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## Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles

#### Ardam Haseeb Mohammed Ali Kahya [1] , Klaus Werner Schmidt [2]

##### 77 143

The subject of this paper is the efficient computation of lane change trajectories for self-driving vehicles. The paper first identifies that a certain type of clothoid-based bi-elementary paths can be used to represent lane change trajectories for vehicles. It is further highlighted that the curvature of such trajectories must be adjusted to the driving situation in order to obtain feasible lane change trajectories. Accordingly, the paper establishes an analytical relation between the maximum admissible curvature of the lane change trajectory and the velocity profile during a lane change. Using this relation, the paper proposes an efficient Newton iteration for computing the parameters of bi-elementary paths for lane changes. The resulting lane change trajectories are as short as possible, while meeting the constraint on the maximum curvature. Simulation experiments for various driving situations show that the computed bi-elementary paths can be computed efficiently and constitute suitable lane change trajectories.

Autonomous vehicles, lane changes, clothoid trajectories
• [1] “IEEE news release,” http://www.ieee.org/about/news/2012/5september 2 2012.html, 2. September 2012.
• [2] “Autonomous cars – self-driving the new auto industry paradigm,” Morgan Stanley Blue Paper, Tech. Rep., November 2013.
• [3] R. Attia, R. Orjuela, and M. Basset, “Coupled longitudinal and lateral control strategy improving lateral stability for autonomous vehicle,” in American Control Conference (ACC), 2012, June 2012, pp. 6509–6514.
• [4] K. G. Baass, “The use of clothoid templates in highway design,” Transportation Forum, vol. 1, pp. 47–52, 1984.
• [5] J. L. Buchanan and P. R. Turner, Numerical Methods and Analysis. McGraw-Hill, Inc., New York, 1992.
• [6] J. Chen, P. Zhao, T. Mei, and H. Liang, “Lane change path planning based on piecewise bezier curve for autonomous vehicle,” in 2013 IEEE International Conference on Vehicular Electronics and Safety (ICVES), 2013, pp. 17–22.
• [7] P. J. Davis, Spirals: from Theodorus to Chaos. A. K. Peters, Wellesley, Maine, 1993.
• [8] P. Dingle and L. Guzzella, “Optimal emergency maneuvers on highways for passenger vehicles with two- and four-wheel active steering,” in American Control Conference (ACC), 2010, June 2010, pp. 5374–5381.
• [9] E. Dovgan, T. Tu˘sar, M. Javorski, and B. Filipi˘c, “Discovering comfortable driving strategies using simulationbased multiobjective optimization,” Informatica, vol. 36, no. 3, pp. 319–326, 2012.
• [10] P. Falcone, M. Tufo, F. Borrelli, J. Asgari, and H. Tsengz, “A linear time varying model predictive control approach to the integrated vehicle dynamics control problem in autonomous systems,” in Decision and Control, 2007 46th IEEE Conference on, Dec 2007, pp. 2980–2985.
• [11] J. Funke and J. C. Gerdes, “Simple clothoid lane change trajectories for automated vehicles incorporating friction constraints,” ASME. J. Dyn. Sys., Meas., Control, vol. 138, no. 2, pp. 021 002–021 002–9, 2015.
• [12] M. P. Gianpiero Mastinu, Ed., Road and Off-Road Vehicle System Dynamics Handbook. CRC Press, 2014.
• [13] K. Kritayakirana and J. C. Gerdes, “Autonomous vehicle control at the limits of handling,” International Journal of Vehicle Autonomous Systems, vol. 10, no. 4, pp. 271–296, 2012.
• [14] Z. Li and D. Meek, “Smoothing an arc spline,” Computers & Graphics, vol. 29, no. 4, pp. 576–587, 2005. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0097849305000907
• [15] R. Marino, S. Scalzi, and M. Netto, “Nested {PID} steering control for lane keeping in autonomous vehicles,” Control Engineering Practice, vol. 19, no. 12, pp. 1459–1467, 2011.
• [16] B. Mashadi and M. Majidi, “Two-phase optimal path planning of autonomous ground vehicles using pseudospectral method,” Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 2014. [Online]. Available: http://pik.sagepub.com/content/early/2014/06/11/1464419314538245.abstract
• [17] D. S. Meek and D. J. Walton, “An arc spline approximation to a clothoid,” J. Comput. Appl. Math., vol. 170, no. 1, pp. 59–77, Sep. 2004. [Online]. Available: http://dx.doi.org/10.1016/j.cam.2003.12.038
• [18] D. Meek and D. Walton, “A note on finding clothoids,” Journal of Computational and Applied Mathematics, vol. 170, no. 2, pp. 433–453, 2004. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0377042704000925
• [19] A. K. Nandi, D. Chakraborty, and W. Vaz, “Design of a comfortable optimal driving strategy for electric vehicles using multi-objective optimization,” Journal of Power Sources, vol. 283, pp. 1–18, 2015.
