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
2022
article
Autonomous traffic at intersections: An optimization-based analysis of possible time, energy, and CO savings
Networks
@article{Le2022,
author = {Le, Do Duc and Merkert, Maximilian and Sorgatz, Stephan and Hahn, Mirko and Sager, Sebastian},
title = {Autonomous traffic at intersections: An optimization-based analysis of possible time, energy, and CO savings},
journal = {Networks},
publisher = {Wiley},
year = {2022},
volume = {79},
number = {3},
pages = {338--363},
url = {https://optimization-online.org/?p=16226},
doi = {10.1002/net.22078}
}
2021
incollection
Mathematical Optimization and Machine Learning for Efficient Urban Traffic
German Success Stories in Industrial Mathematics
@incollection{Bethge2022,
author = {Bethge, Johanna and Findeisen, Rolf and Duc Le, Do and Merkert, Maximilian and Sager, Sebastian and Savchenko, Anton and Rewald, Hannes},
title = {Mathematical Optimization and Machine Learning for Efficient Urban Traffic},
booktitle = {German Success Stories in Industrial Mathematics},
publisher = {Springer International Publishing},
year = {2021},
editor = {K\"{u}fer, Karl-Heinz and Maass, Peter and Milde, Anja and Schulz, Volker},
series = {Mathematics in Industry},
pages = {113--120},
url = {https://mathopt.de/publications/Bethge2020.pdf},
doi = {10.1007/978-3-030-81455-7_19}
}
2021
article
Multiphase Mixed-Integer Nonlinear Optimal Control of Hybrid Electric Vehicles
Automatica
@article{Robuschi2021,
author = {Robuschi, Nicol\`o and Zeile, Clemens and Sager, Sebastian and Braghin, Francesco},
title = {Multiphase Mixed-Integer Nonlinear Optimal Control of Hybrid Electric Vehicles},
journal = {Automatica},
publisher = {Elsevier BV},
year = {2021},
volume = {123},
pages = {109325},
url = {https://optimization-online.org/?p=15819},
doi = {10.1016/j.automatica.2020.109325}
}
2016
phdthesis
Optimization of Vehicular Traffic at Traffic-Light Controlled Intersections
Otto von Guericke University Magdeburg
@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}
}
2015
article
Efficient upper and lower bounds for global mixed-integer optimal control
Journal of Global Optimization
@article{Sager2015,
author = {Sager, Sebastian and Claeys, Mathieu and Messine, Fr\'ed\'eric},
title = {{E}fficient upper and lower bounds for global mixed-integer optimal control},
journal = {Journal of Global Optimization},
publisher = {Springer Science and Business Media LLC},
year = {2015},
volume = {61},
number = {4},
pages = {721--743},
doi = {10.1007/s10898-014-0156-4}
}
2014
incollection
Model Predictive Control of Autonomous Vehicles
Optimization and Optimal Control in Automotive Systems
@incollection{Zanon2014,
author = {Zanon, Mario and Frasch, Janick V. 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},
doi = {10.1007/978-3-319-05371-4_3}
}
2013
inproceedings
An Auto-generated Nonlinear MPC Algorithm for Real-Time Obstacle Avoidance of Ground Vehicles
2013 European Control Conference (ECC)
@inproceedings{Frasch2013b,
author = {Frasch, Janick V. and Gray, Andrew and Zanon, Mario and Ferreau, Hans Joachim and Sager, Sebastian and Borrelli, Francesco and Diehl, Moritz},
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 = {2013 European Control Conference (ECC)},
publisher = {IEEE},
year = {2013},
pages = {4136--4141},
doi = {10.23919/ecc.2013.6669836}
}
2013
inproceedings
Mixed-integer NMPC for predictive cruise control of heavy-duty trucks
2013 European Control Conference (ECC)
@inproceedings{Kirches2013,
author = {Kirches, Christian and Bock, Hans Georg and Schloder, Johannes P. and Sager, Sebastian},
title = {{M}ixed-integer {NMPC} for predictive cruise control of heavy-duty trucks},
booktitle = {2013 European Control Conference (ECC)},
publisher = {IEEE},
year = {2013},
pages = {4118--4123},
address = {Zurich, Switzerland},
doi = {10.23919/ecc.2013.6669210}
}
2013
inproceedings
Nonlinear Moving Horizon Estimation for Combined State and Friction Coefficient Estimation in Autonomous Driving
Proceedings of the European Control Conference
@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}
}
2012
inproceedings
Moving Horizon Observation for Autonomous Operation of Agricultural Vehicles
Proceedings of the European Control Conference (ECC)
@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}
}
2012
inproceedings
Spatial Predictive Control for Agile Semi-Autonomous Ground Vehicles
Proceedings of the 11th International Symposium on Advanced Vehicle Control
@inproceedings{Gao2012,
author = {Gao, Y. and Gray, A. and Frasch, J. V. and Lin, T. and Tseng, E. and Hedrick, J.K. and Borrelli, F.},
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}
}
2011
article
Optimal control of Formula 1 race cars in a VDrift based virtual environment
IFAC Proceedings Volumes
Proceedings of the 18th IFAC World Congress
@article{Kehrle2011,
author = {Kehrle, Florian and Frasch, Janick V. and Kirches, Christian and Sager, Sebastian},
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},
journal = {IFAC Proceedings Volumes},
publisher = {Elsevier BV},
year = {2011},
editor = {Bittanti, S. and Cenedese, A. and Zampieri, S.},
volume = {44},
number = {1},
pages = {11907--11912},
address = {Milan, Italy},
url = {https://mathopt.de/publications/Kehrle2011.pdf},
doi = {10.3182/20110828-6-it-1002.02954}
}
2010
mastersthesis
Auf Dynamischer Programmierung basierende nichtlineare modellprädiktive Regelung f̈̊ LKW
Ruprecht-Karls-Universität Heidelberg
@mastersthesis{Buchner2010,
author = {Buchner, A.},
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}
}
2010
patent
Verfahren zum Steuern des Betriebs eines Fahrzeugs
@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}
}
2010
article
Time-optimal control of automobile test drives with gear shifts
Optimal Control Applications and Methods
@article{Kirches2010,
author = {Kirches, Christian and Sager, Sebastian and Bock, Hans Georg and Schl\"oder, Johannes P.},
title = {{T}ime-optimal control of automobile test drives with gear shifts},
journal = {Optimal Control Applications and Methods},
publisher = {Wiley},
year = {2010},
volume = {31},
number = {2},
pages = {137--153},
url = {https://mathopt.de/publications/Kirches2010.pdf},
doi = {10.1002/oca.892}
}