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Real-Time Efficient Trajectory Planning for Quadrotor Based on Hard Constraints

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Abstract

Trajectory planning for quadrotor has been extensively studied in terms of safety, smoothness, and dynamical feasibility. However, few methods have been proposed for the optimization of efficiency in long-distance navigation. Quadrotor often has high computational complexity when performing tasks that involve at least multiple computing modules such as location, mapping, planning, etc. Therefore, improving planning efficiency and flight efficiency can save computing resources and improve transport efficiency to complete more tasks. This paper presents a real-time trajectory planning method that can achieve long-distance navigation with less planning number and calculation time while greatly reducing flight time to reach the target point quickly. Our method is built on hard constraints such as safety distance, free-space flight corridors, and smoothness constraints that can ensure trajectory quality. For each scenario, our improved Theta* algorithm can obtain a shortest initial trajectory with several key waypoints. Low-quality segments of the initial trajectory are then screened and optimized by local replanning detection and flight corridor-based optimization, respectively. Flight efficiency, continuity, and dynamical feasibility are greatly boosted by the distributed time allocation method. Experimental results show that the flight time of our method is 22%–56% less than that of the state-of-the-art hard-constrained methods in about 50 m flight, and total calculation time is 19%–84% less, which is attributable to the reduction of planning number. The proposed trajectory planning method is also integrated into a quadrotor platform and its competence is validated by presenting autonomous flight in unknown indoor environments.

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Data Availability

The data and material of the current study are available from the corresponding author on reasonable request.

References

  1. LaValle, S.M., Kuffner, J.J.: Randomized kinodynamic planning. The International Journal of Robotics Research. 20(5), 378–400 (2001)

    Article  Google Scholar 

  2. Karaman, S., Frazzoli, E.: Sampling-based algorithms for optimal motion planning. The International Journal of Robotics Research. 30(1), 846–894 (2011)

    Article  Google Scholar 

  3. Gao, F., Shen, S.: Online Quadrotor Trajectory Generation and Autonomous Navigation on Point Clouds. IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), Lausanne, Switzerland, pp. 139–146 (2016)

  4. Gao, F., Wu, W., Gao, W., Shen, S.: Flying on point clouds: online trajectory generation and autonomous navigation for quadrotors in cluttered environments. Journal of Field Robotics. 36(4), 710–733 (2019)

    Article  Google Scholar 

  5. Tang, Z., Chen, B., Lan, R., et al.: Vector field guided RRT* based on motion primitives for quadrotor Kinodynamic planning. J. Intell. Robot. Syst. 100, 1325–1339 (2020)

    Article  Google Scholar 

  6. Singh, Y., Bibuli, M., Zereik, E., et al.: A novel double layered hybrid multi-robot framework for guidance and navigation of unmanned surface vehicles in a practical maritime environment. Journal of Marine Science and Engineering. 8(9), 624 (2020)

    Article  Google Scholar 

  7. Chen, J., Liu, T., Shen, S.: Online Generation of Collision-Free Trajectories for Quadrotor Flight in Unknown Cluttered Environments, pp. 1476–1483. IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Switzerland (2016)

    Google Scholar 

  8. Likhachev, M., Gordon, G.J., Thrun, S.: ARA*: Anytime a* with Provable Bounds on Sub-Optimality, pp. 767–774. Conference and Workshop on Neural Information Processing Systems (NIPS), Vancouver and Whistler, Canada (2003)

    Google Scholar 

  9. Harabor, D., Grastien, A.: Online Graph Pruning for Pathfinding on Grid Maps, pp. 1114–1119. Twenty-Fifth AAAI Conference on Artificial Intelligence, San Francisco, USA (2011)

    Google Scholar 

  10. Maw, A.A., Tyan, M., Lee, J.W.: iADA*: improved anytime path planning and Replanning algorithm for autonomous vehicle. Journal of Intelligent & Robotic Systems. 100, 1005–1013 (2020)

    Article  Google Scholar 

  11. Daniel, K., Nash, A., Koenig, S., Felner, A.: Theta*: any-angle path planning on grids. J. Artif. Intell. Res. 39(1), 533–579 (2010)

