of vehicles is a reality. Actually driving vehicles, the use of integrated training devices that tell drivers what they should do, and GPS based look-ahead control strategies raise the question of what the optimal way of driving the vehicle would be. Optimality typically refers to energy consumption, time, driver's comfort, hardware wear-off, or a combination of these objectives.
Control problems that arise in this research field have at least two characteristics which stimulate development of novel mathematical methods. First, the real-time requirements are high as the time between measurements and a reaction of the controler is limited due to the possibly high driving speed. Second, models of interest involve discrete decisions, such as the optimal choice of gear or mode of operation in hybrid vehicles. Or switching behavior of traffic lights. Nonlinear Model Predictive Control problems in Automotive Engineering are hence in the class of MIOCP.
This YouTube video is an exemplary visualization of a time-optimal ride on the Hockenheim ring, by Florian Kehrle and Sebastian Sager. The solution has been calculated with modern mathematical methods. It is based on a simplified dynamical model, including nonlinear tire dynamics. The optimization took the gear choice explicitely into account. The solution is open loop without any feedback and for one complete round.
Selected publications
| Author | Title | Year | Journal/Proceedings | Reftype | Link |
|---|---|---|---|---|---|
| Robuschi, N., Zeile, C., Sager, S. & Braghin, F. | Multiphase Mixed-Integer Nonlinear Optimal Control of Hybrid Electric Vehicles [BibTeX] |
2021 | Automatica | article | url |
BibTeX:
@article{Robuschi2021,
author = {N. Robuschi and C. Zeile and S. Sager and F. Braghin},
title = {Multiphase Mixed-Integer Nonlinear Optimal Control of Hybrid Electric Vehicles},
journal = {Automatica},
year = {2021},
volume = {123},
pages = {109325},
url = {http://www.optimization-online.org/DB_HTML/2019/05/7223.html}
}
|
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| Bethge, J., Findeisen, R., Le, D., Merkert, M., H., R., Sager, S., Savchenko, A. & Sorgatz, S. | Mathematical Optimization and Machine Learning for Efficient Urban Traffic [BibTeX] |
2020 | KoMSO Success Stories on Mathematics in Industry | incollection | url |
BibTeX:
@incollection{Bethge2020,
author = {Bethge, J. and Findeisen, R. and Le, D.D. and Merkert, M. and Rewald H. and Sager, S. and Savchenko, A. and Sorgatz, S.},
title = {Mathematical Optimization and Machine Learning for Efficient Urban Traffic},
booktitle = {KoMSO Success Stories on Mathematics in Industry},
publisher = {Springer},
year = {2020},
editor = {Karl-Heinz K\"{u}fer and Peter Maass and Anja Milde and Volker Schulz},
note = {accepted},
url = {https://mathopt.de/publications/Bethge2020.pdf}
}
|
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| Le, D., Merkert, M., Sorgatz, S., Hahn, M. & Sager, S. | Autonomous traffic at intersections: an optimization-based analysis of possible time, energy, and CO2 savings [BibTeX] |
2020 | Preprint (Optimization Online), submitted to Networks | article | url |
BibTeX:
@article{Le2020,
author = {Le, D.D. and Merkert, M. and Sorgatz, S. and Hahn, M. and Sager, S.},
title = {Autonomous traffic at intersections: an optimization-based analysis of possible time, energy, and {CO2} savings},
journal = {Preprint (Optimization Online), submitted to {Networks}},
year = {2020},
note = {submitted},
url = {http://www.optimization-online.org/DB_HTML/2020/02/7600.html}
}
|
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| Sorgatz, S. | Optimization of Vehicular Traffic at Traffic-Light Controlled Intersections [BibTeX] |
