On the Backward Path Tracking Control of N-Trailer Systems

Julius Kolb; Gunter Nitzsche; Sebastian Wagner; Klaus Röbenack

doi:10.52846/stccj.2021.1.1.6

Authors

Julius Kolb Fraunhofer Institute for Transportation and Infrastructure Systems IVI
Gunter Nitzsche
Sebastian Wagner Fraunhofer Institute for Transportation and Infrastructure Systems IVI
Klaus Röbenack Technische Universität Dresden

DOI:

https://doi.org/10.52846/stccj.2021.1.1.6

Keywords:

truck-trailer, articulated vehicle, backward motion, path tracking, nonlinear control, exact linearization, stabilization

Abstract

This paper considers the lateral control of articulated wheeled vehicles in backward motion. The parameterized articulated vehicle is composed of a car-like truck and N passive trailers, resulting in one single steerable axle. First a nonlinear path tracking control law based on exact linearization of an offset model is reviewed and the general stability conditions of such systems is presented. Second, a stability analysis for some vehicle cases is performed and verified in simulation. The possible application of this path tracking control law in real world articulated vehicles is discussed, and its limitations are shown.

References

M. Riesmeier, O. Schnabel, F. Woittennek, and T. Kn¨uppel, “Zur Folgeregelung mehrachsiger Fahrzeuge,” at - Automatisierungstechnik, vol. 64, no. 8, 2016.

C. Altafini, “The general n-trailer problem: conversion into chained form,” in Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171). IEEE, 1998.

P. Rouchon, M. Fliess, J. Levine, and P. Martin, “Flatness, motion planning and trailer systems,” in Proceedings of 32nd IEEE Conference on Decision and Control. IEEE, 1993.

M. Sampei, T. Tamura, T. Kobayashi, and N. Shibui, “Arbitrary path tracking control of articulated vehicles using nonlinear control theory,” IEEE Transactions on Control Systems Technology, vol. 3, no. 1, pp. 125–131, 1995.

M. Werling, M. Heidingsfeld, P. Reinisch, and L. Gr¨oll, “Assistiertes und automatisiertes R¨uckw¨artsrangieren mit Anh¨anger,” at – Automatisierungstechnik, vol. 62, no. 1, 2014.

B. d’Andr´ea Novel, L. Menhour, M. Fliess, and H. Mounier, “Some remarks on wheeled autonomous vehicles and the evolution of their control design,” IFAC Proceedings Volumes, 2016.

M. M. Michałek, “A highly scalable path-following controller for ntrailers with off-axle hitching,” Control Engineering Practice, vol. 29, pp. 61–73, 2014.

J. Kolb, G. Nitzsche, S. Wagner, and K. Robenack, “Path Tracking of Articulated Vehicles in Backward Motion,” in 2020 24th International Conference on System Theory, Control and Computing (ICSTCC). IEEE, 2020.

P. Bolzern, R. DeSantis, A. Locatelli, and D. Masciocchi, “Path-tracking for articulated vehicles with off-axle hitching,” IEEE Transactions on Control Systems Technology, vol. 6, no. 4, pp. 515–523, 1998.

P. Bolzern, R. M. DeSantis, and A. Locatelli, “An input-output linearization approach to the control of an n-body articulated vehicle,” Journal of Dynamic Systems, Measurement, and Control, vol. 123, no. 3, pp. 309–316, 2001.

R. DeSantis, “Path-tracking for articulated vehicles via exact and jacobian linearization,” IFAC Proceedings Volumes, vol. 31, no. 3, pp. 159–164, 1998.

R. DeSantis, J. Bourgeot, J. Todeschi, and R. Hurteau, “Path-tracking for tractor-trailers with hitching of both the on-axle and the off-axle kind,” in Proceedings of the IEEE Internatinal Symposium on Intelligent Control. IEEE, 2002.

J. Morales, J. L. Martinez, A. Mandow, and A. J. Garcia-Cerezo, “Steering the last trailer as a virtual tractor for reversing vehicles with passive on- and off-axle hitches,” IEEE Transactions on Industrial Electronics, vol. 60, no. 12, pp. 5729–5736, 2013.

D. A. Liz´arraga, P. Morin, and C. Samson, “Exponential Stabilization of Certain Configurations of the General N-Trailer System,” INRIA, Tech. Rep. RR-3412, 1998.

M. Werling and L. Groll, “Low-level controllers realizing high-level decisions in an autonomous vehicle,” in 2008 IEEE Intelligent Vehicles Symposium. IEEE, 2008.

A. Isidori, Nonlinear Control Systems. Springer London, 1995, ISBN: 978-1-4471-3909-6.

K. R¨obenack, Nichtlineare Regelungssysteme. Springer Berlin Heidelberg, 2017, ISBN: 978-3-662-44091-9.

——, “On the Direct Computation of the Byrnes-Isidori Normal Form,” PAMM, vol. 17, no. 1, pp. 811–812, 2017.

——, “Computation of multiple Lie derivatives by algorithmic differentiation,” Journal of computational and applied mathematics, vol. 213, pp. 454–464, 2008.

F. Svaricek, “Nulldynamik linearer und nichtlinearer Systeme: Definitionen, Eigenschaften und Anwendungen,” at - Automatisierungstechnik, vol. 54, 2006.

J. K. Kolb, G. Nitzsche, and S. Wagner, “A simple yet efficient path tracking controller for autonomous trucks,” IFAC-PapersOnLine, vol. 52, no. 8, pp. 307–312, 2019.

G. Nitzsche, S.Wagner, and N. Belov, “helyOS – Highly Efficient Online Yard Operating System,” in Commercial Vehicles 2019. VDI Verlag, 2019, pp. 329–338.

J. Morales, J. L. Martinez, A. Mandow, and I. J. Medina, “Virtual steering limitations for reversing an articulated vehicle with off-axle passive trailers,” in 2009 35th Annual Conference of IEEE Industrial Electronics. IEEE, 2009.