    Article  MathSciNet  Google Scholar 

  12. Kim, H., Kim, D., Shin, J., et al.: Angular rate-constrained path planning algorithm for unmanned surface vehicles. Ocean Eng. 84(Suppl. C), 37–44 (2014)

    Article  Google Scholar 

  13. Wang, N., Xu, H.: Dynamics-constrained global-local hybrid path planning of an autonomous surface vehicle. IEEE Trans. Veh. Technol. 69(7), 6928–6942 (2020)

    Article  Google Scholar 

  14. Koren, Y., Borenstein, J.: Potential Field Methods and their Inherent Limitations for Mobile Robot Navigation, pp. 1398–1404. IEEE International Conference on Robotics and Automation (ICRA), Sacramento, USA (1991)

    Google Scholar 

  15. Gao, F., Wu, W., Lin, Y., Shen, S.: Online Safe Trajectory Generation for Quadrotors Using Fast Marching Method and Bernstein Basis Polynomial, pp. 344–351. IEEE International Conference on Robotics and Automation (ICRA), Brisbane, Australia (2018)

    Google Scholar 

  16. Li, Y., Liu, C.: Efficient and safe motion planning for quadrotors based on unconstrained quadratic programming. Robotica. 1–17 (2020)

  17. Liang, X., Meng, G., Xu, Y., Luo, H.: A geometrical path planning method for unmanned aerial vehicle in 2D/3D complex environment. Intell. Serv. Robot. 11, 301–312 (2018)

    Article  Google Scholar 

  18. Ding, W., Gao, W., Wang, K., Shen, S.: An efficient B-spline-based Kinodynamic Replanning framework for quadrotors. IEEE Trans. Robot. 35(6), 1287–1306 (2019)

    Article  Google Scholar 

  19. Ratliff, N., Zucker, M., Bagnell, J.A., Srinivasa, S.: Chomp: Gradient Optimization Techniques for Efficient Motion Planning, pp. 489–494. IEEE International Conference on Robotics and Automation (ICRA), Kobe, Japan (2009)

    Google Scholar 

  20. Mellinger, D., Kumar, V.: Minimum Snap Trajectory Generation and Control for Quadrotors, pp. 2520–2525. IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China (2011)

    Google Scholar 

  21. Almeida, M.M.D., Moghe, R., Akella, M.: Real-Time Minimum Snap Trajectory Generation for Quadcopters: Algorithm Speed-Up through Machine Learning, pp. 683–689. IEEE International Conference on Robotics and Automation (ICRA), Montreal, Canada (2019)

    Google Scholar 

  22. Richter, C., Bry, A., Roy, N.: Polynomial Trajectory Planning for Aggressive Quadrotor Flight in Dense Indoor Environments, pp. 649–666. International Society of Root Research (ISRR), Singapor (2013)

    Google Scholar 

  23. Sanchez-Lopez, J.L., Castillo-Lopez, M., Olivares-Mendez, M.A., et al.: Trajectory tracking for aerial robots: an optimization-based planning and control approach. J. Intell. Robot. Syst. 100, 531–574 (2020)

    Article  Google Scholar 

  24. Lin, Y., Gao, F., Qin, T., et al.: Autonomous aerial navigation using monocular visual-inertial fusion. Journal of Field Robotics. 35(1), 23–51 (2018)

    Article  Google Scholar 

  25. Zhou, B., Gao, F., Wang, L., et al.: Robust and efficient quadrotor trajectory generation for fast autonomous flight. IEEE Robotics and Automation Letters. 4(4), 3529–3536 (2019)

    Article  Google Scholar 

  26. Zhou, B., Gao, F., Pan, J., Shen, S.: Robust Real-Time UAV Replanning Using Guided Gradient-Based Optimization and Topological Paths, pp. 1208–1214. IEEE International Conference on Robotics and Automation (ICRA), Paris, France (2020)

    Google Scholar 

  27. Wang, N., Zhang, Y., Ahn, C., Xu, Q.: Autonomous pilot of unmanned surface vehicles: bridging path planning and tracking. IEEE Trans. Veh. Technol. (2021). https://doi.org/10.1109/TVT.2021.3136670

