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Model Predictive Control of Autonomous Vehicles

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Optimization and Optimal Control in Automotive Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 455))

Abstract

The control of autonomous vehicles is a challenging task that requires advanced control schemes. Nonlinear Model Predictive Control (NMPC) and Moving Horizon Estimation (MHE) are optimization-based control and estimation techniques that are able to deal with highly nonlinear, constrained, unstable and fast dynamic systems. In this chapter, these techniques are detailed, a descriptive nonlinear model is derived and the performance of the proposed control scheme is demonstrated in simulations of an obstacle avoidance scenario on a low-fricion icy road.

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References

  1. Falcone P, Borrelli F, Asgari J, Tseng H, Hrovat D (2008) Low complexity MPC schemes for integrated vehicle dynamics control problems. 9\(^{th}\) international symposium on advanced vehicle, control

    Google Scholar 

  2. Gao Y, Gray A, Frasch JV, Lin T, Tseng E, Hedrick J, Borrelli F (2012) Spatial predictive control for agile semi-autonomous ground vehicles. In: Proceedings of the 11th international symposium on advanced vehicle, control

    Google Scholar 

  3. Gao Y, Lin T, Borrelli F, Tseng E, Hrovat D (2010) Predictive control of autonomous ground vehicles with obstacle avoidance on slippery roads. In: Dynamic systems and control conference

    Google Scholar 

  4. Gray A, Gao Y, Lin T, Hedrick J, Tseng E, Borrelli F (2012) Predictive control for agile semi-autonomous ground vehicles using motion primitves. In: American control conference, ACC

    Google Scholar 

  5. Frasch JV, Gray AJ, Zanon M, Ferreau HJ, Sager S, Borrelli F, Diehl M (2013) An auto-generated nonlinear MPC algorithm for real-time obstacle avoidance of ground vehicles. In: Proceedings of the European control conference (2013)

    Google Scholar 

  6. Diehl M, Bock H, Schlöder J, Findeisen R, Nagy Z, Allgöwer F (2002) Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations. J Process Control 12(4):577–585

    Article  Google Scholar 

  7. Bock H, Plitt K (1984) A multiple shooting algorithm for direct solution of optimal control problems. In: Proceedings 9th IFAC World Congress Budapest. Pergamon Press, NY, pp 242–247

    Google Scholar 

  8. Zanon M, Frasch J, Diehl M (2013) Nonlinear moving horizon estimation for combined state and friction coefficient estimation in autonomous driving. In: Proceedings of the European control conference

    Google Scholar 

  9. Zanon M, Gros S, Diehl M (2013) Airborne wind energy. Control of rigid-airfoil airborne wind energy systems. Springer, Berlin

    Google Scholar 

  10. Mayne D, Rawlings J, Rao C, Scokaert P (2000) Constrained model predictive control: stability and optimality. Automatica 26(6):789–814

    Article  MathSciNet  Google Scholar 

  11. Grüne L (2012) NMPC without terminal constraints. In: Proceedings of the IFAC conference on nonlinear model predictive, control 2012

    Google Scholar 

  12. Rao C (2000) Moving horizon estimation of constrained and nonlinear systems. Ph.D. Thesis, University of Wisconsin-Madison

    Google Scholar 

  13. Kühl P, Diehl M, Kraus T, Schlöder JP, Bock HG (2011) A real-time algorithm for moving horizon state and parameter estimation. Comput Chem Eng 35(1):71–83. doi:10.1016/j.compchemeng.2010.07.012

    Article  Google Scholar 

  14. Biegler L, Rawlings J (1991) Optimization approaches to nonlinear model predictive control. In: Ray W, Arkun Y (eds) Proceedings of 4th international conference on chemical process control-CPC IV. AIChE, CACHE, pp 543–571

    Google Scholar 

  15. de Oliveira N, Biegler L (1995) An extension of Newton-type algorithms for nonlinear process control. Automatica 31(2):281–286

    Article  MATH  MathSciNet  Google Scholar 

  16. Mayne DQ, Michalska H (1990) Receding horizon control of nonlinear systems. IEEE Trans Autom Control 35(7):814–824

    Article  MATH  MathSciNet  Google Scholar 

  17. Frasch JV, Sager S, Diehl M (2013) A parallel quadratic programming method for dynamic optimization problems. Submitted

    Google Scholar 

  18. Diehl M, Findeisen R, Allgöwer F (2007) A stabilizing real-time implementation of nonlinear model predictive control. In: Biegler L, Ghattas O, Heinkenschloss M, Keyes D, van Bloemen Waanders B (eds) Real-time and online PDE-constrained optimization, SIAM, pp 23–52

    Google Scholar 

  19. Ferreau HJ, Bock HG, Diehl M (2008) An online active set strategy to overcome the limitations of explicit MPC. Int J Robust Nonlinear Control 18(8):816–830. doi:10.1002/rnc.1251

    Article  MATH  MathSciNet  Google Scholar 

  20. Houska B, Ferreau H, Diehl M (2011) An auto-generated real-time iteration algorithm for nonlinear MPC in the microsecond range. Automatica 47(10):2279–2285. doi:10.1016/j.automatica.2011.08.020

    Article  MATH  MathSciNet  Google Scholar 

  21. Houska B, Ferreau H, Diehl M (2011) ACADO toolkit—An open source framework for automatic control and dynamic optimization. Optimal Control Appl Methods 32(3):298–312. doi:10.1002/oca.939

