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

2021
incollection
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
KoMSO Success Stories on Mathematics in Industry
@incollection{Bethge2021,
    author = {Bethge, J. and Findeisen, R. and Le, D.D. and Merkert, M. and H., Rewald 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 = {2021},
    editor = {K\"{u}fer, Karl-Heinz and Maass, Peter and Milde, Anja and Schulz, Volker},
    note = {accepted},
    url = {https://mathopt.de/publications/Bethge2020.pdf}
}
2021
article
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
Networks
@article{Le2021,
    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 = {Networks},
    year = {2021},
    url = {http://www.optimization-online.org/DB_HTML/2020/02/7600.html},
    doi = {10.1002/net.22078}
}
2021
article
Robuschi, N., Zeile, C., Sager, S., Braghin, F.
Multiphase Mixed-Integer Nonlinear Optimal Control of Hybrid Electric Vehicles
Automatica
@article{Robuschi2021,
    author = {Robuschi, N. and Zeile, C. and Sager, S. and Braghin, F.},
    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}
}
2016
phdthesis
Sorgatz, S.
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
Sager, S., Claeys, M., Messine, F.
Efficient upper and lower bounds for global mixed-integer optimal control
Journal of Global Optimization
@article{Sager2015,
    author = {Sager, S. and Claeys, M. and Messine, F.},
    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 = {10.1007/s10898-014-0156-4}
}
2014
incollection
Zanon, M., Frasch, J., Vukov, M., Sager, S., Diehl, M.
Model Predictive Control of Autonomous Vehicles
Optimization and Optimal Control in Automotive Systems
@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},
    doi = {10.1007/978-3-319-05371-4_3}
}
2013
inproceedings
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
Proceedings of the European Control Conference
@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}
}
2013
inproceedings
Kirches, C., Bock, H., Schlöder, J., Sager, S.
Mixed-integer NMPC for predictive cruise control of heavy-duty trucks
European Control Conference
@inproceedings{Kirches2013,
    author = {Kirches, C. and Bock, H.G. and Schl\"oder, J.P. and Sager, S.},
    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}
}
2013
inproceedings
Zanon, M., Frasch, J., Diehl, M.
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
Frasch, J. V., Kraus, T., Saeys, W., Diehl, M.
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
Gao, Y., Gray, A., Frasch, J. V., Lin, T., Tseng, E., Hedrick, J., Borrelli, F.
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
inproceedings
Kehrle, F., Frasch, J., Kirches, C., Sager, S.
Optimal control of Formula 1 race cars in a VDrift based virtual environment
Proceedings of the 18th IFAC World Congress
@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 = {Bittanti, S. and Cenedese, A. and Zampieri, S.},
    pages = {11907--11912},
    address = {Milan, Italy},
    url = {https://mathopt.de/publications/Kehrle2011.pdf},
    doi = {10.3182/20110828-6-IT-1002.02954}
}
2010
mastersthesis
Buchner, A.
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
Gehring, O., Kauffmann, F., Bock, H., Kirches, C., Sager, S., Schloeder, J.
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
Kirches, C., Sager, S., Bock, H., Schlöder, J.
Time-optimal control of automobile test drives with gear shifts
Optimal Control Applications and Methods
@article{Kirches2010,
    author = {Kirches, C. and Sager, S. and Bock, H.G. and Schl\"oder, J.P.},
    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}
}

Prof. Dr. rer.nat. habil. Sebastian Sager
Head of MathOpt group
at the Institute of Mathematical Optimization
at the Faculty of Mathematics
at the Otto von Guericke University Magdeburg

Universitätsplatz 2, G02-224
39106 Magdeburg, Germany

: +49 391 67 58745
: +49 391 67 11171
:

Susanne Heß

Universitätsplatz 2, G02-206
39106 Magdeburg, Germany

: +49 391 67-58756
: +49 391 67-11171
:

Prof. Dr. rer.nat. habil. Sebastian Sager
Head of MathOpt group
at the Institute of Mathematical Optimization
at the Faculty of Mathematics
at the Otto von Guericke University Magdeburg

Universitätsplatz 2, G02-224
39106 Magdeburg, Germany

: +49 391 67 58745
: +49 391 67 11171
:

Susanne Heß

Universitätsplatz 2, G02-206
39106 Magdeburg, Germany

: +49 391 67-58756
: +49 391 67-11171
: