Skip to main content
SpringerLink
Log in

A unified optimal planner for autonomous parking vehicle

  • Published:
Control Theory and Technology Aims and scope Submit manuscript

Abstract

In order to reduce the controlling difficulty caused by trajectory meandering and improve the adaptability to parking into regular lots, a versatile optimal planner (OP) is proposed. Taking advantage of the low speed specificity of parking vehicle, the OP algorithm was modeled the planning problem as a convex optimization problem. Collision-free constraints were formalized into the shortest distance between convex sets by describing obstacles and autonomous vehicle as affine set. Since employing Lagrange dual function and combining KKT conditions, the collision-free constraints translated into convex functions. Taking the national standard into account, 5 kinds of regular parking scenario, which contain 0°, 30°, 45°, 60° and 90° parking lots, were designed to verify the OP algorithm. The results illustrate that it is benefit from the continuous and smooth trajectory generated by the OP method to track, keep vehicle’s stability and improve ride comfort, compared with A* and hybrid A* algorithms. Moreover, the OP method has strong generality since it can ensure the success rate no less than 82% when parking planning is carried out at the start node of 369 different locations. Both of evaluation criteria, as the pear error and RMSE in x direction, y axis and Euclidean distance d, and heading deviation θ, are stable and feasible in real tests, which illustrates that the OP planner can satisfy the requirements of regular parking scenarios.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Moon, I. Bae, S. Kim. Real-time near-optimal path and maneuver planning in automatic parking using a simultaneous dynamic optimization approach. IEEE Intelligent Vehicles Symposium, California: IEEE, 2017: 193–196.

    Google Scholar 

  2. SAE International in United States. Taxonomy and Definitions for Terms Related to Driving Automation Systems for On-Road Motor Vehicles. 2018: https://doi.org/saemobilus.sae.org/content/J3016_201806/.

  3. H. Li, K. Guo, X. Song, et al. Trajectory planning of automatic parallel parking with multi-constraints based on Matlab. Journal of Central South University (Science and Technology), 2013, 44(1): 101–107.

    Google Scholar 

  4. W. Jing, D. Feng, P. Zhang, et al. A multi-objective optimization-based path planning method for parallel parking of autonomous vehicle via nonlinear programming. Proceedings of the 15th International Conference on Control, Automation, Robotics and Vision, Singapore: IEEE, 2018: 1665–1670.

    Google Scholar 

  5. F. Gomez-Bravo, F. Cuesta, A. Ollero. Parallel and diagonal parking in nonholonomic autonomous vehicles. Engineering Applications of Artificial Intelligence, 2001, 14(4): 419–434.

    Article  Google Scholar 

  6. P. Li. A Study on Path Planning and Tracking Control Strategy for Automatic Parking System. Chongqing: Chongqing University of Technology, 2017.

    Google Scholar 

  7. C. Wang, H. Zhang, M. Yang, et al. Automatic parking based on a bird’s eye view vision system. Advances in Mechanical Engineering, 2015, 6: DOI https://doi.org/10.1155/2014/847406.

    Article  Google Scholar 

  8. Z. Lv, L. Zhao, Z. Liu. A path-planning algorithm for parallel automatic parking. Proceedings of the 3rd International Conference on Instrumentation, Measurement, Computer, Communication and Control, Shenyang: IEEE, 2013: 474–478.

    Google Scholar 

  9. B. Muller, J. Deutscher, S. Grodde. Continuous curvature trajectory design and feedforward control for parking a car. IEEE Transactions on Control Systems Technology, 2007, 15(3): 541–553.

    Article  Google Scholar 

  10. D. Kim, W. Chung, S. Park. Practical motion planning for car-parking control in narrow environment. IET Control Theory & Applications, 2010, 4(1): 129–139.

    Article  Google Scholar 

  11. S. Choi, C. Boussard, B. d’Andrea-Novel. Easy path planning and robust control for automatic parallel parking. IFAC Proceedings Volumes, Milano: IFAC, 2011: 656–661.

    Google Scholar 

  12. P. Li, J. Huang, H. Yang, et al. Trajectory planning method based on double constant speed for automatic parking systems. Journal of Chongqing University of Technology (Natural Science), 2017, 31(9): 36–44.

    Google Scholar 

  13. S. Zhang, M. Simkani, M. Zadeh. Automatic vehicle parallel parking design using fifth degree polynomial path planning. IEEE Vehicular Technology Conference, Budapest: IEEE, 2011: DOI https://doi.org/10.1109/VETECF.2011.6093275.

    Google Scholar 

  14. M. Saleh, M. Ismail, N. Riman. Enhanced algorithm for autonomous parallel parking of a car-like mobile robot. IEEE International Multidisciplinary Conference on Engineering Technology, Beirout: IEEE, 2016: 191–195.

    Google Scholar 

  15. F. Gomez-Bravo, F. Cuesta, A. Ollero, et al. Continuous curvature path generation based on β-spline curves for parking manoeuvres. Robotics and Autonomous Systems, 2008, 56(4): 360–372.

    Article  Google Scholar 

  16. Z. Liang, G. Zheng, J. Li. Automatic parking path optimization based on bezier curve fitting. Proceeding of the IEEE International Conference on Automation and Logistics, Zhengzhou: IEEE, 2012: 583–587.

    Google Scholar 

  17. K. Kawabata, L. Ma, J. Xue, et al. A path generation method for automated vehicles based on Bezier curve. ASME International Conference on Advanced Intelligent Mechatronics, Wollongong: IEEE, 2011: 991–996.

    Google Scholar 

  18. J. Moon, I. Bae, J. Cha, et al. A trajectory planning method based on forward path generation and backward tracking algorithm for automatic parking systems. Proceedings of the 17th International Conference on Intelligent Transportation Systems, Qingdao: IEEE, 2014: 719–724.

    Google Scholar 

  19. J. Moon, I. Bae, J. Cha, et al. Integrated lateral and longitudinal control system for autonomous vehicles. Proceedings of the 17th International Conference on Intelligent Transportation Systems, Qingdao: IEEE, 2014: 719–724.

    Google Scholar 

  20. K. Zheng, S. Liu. RRT based path planning for autonomous parking of vehicle. Proceedings of the 7th Data Driven Control and Learning Systems Conference, Hubei: IEEE, 2018: 627–632.

    Google Scholar 

  21. L. Han, Q. Do, S. Mita. Unified path planner for parking an autonomous vehicle based on RRT. IEEE International Conference on Robotics and Automation, Shanghai: IEEE, 2011: 5622–5627.

    Google Scholar 

  22. Z. Feng, S. Chen, Y. Chen, et al. Model-based Decision making with imagination for autonomous parking. IEEE Intelligent Vehicles Symposium, Suzhou: IEEE, 2018: 2216–2223.

    Google Scholar 

  23. W. Xu, J. Wei, J. Dolan, et al. A real-time motion planner with trajectory optimization for autonomous vehicles. IEEE International Conference on Robotics and Automation, Minnesota: IEEE, 2012: 2061–2067.

    Google Scholar 

  24. W. Lim, S. Lee, M. Sunwoo, et al. Hierarchical trajectory planning of an autonomous car based on the integration of a sampling and an optimization method. IEEE Transactions on Intelligent Transportation Systems, 2018, 19(2): 613–626.

    Article  Google Scholar 

  25. Y. Jiang, Q. Wang, J. Gong, et al. Research on temporal consistency and robustness in local planning of intelligent vehicles. Acta Automatica SinicA, 2015, 41(3): 518–527.

    Google Scholar 

  26. D. Kularatne, S. Bhattacharya, M. Hsieh. Optimal path planning in time-varying flows using adaptive discretization. IEEE Robotics and Automation Letters, 2018, 3(1): 458–465.

    Article  Google Scholar 

  27. S. Klaudt, A. Zlocki, L. Eckstein. A-Priori map information and path planning for automated valet-parking. IEEE Intelligent Vehicles Symposium, California: IEEE, 2017: 1770–1775.

    Google Scholar 

  28. D. Dolgov, S. Thrun, M. Montemerlo, et al. Path planning for autonomous driving in unknown environments. Experimental Robotics, the 11th International symposium, Berlin: Springer, 2009: 55–64.

    Chapter  Google Scholar 

  29. H. Banzhaf, D. Nienhuser, S. Knoop, et al. The future of parking: a survey on automated valet parking with an outlook on high density parking. IEEE Intelligent Vehicles Symposium, California: IEEE, 2017: 1827–1834.

    Google Scholar 

  30. C. Chen, M. Rickert, A. Knoll. Path planning with orientation-aware space exploration guided heuristic search for autonomous parking and maneuvering. IEEE Intelligent Vehicles Symposium, Seoul: IEEE, 2015: 1148–1153.

    Google Scholar 

  31. L. Ma, J. Xue, K. Kawabata. Efficient sampling-based motion planning for on-road autonomous driving. IEEE Transactions on Intelligent Transportation Systems, 2015, 16(4): 1961–1976.

    Article  Google Scholar 

  32. Q. Do, S. Mita, K. Yoneda, et al. A practical and optimal path planning for autonomous parking using fast marching algorithm and support vector machine. IEICE Transactions on Information and Systems, 2013, 96(12): 2795–2804.

    Article  Google Scholar 

  33. T. Lau. Learning autonomous drift parking from one demonstration. Proceedings of the IEEE International Conference on Robotics and Biomimetics, Phuket: IEEE, 2011: 1456–1461.