• [20] F. E. P. E.˜Jahnke, Tables of Functions with Formulae and Curves, 4th ed. Dover Publications, New York, 1945.
• [21] H. B. Pacejka, Tire and Vehicle Dynamics, 3rd ed. Oxford: Butterworth-Heinemann, 2012.
• [22] H. B. Pacejka and I. J. M. Besselink, “Magic formula tyre model with transient properties,” Vehicle System Dynamics, vol. 27, no. sup001, pp. 234–249, 1997. [Online]. Available: http://dx.doi.org/10.1080/00423119708969658
• [23] R. Pepy, A. Lambert, and H. Mounier, “Path planning using a dynamic vehicle model,” in Information and Communication Technologies, 2006. ICTTA ’06. 2nd, vol. 1, 2006, pp. 781–786.
• [24] G. Rafiq, B. Talha, M. Patzold, J. Gato Luis, G. Ripa, I. Carreras, C. Coviello, S. Marzorati, G. Perez Rodriguez, G. Herrero, and M. Desaeger, “What?s new in intelligent transportation systems?: An overview of european projects and initiatives,” Vehicular Technology Magazine, IEEE, vol. 8, no. 4, pp. 45–69, Dec 2013.
• [25] A. Rucco, G. Notarstefano, and J. Hauser, “Optimal control based dynamics exploration of a rigid car with longitudinal load transfer,” Control Systems Technology, IEEE Transactions on, vol. 22, no. 3, pp. 1070–1077, May 2014.
• [26] ——, “Optimal control based dynamics exploration of a rigid car with longitudinal load transfer,” Control Systems Technology, IEEE Transactions on, vol. 22, no. 3, pp. 1070–1077, May 2014.
• [27] A. Schindler, G. Maier, and S. Pangerl, “Exploiting arc splines for digital maps,” in 2011 14th International IEEE Conference on Intelligent Transportation Systems (ITSC), Oct 2011, pp. 1–6.
• [28] T. S. L. Sumit Ghosh, Intelligent Transportation Systems: Smart and Green Infrastructure Design. CRC Press, 2010.
• [29] J. S. Sussman, Perspectives on Intelligent Transportation Systems (ITS), 1st ed. Springer US, 2005.
• [30] P. Varaiya, “Smart cars on smart roads: problems of control,” Automatic Control, IEEE Transactions on, vol. 38, no. 2, pp. 195–207, Feb 1993.
• [31] M. Werling, S. Kammel, J. Ziegler, and L. Gr¨oll, “Optimal trajectories for time-critical street scenarios using discretized terminal manifolds,” The International Journal of Robotics Research, vol. 31, no. 3, pp. 346–359, 2012. [Online]. Available: http://ijr.sagepub.com/content/31/3/346.abstract
• [32] Z. Wu, Y. Liu, and G. Pan, “Smart car control model for brake comfort based on car following,” IEEE Transactions on Intelligent Transportation Systems, vol. 10, no. 1, pp. 42–46, 2009.
• [33] H. Yoshida, S. Shinohara, and M. Nagai, “Lane change steering manoeuvre using model predictive control theory,” Vehicle System Dynamics, vol. 46, no. sup1, pp. 669–681, 2008. [Online]. Available: http://dx.doi.org/10.1080/00423110802033072
Subjects Engineering Articles Author: Ardam Haseeb Mohammed Ali Kahya Author: Klaus Werner Schmidt
 Bibtex @research article { cankujse368709, journal = {Cankaya University Journal of Science and Engineering}, issn = {1309-6788}, eissn = {2564-7954}, address = {Cankaya University}, year = {2017}, volume = {14}, pages = { - }, doi = {}, title = {Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles}, key = {cite}, author = {Kahya, Ardam Haseeb Mohammed Ali and Schmidt, Klaus Werner} } APA Kahya, A , Schmidt, K . (2017). Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles. Cankaya University Journal of Science and Engineering, 14 (2), . Retrieved from http://dergipark.gov.tr/cankujse/issue/33106/368709 MLA Kahya, A , Schmidt, K . "Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles". Cankaya University Journal of Science and Engineering 14 (2017): Chicago Kahya, A , Schmidt, K . "Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles". Cankaya University Journal of Science and Engineering 14 (2017): RIS TY - JOUR T1 - Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles AU - Ardam Haseeb Mohammed Ali Kahya , Klaus Werner Schmidt Y1 - 2017 PY - 2017 N1 - DO - T2 - Cankaya University Journal of Science and Engineering JF - Journal JO - JOR SP - EP - VL - 14 IS - 2 SN - 1309-6788-2564-7954 M3 - UR - Y2 - 2019 ER - EndNote %0 Cankaya University Journal of Science and Engineering Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles %A Ardam Haseeb Mohammed Ali Kahya , Klaus Werner Schmidt %T Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles %D 2017 %J Cankaya University Journal of Science and Engineering %P 1309-6788-2564-7954 %V 14 %N 2 %R %U ISNAD Kahya, Ardam Haseeb Mohammed Ali , Schmidt, Klaus Werner . "Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles". Cankaya University Journal of Science and Engineering 14 / 2 (November 2017): -.