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Generating Parameterized Smooth Paths with a Curve-Fitting Algorithm

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Proceedings of 2022 International Conference on Autonomous Unmanned Systems (ICAUS 2022) (ICAUS 2022)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 1010))

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Abstract

Path smoothness is essential in path tracking for autonomous driving, while smooth means that the curvature of path is continuous. Parameterizing the path as a profile of \(curvature\ \kappa \), that is a function of \(arc\ length\ s\), not only simplifies description of the reference path, but also improve path tracking performance. To achieve this, there must be a trade-off between the smoothness of the curvature profile and the precision of the curve-fitting. This paper describes an algorithm which fits the reference path described by a sequence of cartesian points. The algorithm utilizes piecewise linearized \(\kappa -s\) profile to represent the reference path. The curvature profile is smooth subject to the constraints of lateral deviation.

The research was partly funded by the Natural Science Foundation of China under Grant 62003362.

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References

  1. Nagy, B., Kelly, A.: Trajectory generation for car-like robots using cubic curvature polynomials (2001)

    Google Scholar 

  2. Guarino Lo Bianco, C., Piazzi, A.: Optimal trajectory planning with quintic G2-splines, pp. 620 – 625 (2000)

    Google Scholar 

  3. Villagra, J., Milanes, V., Pérez, J., Godoy, J., Onieva, E.: Path and speed planning for smooth autonomous navigation (2012)

    Google Scholar 

  4. Lau, B., Sprunk, C., Burgard, W.: Kinodynamic motion planning for mobile robots using splines. In: 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2009 pp. 2427–2433 (12 2009)

    Google Scholar 

  5. Chen, C., He, Y.Q., Bu, C., Han, J., Zhang, X.: Quartic Bézier curve based trajectory generation for autonomous vehicles with curvature and velocity constraints. In: Proceedings - IEEE International Conference on Robotics and Automation, pp. 6108–6113 (2014)

    Google Scholar 

  6. Chebly, A., Tagne, G., Talj, R., Charara, A.: Local trajectory planning and tracking for autonomous vehicle navigation using clothoid tentacles method (2015)

    Google Scholar 

  7. Gu, T., Dolan, J.: Toward human-like motion planning in urban environments. In: IEEE Intelligent Vehicles Symposium, Proceedings, pp. 350–355 (2014)

    Google Scholar 

  8. Marzbani, H., Simic, M., Fard, M., Jazar, R.N.: Better road design for autonomous vehicles using clothoids. In: Damiani, E., Howlett, R.J., Jain, L.C., Gallo, L., De Pietro, G. (eds.) Intelligent Interactive Multimedia Systems and Services. SIST, vol. 40, pp. 265–278. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19830-9_24

    Chapter  Google Scholar 

  9. Dubins, L.: On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Am. J. Math. 79, 497–516 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  10. Reeds, J., Shepp, L.: Optimal paths for a car that goes both forward and backward. Pac. J. Math. 145, 367–393 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  11. Solea, R., Nunes, U.: Trajectory planning with velocity planner for fully-automated passenger vehicles. In: IEEE Conference on Intelligent Transportation Systems, Proceedings, ITSC, pp. 474 – 480 (2006)

    Google Scholar 

  12. Qian, X., Navarro, I., de La Fortelle, A., Moutarde, F.: Motion planning for urban autonomous driving using Bézier curves and MPC, pp. 826–833 (2016)

    Google Scholar 

  13. Gonzalez Bautista, D., Pérez, J., Lattarulo, R., Milanes, V., Nashashibi, F.: Continuous curvature planning with obstacle avoidance capabilities in urban scenarios. In: 2014 17th IEEE International Conference on Intelligent Transportation Systems, ITSC 2014 (2014)

    Google Scholar 

  14. Pérez, J., Lattarulo, R., Nashashibi, F.: Dynamic trajectory generation using continuous-curvature algorithms for door to door assistance vehicles. In: IEEE Intelligent Vehicles Symposium, Proceedings, pp. 510–515 (2014)

    Google Scholar 

  15. Funke, J., Gerdes, J.: Simple clothoid lane change trajectories for automated vehicles incorporating friction constraints. J. Dyn. Syst. Meas. Control 138, 021002 (2016)

    Article  Google Scholar 

  16. Wilde, D.K.: Computing clothoid-arc segments for trajectory generation, pp. 2440–2445 (2009)

    Google Scholar 

  17. Mejia, J., Theodosis, P., Gerdes, J.: Using a path-fitting algorithm to analyze the racing techniques of a skilled driver. In: ASME 2013 Dynamic Systems and Control Conference, DSCC 2013 (2013)

    Google Scholar 

  18. Zhang, P., Wang, C.B., Ye, L.: A type III radio burst automatic analysis system and statistic results for a half solar cycle with nançay decameter array data. Astron. Astrophys. 618, A165 (2018)

    Article  Google Scholar 

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Correspondence to Zhenping Sun .

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© 2023 Beijing HIWING Sci. and Tech. Info Inst

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Zhong, W., Li, X., Sun, Z. (2023). Generating Parameterized Smooth Paths with a Curve-Fitting Algorithm. In: Fu, W., Gu, M., Niu, Y. (eds) Proceedings of 2022 International Conference on Autonomous Unmanned Systems (ICAUS 2022). ICAUS 2022. Lecture Notes in Electrical Engineering, vol 1010. Springer, Singapore. https://doi.org/10.1007/978-981-99-0479-2_220

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