2016 | School: Otto-von-Guericke University Magdeburg | phdthesis | url |
BibTeX:
@phdthesis{Sorgatz2016,
author = {Sorgatz, S.},
title = {Optimization of Vehicular Traffic at Traffic-Light Controlled Intersections},
school = {Otto-von-Guericke University Magdeburg},
year = {2016},
url = {https://mathopt.de/publications/Sorgatz2016.pdf}
}
|
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| Sager, S., Claeys, M. & Messine, F. | Efficient upper and lower bounds for global mixed-integer optimal control [BibTeX] |
2015 | Journal of Global Optimization | article | DOI |
BibTeX:
@article{Sager2015,
author = {Sager, S. and M. Claeys and F. Messine},
title = {{E}fficient upper and lower bounds for global mixed-integer optimal control},
journal = {{J}ournal of {G}lobal {O}ptimization},
year = {2015},
volume = {61},
number = {4},
pages = {721--743},
doi = {http://dx.doi.org/10.1007/s10898-014-0156-4}
}
|
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| Zanon, M., Frasch, J., Vukov, M., Sager, S. & Diehl, M. | Model Predictive Control of Autonomous Vehicles [BibTeX] |
2014 | Optimization and Optimal Control in Automotive Systems | incollection | DOI url |
BibTeX:
@incollection{Zanon2014,
author = {Zanon, Mario and Frasch, JanickV. and Vukov, Milan and Sager, Sebastian and Diehl, Moritz},
title = {Model Predictive Control of Autonomous Vehicles},
booktitle = {Optimization and Optimal Control in Automotive Systems},
publisher = {Springer International Publishing},
year = {2014},
editor = {Waschl, Harald and Kolmanovsky, Ilya and Steinbuch, Maarten and del Re, Luigi},
volume = {455},
series = {Lecture Notes in Control and Information Sciences},
pages = {41--57},
url = {http://dx.doi.org/10.1007/978-3-319-05371-4_3},
doi = {http://dx.doi.org/10.1007/978-3-319-05371-4_3}
}
|
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| Frasch, J. V., Gray, A. J., Zanon, M., Ferreau, H. J., Sager, S., Borrelli, F. & Diehl, M. | An Auto-generated Nonlinear MPC Algorithm for Real-Time Obstacle Avoidance of Ground Vehicles [BibTeX] |
2013 | Proceedings of the European Control Conference | inproceedings | |
BibTeX:
@inproceedings{Frasch2013b,
author = {Frasch, J. V. and Gray, A. J. and Zanon, M. and Ferreau, H. J. and Sager, S. and Borrelli, F. and Diehl, M.},
title = {{A}n {A}uto-generated {N}onlinear {MPC} {A}lgorithm for {R}eal-{T}ime {O}bstacle {A}voidance of {G}round {V}ehicles},
booktitle = {{P}roceedings of the {E}uropean {C}ontrol {C}onference},
year = {2013}
}
|
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| Kirches, C., Bock, H., Schlöder, J. & Sager, S. | Mixed-integer NMPC for predictive cruise control of heavy-duty trucks [BibTeX] |
2013 | European Control Conference | inproceedings | |
BibTeX:
@inproceedings{Kirches2013,
author = {C. Kirches and H.G. Bock and J.P. Schl\"oder and S. Sager},
title = {{M}ixed-integer {NMPC} for predictive cruise control of heavy-duty trucks},
booktitle = {{E}uropean {C}ontrol {C}onference},
year = {2013},
pages = {4118--4123},
address = {Zurich, Switzerland}
}
|
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| Zanon, M., Frasch, J. & Diehl, M. | Nonlinear Moving Horizon Estimation for Combined State and Friction Coefficient Estimation in Autonomous Driving [BibTeX] |
2013 | Proceedings of the European Control Conference | inproceedings | |
BibTeX:
@inproceedings{Zanon2013b,
author = {Zanon, M. and Frasch, J. and Diehl, M.},
title = {{N}onlinear {M}oving {H}orizon {E}stimation for {C}ombined {S}tate and {F}riction {C}oefficient {E}stimation in {A}utonomous {D}riving},
booktitle = {{P}roceedings of the {E}uropean {C}ontrol {C}onference},
year = {2013}
}
|
