Abstract
This work considers dynamically feasible point-to-point trajectory generation problem for a quadrotor flying through a constrained planner region referred as window (narrow gap). A four parameter logistic (4PL) curve is investigated as a prospective candidate and closed-form conditions are derived on the 4PL design parameters to satisfy the window traversability and vehicle dynamic feasibility constraints. A hierarchical approach first computes a dynamically feasible design parameter set for decoupled trajectory components and then obtains a solution set satisfying 3-D axis-coupled window traversability conditions. Numerical examples with a comparative study are presented to validate the analytical findings that highlight the quick computation of the dynamically feasible window traversing trajectories in complex window scenarios.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Delmerico, J., Mintchev, S., Giusti, A., Gromov, B., Melo, K., Horvat, T., Cadena, C., Hutter, M., Ijspeert, A., Floreano, D., Gambardella, L.M., Siegwart, R., Scaramuzza, D.: The current state and future outlook of rescue robotics. J. Field Robot. 36, 1171–1191 (2019). https://doi.org/10.1002/rob.21887
Moon, H., Martinez-Carranza, J., Cieslewski, T., Faessler, M., Falanga, D., Simovic, A., Scaramuzza, D., Li, S., Ozo, M., Wagter, C.D., Croon, G.D., Hwang, S., Jung, S., Shim, H., Kim, H., Park, M., Au, T.C., Kim, S.J.: Challenges and implemented technologies used in autonomous drone racing. Intell. Serv. Robot. 12, 137–148 (2019). https://doi.org/10.1007/s11370-018-00271-6
Birk, A., Wiggerich, B., Bülow, H., Pfingsthorn, M., Schwertfeger, S.: Safety, security, and rescue missions with an unmanned aerial vehicle. J. Intell. Robot. Syst. 64, 57–76 (2011). https://doi.org/10.1007/s10846-011-9546-8
Sampedro, C., Rodriguez-Ramos, A., Bavle, H., Carrio, A., Puente, P.D.L., Campoy, P.: A fully-autonomous aerial robot for search and rescue applications in indoor environments using learning-based techniques. J. Intell. Robot. Syst. 95, 601–627 (2019). https://doi.org/10.1007/s10846-018-0898-1
Falanga, D., Mueggler, E., Faessler, M., Scaramuzza, D.: Aggressive quadrotor flight through narrow gaps with onboard sensing and computing using active vision. In: IEEE International Conference on Robotics and Automation, pp. 5774–5781 (2017)
Loianno, G., Brunner, C., McGrath, G., Kumar, V.: Estimation, control, and planning for aggressive flight with a small quadrotor with a single camera and IMU. IEEE Robot. Autom. Lett. 2, 404–411 (2017). https://doi.org/10.1109/LRA.2016.2633290
Jung, S., Hwang, S., Shin, H., Shim, D.H.: Perception, guidance, and navigation for indoor autonomous drone racing using deep learning. IEEE Robot. Autom. Lett. 3, 2539–2544 (2018)
Kaufmann, E., Gehrig, M., Foehn, P., Ranftl, R., Dosovitskiy, A., Koltun, V., Scaramuzza, D.: Beauty and the beast: Optimal methods meet learning for drone racing. In: International Conference on Robotics and Automation, pp. 690–696 (2019)
Lin, J., Wang, L., Gao, F., Shen, S., Zhang, F.: Flying through a narrow gap using neural network: An end-to-end planning and control approach. In: IEEE/RSJ International Conference on Intell, Robots and Systems, pp. 3526–3533 (2019)
Guo, M., Gu, D., Zha, W, Zhu, X., Su, Y.: Controlling a quadrotor carrying a cable-suspended load to pass through a window. J. Intell. Robot. Syst. 98, 387–401 (2020)
Liu, S., Mohta, K., Atanasov, N., Kumar, V.: Search-based motion planning for aggressive flight in SE(3). IEEE Robot. Autom. Lett. 3, 2439–2446 (2018). https://doi.org/10.1109/LRA.2018.2795654
Schouwenaars, T., How, J., Feron, E.: Receding horizon path planning with implicit safety guarantees. In: Proc. of the 2004 American Control Conference, pp. 5576–5581 (2004)