  28. Liu, S., Watterson, M., Mohta, K., et al.: Planning dynamically feasible trajectories for quadrotors using safe flight corridors in 3-D complex environments. IEEE Robotics & Automation Letters. 2(3), 1688–1695 (2017)

    Article  Google Scholar 

  29. Blochliger, F., Fehr, M., Dymczyk, M., et al.: Topomap: Topological Mapping and Navigation Based on Visual SLAM Maps, pp. 3818–3825. IEEE International Conference on Robotics and Automation (ICRA), Brisbane, Australia (2018)

    Google Scholar 

  30. Gao, F., Wang, L., Zhou, B., et al.: Teach-repeat-Replan: a complete and robust system for aggressive flight in complex environments. IEEE Trans. Robot. 36(5), 1526–1545 (2020)

    Article  Google Scholar 

  31. Gao, F., Wu, W., Pan, J., et al.: Optimal Time Allocation for Quadrotor Trajectory Generation, pp. 4715–4722. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain (2018)

    Google Scholar 

  32. Nagy, A., Vajk, I.: Sequential time-optimal path-tracking algorithm for robots. IEEE Trans. Robot. 35(5), 1253–1259 (2019)

    Article  Google Scholar 

  33. Han, Z., Zhang, R., Pan, N., et al.: Fast-Tracker: a Robust Aerial System for Tracking Agile Target in Cluttered Environments, pp. 328–334. IEEE International Conference on Robotics and Automation (ICRA), Xi'an, China (2021)

    Google Scholar 

  34. Nash, A., Koenig, S., Tovey, C.: Lazy Theta*: any-Angle Path Planning and Path Length Analysis in 3D, pp. 147–154. Twenty-Fourth AAAI Conference on Artificial Intelligence, Atlanta, USA (2010)

    Google Scholar 

  35. Qin, T., Li, P., Shen, S.: VINS-Mono: A Robust and Versatile Monocular Visual-Inertial State Estimator. IEEE Trans. Robot. 34(4), 1004–1020 (2018)

    Article  Google Scholar 

  36. Wang, K., Gao, F., Shen, S.: Real-Time Scalable Dense Surfel Mapping, pp. 6919–6925. IEEE International Conference on Robotics and Automation (ICRA), Montreal, Canada (2019)

    Google Scholar 

  37. Lee, T., Leoky, M., McClamroch, N.: Geometric Tracking Control of a Quadrotor Uav on se (3), pp. 5420–5425. IEEE Conference on Decision and Control (CDC), Atlanta, USA (2010)

    Google Scholar 

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Code Availability

The code of the current study is available from the corresponding author on reasonable request.

Funding

This work was supported in part by the Natural Science Foundation of China under Grant U1909203, 62036009, the Zhejiang Provincial Natural Science Foundation of China under Grant LQ22F020007, the Zhejiang Postdoctoral Science Foundation under Grant ZY21191190003, and the Ten Thousand Talent Program of Zhejiang Province.

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Authors and Affiliations

  1. College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou, 310023, China

    Peng Chen, Yuanjie Dang, Tianwei Yu & Ronghua Liang

  2. College of Information Science and Technology, Zhejiang University of Technology, Hangzhou, 310023, China

    Yongqi Jiang

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  1. Peng Chen
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  4. Tianwei Yu
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  5. Ronghua Liang
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Contributions

Peng Chen and Yongqi Jiang contributed to the conception of the study, performed the experiment, and wrote the manuscript;

Yuanjie Dang and Ronghua Liang helped perform the analysis with constructive discussions; Tianwei Yu helped perform the indoor autonomous flight.

Corresponding author

Correspondence to Yuanjie Dang.

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Chen, P., Jiang, Y., Dang, Y. et al. Real-Time Efficient Trajectory Planning for Quadrotor Based on Hard Constraints. J Intell Robot Syst 105, 52 (2022). https://doi.org/10.1007/s10846-022-01662-9

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  • DOI: https://doi.org/10.1007/s10846-022-01662-9

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