    Article  MATH  MathSciNet  Google Scholar 

  22. ACADO Toolkit Homepage. http://www.acadotoolkit.org (2009–2013)

  23. Ferreau H, Kraus T, Vukov M, Saeys W, Diehl M (2012) High-speed moving horizon estimation based on automatic code generation. In: Proceedings of the 51th IEEE conference on decision and control (CDC 2012)

    Google Scholar 

  24. Quirynen R, Gros S, Diehl M (2013) Fast auto generated ACADO integrators and application to MHE with multi-rate measurements. In: Proceedings of the European control conference

    Google Scholar 

  25. Quirynen R, Vukov M, Diehl M (2012) Auto generation of implicit integrators for embedded NMPC with microsecond sampling times. In: Lazar M, Allgöwer F (eds) Proceedings of the 4th IFAC nonlinear model predictive control conference

    Google Scholar 

  26. Pacejka HB (2006) Tyre and vehicle dynamics. Elsevier, Amsterdam

    Google Scholar 

  27. Kehrle F, Frasch JV, Kirches C, Sager S (2011) Optimal control of formula 1 race cars in a VDrift based virtual environment. In: Bittanti S, Cenedese A, Zampieri S (eds) Proceedings of the 18th IFAC World Congress, pp 11,907–11,912

    Google Scholar 

  28. Kiencke U, Nielsen L (2005) Automotive control systems. Springer, Berlin

    Google Scholar 

  29. Gray A, Zanon M, Frasch J (2012) Parameters for a Jaguar X-Type. http://www.mathopt.de/RESEARCH/obstacleAvoidance.php

  30. Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  31. Gerdts M (2006) A variable time transformation method for mixed-integer optimal control problems. Optim Control Appl Methods 27(3):169–182

    Article  MathSciNet  Google Scholar 

  32. Kirches C, Sager S, Bock H, Schlöder J (2010) Time-optimal control of automobile test drives with gear shifts. Optimal Control Appl Methods 31(2):137–153

    Article  MATH  MathSciNet  Google Scholar 

  33. Terwen S, Back M, Krebs V (2004) Predictive powertrain control for heavy duty trucks. In: Proceedings of IFAC symposium in advances in automotive control, Salerno, Italy, pp 451–457

    Google Scholar 

  34. Kirches C (2011) Fast numerical methods for mixed-integer nonlinear model-predictive control. Advances in numerical mathematics. Springer, Wiesbaden

    Book  Google Scholar 

  35. Sager S, Reinelt G, Bock H (2009) Direct methods with maximal lower bound for mixed-integer optimal control problems. Math Prog 118(1):109–149

    Article  MATH  MathSciNet  Google Scholar 

  36. Sager S, Bock H, Diehl M (2012) The integer approximation error in mixed-integer optimal control. Math Prog A 133(1–2):1–23

    Article  MATH  MathSciNet  Google Scholar 

  37. Jung M, Kirches C, Sager S (2013) On perspective functions and canishing constraints in mixed-integer nonlinear optimal control. In: Facets of combinatorial optimization—Festschrift for Martin Grötschel (2013, to appear)

    Google Scholar 

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Acknowledgments

This research was supported by Research Council KUL: PFV/10/002 Optimization in Engineering Center OPTEC, GOA/10/09 MaNet and GOA/10/11 Global real-time optimal control of autonomous robots and mechatronic systems. Flemish Government: IOF / KP / SCORES4CHEM, FWO: PhD/postdoc grants and projects: G.0320.08 (convex MPC), G.0377.09 (Mechatronics MPC); IWT: PhD Grants, projects: SBO LeCoPro; Belgian Federal Science Policy Office: IUAP P7 (DYSCO, Dynamical systems, control and optimization, 2012-2017); EU: FP7- EMBOCON (ICT-248940), FP7-SADCO (MC ITN-264735), ERC ST HIGHWIND (259 166), Eurostars SMART, ACCM.

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Authors and Affiliations

  1. Electrical Engineering Department (ESAT-SCD) and the Optimization in Engineering Center (OPTEC), KU, Leuven, Belgium

    Mario Zanon, Janick V. Frasch, Milan Vukov & Moritz Diehl

  2. Institute of Microsystems Engineering (IMTEK), University of Freiburg, Georges-Köhler-Allee 102, 79110, Freiburg, Germany

    Moritz Diehl

  3. Institute for Mathematics, University of Magdeburg, Magdeburg, Germany

    Janick V. Frasch & Sebastian Sager

Authors
  1. Mario Zanon
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  2. Janick V. Frasch
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  3. Milan Vukov
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  4. Sebastian Sager
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  5. Moritz Diehl
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Corresponding author

Correspondence to Mario Zanon .

Editor information

Editors and Affiliations

  1. Institute for Design and Control of Mechatronical Systems, Johannes Kepler, University Linz, Linz, Austria

    Harald Waschl

  2. Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan, USA

    Ilya Kolmanovsky

  3. Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Maarten Steinbuch

  4. Institute for Design and Control of Mechatronical Systems, Johannes Kepler University Linz, Linz, Austria

    Luigi del Re

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Zanon, M., Frasch, J.V., Vukov, M., Sager, S., Diehl, M. (2014). Model Predictive Control of Autonomous Vehicles. In: Waschl, H., Kolmanovsky, I., Steinbuch, M., del Re, L. (eds) Optimization and Optimal Control in Automotive Systems. Lecture Notes in Control and Information Sciences, vol 455. Springer, Cham. https://doi.org/10.1007/978-3-319-05371-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-05371-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05370-7

  • Online ISBN: 978-3-319-05371-4

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