Hoffmann, G.M., Waslander, S.L., Tomlin, C.J.: Quadrotor helicopter trajectory tracking control. In: AIAA Guidance, Navigation and Control Conference and Exhib. AIAA, pp. 2008–7410 (2008)
Cowling, I.D., Yakimenko, O.A., Whidborne, J.F., Cooke, A.K.: A prototype of an autonomous controller for a quadrotor UAV. In: European Control Conference, pp. 4001–4008 (2007)
Bouktir, Y., Haddad, M., Chettibi, T.: Trajectory planning for a quadrotor helicopter. In: Mediterranean Conference on Control and Automation, pp. 1258–1263 (2008)
Hehn, M., Ritz, R., D’Andrea, R.: Performance benchmarking of quadrotor systems using time-optimal control. Auton. Robot. 33, 69–88 (2012). https://doi.org/10.1007/s10514-012-9282-3
Geisert, M., Mansard, N: Trajectory generation for quadrotor based systems using numerical optimal control. In: IEEE International Conference on Robotics and Automation, pp. 2958–2964 (2016)
Neunert, M., Crousaz, C.D., Furrer, F., Kamel, M., Farshidian, F., Siegwart, R., Buchli, J.: Fast nonlinear model predictive control for unified trajectory optimization and tracking. In: IEEE International Conference on Robotics and Automation, pp. 1398–1404 (2016)
Yu, X., Zhou, X., Zhang, Y.: Collision-free trajectory generation and tracking for uavs using Markov decision process in a cluttered environment. J. Intell. Robotics Systems 93, 17–32 (2019). https://doi.org/10.1007/s10846-018-0802-z
Mellinger, D., Kumar, V.: Minimum snap trajectory generation and control for quadrotors. In: IEEE International Conference on Robotics and Automation, pp. 2520–2525 (2011)
Hehn, M., D’Andrea, R.: Quadrocopter trajectory generation and control. IFAC Proc. 44, 1485–1491 (2011). https://doi.org/10.3182/20110828-6-IT-1002.03178
Mueller, M.W., Hehn, M., D’Andrea, R.: A computationally-efficient motion primitive for quadrocopter trajectory generation. IEEE Trans. Robot. 31, 1294–1310 (2015). https://doi.org/10.1109/TRO.2015.2479878
Falanga, D., Foehn, P., Lu, P., Scaramuzza, D.: PAMPC: Perception-aware model predictive control for quadrotors. In: IEEE/RSJ International Conference on Intell, Robots and Systems, pp. 5200–5207 (2018)
Mellinger, D., Michael, N., Kumar, V.: Trajectory generation and control for precise aggressive maneuvers with quadrotors. Int. J. Robot. Res. 31, 664–674 (2012). https://doi.org/10.1177/0278364911434236
Upadhyay, S., Ratnoo, A.: Continuous-curvature path planning with obstacle avoidance using four parameter logistic curves. IEEE Robot. Autom. Lett. 1, 609–616 (2016). https://doi.org/10.1109/LRA.2016.2521165
Upadhyay, S.: Continuous-curvature path planning using four parameter logistic curves. Ph.D. Thesis, Indian Institute of Science (2018)
Upadhyay, S., Richards, A., Richardson, T.: Generation of window-traversing flyable trajectories using logistic curve. In: International Conference on Unmanned Aircr. Systems, pp. 59–65 (2020)
Quan, Q.: Introduction to Multicopter Design and Control. Springer, Singapore (2017)
Cardano’s Method. Brillient.org. https://brilliant.org/wiki/cardano-method/. Accessed: 03 October 2020 (2020)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
A version of the submitted paper appeared in the Proceedings of the 2020 International Conference on Unmanned Aircraft Systems (ICUAS’20), Athens, Greece.
This work is funded by the Engineering and Physical Sciences Research Council CASCADE Programme (ref EP/R009953/1).
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Upadhyay, S., Richardson, T. & Richards, A. Generation of Dynamically Feasible Window Traversing Quadrotor Trajectories Using Logistic Curve. J Intell Robot Syst 105, 16 (2022). https://doi.org/10.1007/s10846-022-01574-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10846-022-01574-8