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Solving Complex Intersection Management Problems Using Bi-level MINLPs and Piecewise Linearization Techniques

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Smart Cities, Green Technologies, and Intelligent Transport Systems (VEHITS 2021, SMARTGREENS 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1612))

Abstract

We investigate a complex Intersection Management Problem (IMP) for automated vehicles and introduce a method for the automated coordination of vehicles with the aim to minimize total clearance time for the intersection. The method is capable of handling multiple vehicles (per lane or distributed over several lanes), multiple lanes, variable arrival times and velocities, and multiple turn options in non-symmetric intersection scenarios. In order to optimally coordinate the vehicles we employ a bi-level optimization formulation coupling a scheduling problem at the upper level with an optimal control problem at the lower level. The latter takes into account the dynamics of the vehicles and the former aims to find an optimal sequence of arrivals at the intersection. Collision avoidance on the complete driving paths, i.e., at, before and after the intersection, is ensured by the problem formulation. In order to solve the resulting mixed-integer nonlinear bi-level optimization problem we develop suitable piecewise linearization techniques for the value function of the optimal control problems which eventually yields a large-scale mixed-integer linear problem. Numerical examples show the efficiency of the proposed approach.

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Acknowledgement

This research is funded by dtec.bw – Digitalization and Technology Research Center of the Bundeswehr [projects MissionLab, MORE, EMERGENCY-VRD] and the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, Award No. FA8655-20-1-7026. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the Air Force Office of Scientific Research, Air Force Materiel Command, USAF.

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Institute of Applied Mathematics and Scientific Computing, Universität der Bundeswehr München, Neubiberg, Germany

    Matthias Gerdts & Sergejs Rogovs

  2. Department of Industrial Engineering, University of Trento, Trento, Italy

    Giammarco Valenti

Authors
  1. Matthias Gerdts
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  2. Sergejs Rogovs
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  3. Giammarco Valenti
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Corresponding author

Correspondence to Sergejs Rogovs .

Editor information

Editors and Affiliations

  1. Siemens, Munich, Germany

    Cornel Klein

  2. RWTH Aachen, Aachen, Germany

    Matthias Jarke

  3. Maynooth University, Maynooth, Kildare, Ireland

    Markus Helfert

  4. Universität Kaiserslautern, Kaiserslautern, Germany

    Karsten Berns

  5. Ford Research and Advanced Engineering, Dearborn, MI, USA

    Oleg Gusikhin

A Quantities, Variables, and Conflict Matrix

A Quantities, Variables, and Conflict Matrix

Conflict matrix for the 10-lane intersection problem:

$$ C = \left[ \begin{array}{ccccccccccc} 4&{}3&{}3&{}0&{}2&{}0&{}0&{}0&{}0&{}0\\ 3&{}4&{}3&{}0&{}1&{}2&{}0&{}0&{}0&{}0\\ 3&{}3&{}4&{}0&{}1&{}1&{}2&{}0&{}0&{}0\\ 0&{}0&{}0&{}4&{}3&{}3&{}0&{}2&{}1&{}0\\ 2&{}1&{}1&{}3&{}4&{}3&{}0&{}0&{}1&{}1\\ 0&{}2&{}1&{}3&{}3&{}4&{}0&{}0&{}1&{}1\\ 0&{}0&{}2&{}0&{}0&{}0&{}4&{}3&{}1&{}1\\ 0&{}0&{}0&{}2&{}0&{}0&{}3&{}4&{}0&{}0\\ 0&{}0&{}0&{}1&{}1&{}1&{}1&{}0&{}4&{}0\\ 0&{}0&{}0&{}0&{}1&{}1&{}1&{}0&{}0&{}4 \end{array}\right] $$
Table 1. Quantities and variables introduced in this paper.
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Gerdts, M., Rogovs, S., Valenti, G. (2022). Solving Complex Intersection Management Problems Using Bi-level MINLPs and Piecewise Linearization Techniques. In: Klein, C., Jarke, M., Helfert, M., Berns, K., Gusikhin, O. (eds) Smart Cities, Green Technologies, and Intelligent Transport Systems. VEHITS SMARTGREENS 2021 2021. Communications in Computer and Information Science, vol 1612. Springer, Cham. https://doi.org/10.1007/978-3-031-17098-0_13

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  • DOI: https://doi.org/10.1007/978-3-031-17098-0_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-17097-3

  • Online ISBN: 978-3-031-17098-0

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