    Google Scholar 

  34. M. Heinen, F. Osorio, F. Heinen, et al. SEVA3D: Using artificial neural networks to autonomous vehicle parking control. International Joint Conference on Neural Networks, Vancouver: IEEE, 2006: 4704–4711.

    Google Scholar 

  35. G. Notomista, M. Botsch. Maneuver segmentation for autonomous parking based on ensemble learning. International Joint Conference on Neural Networks, Kilkenny: IEEE, 2015: DOI https://doi.org/10.1109/IJCNN.2015.7280546.

    Google Scholar 

  36. Ministry of Housing and Urban-Rural Development of the People’s Republic of China. Code for Design of Parking Garage Building. 2015: JGJ 100–2015.

  37. Z. Yu, L. Xia, L. Xiong. A consistency method for autonomous parking path planning. Automobile Technology, 2018, 515(8): 27–32.

    Google Scholar 

  38. S. Boyd, L. Vandenberghe. Convex Optimization. Cambridge: Cambridge University, 2004: 33–286.

    Book  Google Scholar 

  39. R. Zhang, L. Xiong, Z. Yu. Hierarchical control for reference trajectory tracking of autonomous vehicles. Proceedings of the 25th International Symposium on Dynamics of Vehicles on Roads and Tracks, Queensland: CRC, 2017: 283–288.

    Google Scholar 

  40. Z. Yu, R. Zhang, L. Xiong, et al. Robust adaptive anti-slip regulation controller for a distributed-drive electric vehicle considering the driver’s intended driving torque. Proceedings of the Institution of Mechanical Engineers — Part D: Journal of Automobile Engineering, 2017, 232(4): 562–576.

    Google Scholar 

  41. A. Brunker, T. Wohlgemuth, M. Frey, et al. Odometry 2.0: A slip-adaptive eif-based four-wheel-odometry model for parking. IEEE Transactions on Intelligent Vehicles, 2019, 4(1): 114–126.

    Article  Google Scholar 

  42. S. Rathour, V. John, M. Nithilan, et al. Vision and dead reckoning-based end-to-end parking for autonomous vehicles. IEEE Intelligent Vehicles Symposium, Changshu: IEEE, 2018: 2182–2187.

    Google Scholar 

Download references

Acknowledgements

The authors thank the assistance from other people of the School of Automotive Studies, Tongji University.

Author information

Authors and Affiliations

  1. School of Automotive Studies, Tongji University, Shanghai, 201804, China

    Dequan Zeng, Zhuoping Yu, Lu Xiong, Peizhi Zhang & Zhiqiang Fu

  2. Clean Energy Automotive Engineering Center, Tongji University, Shanghai, 201804, China

    Dequan Zeng, Zhuoping Yu, Lu Xiong, Peizhi Zhang & Zhiqiang Fu

Authors
  1. Dequan Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhuoping Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lu Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peizhi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhiqiang Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lu Xiong.

Additional information

This work was supported by the National Key Research and Development Program of China (Nos. 2018YFB0105103, 2018YFB0105101) and the Science and Technology Commission of Shanghai (Nos. 17DZ1100202, 16DZ1100700).

Dequan ZENG received the M.Sc. degree from School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China, in 2016. He is currently working toward the Ph.D. degree with School of Automotive Studies, Tongji University, Shanghai, China. His research interests include trajectory planning and decision making for autonomous vehicle.

Zhuoping YU received the B.Sc. degree from Tongji University, Shanghai, China, in 1985 and the Ph.D. degree form Tsinghua University, Beijing, China, in 1996. Currently, He is professor and doctoral supervisor with School of Automotive Studies, Tongji University, Shanghai, China. His research interests include vehicle engineering.

Lu XIONG received the M.Sc. and Ph.D. degrees from Tongji University, Shanghai, China, in 2002 and in 2005, respectively. Currently, he is professor and doctoral supervisor with School of Automotive Studies, Tongji University, Shanghai, China. His research interests include vehicle engineering.

Peizhi ZHANG received the M.Sc. degree from College of Automotive Engineering, Jilin University, Jilin, China, in 2014. He is currently working toward the Ph.D. degree with the School of Automotive Studies, Tongji University, Shanghai, China. His research interests include motion controlling, trajectory planning, decision making, and simultaneous localization and mapping (SLAM) for autonomous vehicle.

Zhiqiang FU received the M.Sc. degree from Chinesisch-Deutsches Hochschulkolleg, Tongji University, Shanghai, China, in 2018. He is currently working toward the Ph.D. degree with the School of Automotive Studies, Tongji University, Shanghai, China. His research interests include motion controlling, trajectory planning and decision making for autonomous vehicle.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zeng, D., Yu, Z., Xiong, L. et al. A unified optimal planner for autonomous parking vehicle. Control Theory Technol. 17, 346–356 (2019). https://doi.org/10.1007/s11768-019-9121-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-019-9121-6

Keywords

Search

Navigation