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| Frasch, J. V., Kraus, T., Saeys, W. & Diehl, M. | Moving Horizon Observation for Autonomous Operation of Agricultural Vehicles [BibTeX] |
2012 | Proceedings of the European Control Conference (ECC) | inproceedings | |
BibTeX:
@inproceedings{Frasch2012b,
author = {Frasch, J. V. and Kraus, T. and Saeys, W. and Diehl, M.},
title = {{M}oving {H}orizon {O}bservation for {A}utonomous {O}peration of {A}gricultural {V}ehicles},
booktitle = {{P}roceedings of the {E}uropean {C}ontrol {C}onference ({ECC})},
year = {2012}
}
|
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| Gao, Y., Gray, A., Frasch, J. V., Lin, T., Tseng, E., Hedrick, J. & Borrelli, F. | Spatial Predictive Control for Agile Semi-Autonomous Ground Vehicles [BibTeX] |
2012 | Proceedings of the 11th International Symposium on Advanced Vehicle Control | inproceedings | |
BibTeX:
@inproceedings{Gao2012,
author = {Y. Gao and A. Gray and J. V. Frasch and T. Lin and E. Tseng and J.K. Hedrick and F. Borrelli},
title = {{S}patial {P}redictive {C}ontrol for {A}gile {S}emi-{A}utonomous {G}round {V}ehicles},
booktitle = {{P}roceedings of the 11th {I}nternational {S}ymposium on {A}dvanced {V}ehicle {C}ontrol},
year = {2012}
}
|
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| Kehrle, F., Frasch, J., Kirches, C. & Sager, S. | Optimal control of Formula 1 race cars in a VDrift based virtual environment [BibTeX] |
2011 | Proceedings of the 18th IFAC World Congress | inproceedings | DOI url |
BibTeX:
@inproceedings{Kehrle2011,
author = {Kehrle, F. and Frasch, J.V. and Kirches, C. and Sager, S.},
title = {{O}ptimal control of {F}ormula 1 race cars in a {VDrift} based virtual environment},
booktitle = {{P}roceedings of the 18th {IFAC} {W}orld {C}ongress},
year = {2011},
editor = {S. Bittanti and A. Cenedese and S. Zampieri},
pages = {11907--11912},
address = {Milan, Italy},
url = {https://mathopt.de/publications/Kehrle2011.pdf},
doi = {http://dx.doi.org/10.3182/20110828-6-IT-1002.02954}
}
|
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| Buchner, A. | Auf Dynamischer Programmierung basierende nichtlineare modellprädiktive Regelung für LKW [BibTeX] |
2010 | School: Ruprecht-Karls-Universität Heidelberg | mastersthesis | url |
BibTeX:
@mastersthesis{Buchner2010,
author = {A. Buchner},
title = {{A}uf {D}ynamischer {P}rogrammierung basierende nichtlineare modellpr\"adiktive {R}egelung f\"ur {LKW}},
school = {Ruprecht-Karls-Universit\"at Heidelberg},
year = {2010},
url = {https://mathopt.de/publications/Buchner2010.pdf}
}
|
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| Gehring, O., Kauffmann, F., Bock, H., Kirches, C., Sager, S. & Schloeder, J. | Verfahren zum Steuern des Betriebs eines Fahrzeugs [BibTeX] |
2010 | patent | url |
|
BibTeX:
@patent{Gehring2010,
author = {Gehring, O. and Kauffmann, F. and Bock, H.G. and Kirches, C. and Sager, S. and Schloeder, J.P.},
title = {Verfahren zum Steuern des Betriebs eines Fahrzeugs},
year = {2010},
number = {DE102009030784A1},
url = {https://patents.google.com/patent/DE102009030784A1}
}
|
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| Kirches, C., Sager, S., Bock, H. & Schlöder, J. | Time-optimal control of automobile test drives with gear shifts [BibTeX] |
2010 | Optimal Control Applications and Methods | article | url |
BibTeX:
@article{Kirches2010,
author = {C. Kirches and S. Sager and H.G. Bock and J.P. Schl\"oder},
title = {{T}ime-optimal control of automobile test drives with gear shifts},
journal = {{O}ptimal {C}ontrol {A}pplications and {M}ethods},
year = {2010},
volume = {31},
number = {2},
pages = {137--153},
url = {https://mathopt.de/publications/Kirches2010.pdf}
}
|
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Further references of the MathOpt group can be found on this page.