In recent years, effective control methods for underactuated systems of bridge cranes have garnered significant attention. However, designing trajectories that ensure both transient performance and resilience to external disturbances is challenging due to crane characteristics and interference. This paper presents a double-loop feedback compensation trajectory planning approach. An initial conditional trajectory is designed based on a smoothing factor. Subsequently, this trajectory is refined into a final reference trajectory with real-time compensation to enhance its response to adversarial perturbations. An online trajectory optimizer is developed using differential flatness theory, addressing second derivative interference from compensation and improving transient performance by considering the system’s payload shift and payload swing energy relations. The integration of the reference trajectory with the optimizer enables real-time adjustments to trolley displacement to counteract external interferences caused by adverse weather conditions. Experiments verify the method’s 0.01-s trajectory generation and 3-s stabilization under various disturbances without residual swing, demonstrating superior real-time robustness.
BlackburnDSinghoseWKitchenJ, et al. (2009) Command shaping for nonlinear crane dynamics. Journal of Vibration and Control16(4): 477–501. https://doi.org/10.1177/1077546309106142
2.
BoscariolPRichiedeiD (2018) Robust point-to-point trajectory planning for nonlinear underactuated systems: theory and experimental assessment. Robotics and Computer-Integrated Manufacturing50: 256–265. https://doi.org/10.1016/j.rcim.2017.10.001
3.
BurgTDawsonDRahnC, et al. (1996) Nonlinear control of an overhead crane via the saturating control approach of teel. In: Proceedings of the IEEE international conference on robotics and automation, Minneapolis, MN, USA, 22–28 April 1996, pp. 3155–3160. IEEE.
4.
ChenHFangYSunN (2016) Optimal trajectory planning and tracking control method for overhead cranes. IET Control Theory & Applications10(6): 692–699. https://doi.org/10.1049/iet-cta.2015.0809
5.
ChenHFangYSunN (2017) A swing constrained time-optimal trajectory planning strategy for double pendulum crane systems. Nonlinear Dynamics89(2): 1513–1524. https://doi.org/10.1007/s11071-017-3531-0
6.
FangYDixonWEDawsonDM, et al. (2003) Nonlinear coupling control laws for an underactuated overhead crane system. IEEE/ASME Transactions on Mechatronics8(3): 418–423. https://doi.org/10.1109/tmech.2003.816822
7.
FangYMaBWangP (2012) A motion planning-based adaptive control method for an underactuated crane system. IEEE Transactions on Control Systems Technology20(1): 241–248.
8.
GarridoSAbderrahimMGimenezA, et al. (2008) Anti-swinging input shaping control of an automatic construction crane. IEEE Transactions on Automation Science and Engineering5(3): 549–557. https://doi.org/10.1109/tase.2007.909631
9.
HuGMakkarCDixonWE (2007) Energy-based nonlinear control of underactuated Euler-lagrange systems subject to impacts. IEEE Transactions on Automatic Control52(9): 1742–1748. https://doi.org/10.1109/tac.2007.904319
10.
JaafarHIMohamedZAhmadMA, et al. (2020) Control of an underactuated double-pendulum overhead crane using improved model reference command shaping: design, simulation and experiment. Mechanical Systems and Signal Processing151: 107358. https://doi.org/10.1016/j.ymssp.2020.107358
KimDJWangZBehalA (2012) Motion segmentation and control design for UCF-MANU-An intelligent assistive robotic manipulator. IEEE/ASME Transactions on Mechatronics17(5): 936–948. https://doi.org/10.1109/tmech.2011.2149730
13.
LiGMaXLiZ, et al. (2023) Time-polynomial-based optimal trajectory planning for double-pendulum tower crane with full-state constraints and obstacle avoidance. IEEE/ASME Transactions on Mechatronics28(2): 450–462. https://doi.org/10.1109/tmech.2022.3210536
14.
LiGMaXLiY (2024a) Adaptive anti-swing control for 7-DOF overhead crane with double spherical pendulum and varying cable length. IEEE Transactions on Automation Science and Engineering21(4): 5240–5251. https://doi.org/10.1109/tase.2023.3309937
15.
LiGMaXLiY (2024b) Robust command shaped vibration control for stacker crane subject to parameter uncertainties and external disturbances. IEEE Transactions on Industrial Electronics71(11): 14740–14752. https://doi.org/10.1109/tie.2024.3366197
16.
LiGMaXLiY (2025a) Adaptive sliding mode control based on time-delay estimation for underactuated 7-DOF tower crane. IEEE Transactions on Systems, Man, and Cybernetics: Systems55(3): 2277–2288. https://doi.org/10.1109/tsmc.2024.3520174
17.
LiGMaXLiY, et al. (2025b) Adaptive output feedback anti-swing control for underactuated 7-DOF rotary crane with gravitational estimation. Mechanical Systems and Signal Processing229: 112495. https://doi.org/10.1016/j.ymssp.2025.112495
18.
LiangYLiRLiuT, et al. (2024) An enhanced coupling optimal trajectory planning for bridge cranes. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science238(6): 2007–2017. https://doi.org/10.1177/09544062231190797
19.
LuBCaoHHaoY, et al. (2021) Online antiswing trajectory planning for a practical rubber tire container gantry crane. IEEE Transactions on Industrial Electronics69(11): 11512–11521. https://doi.org/10.1109/tie.2021.3088356
20.
LuBLinJFangY, et al. (2022) Online trajectory planning for three-dimensional offshore boom cranes. Automation in Construction140: 104372. https://doi.org/10.1016/j.autcon.2022.104372
21.
MaBFangYZhangY (2010) Switching-based emergency braking control for an overhead crane system. IET Control Theory & Applications4(9): 1739–1747. https://doi.org/10.1049/iet-cta.2009.0277
22.
MiaoXYangLOuyangH (2023) Artificial-neural-network-based optimal smoother design for oscillation suppression control of underactuated overhead cranes with distributed mass beams. Mechanical Systems and Signal Processing200: 110497. https://doi.org/10.1016/j.ymssp.2023.110497
23.
MinYLiuY (2007) Barbalat lemma and its application in system stability analysis. Journal of Shandong University37(3): 51–55.
24.
OttoSSeifriedR (2020) Real-time trajectory control of an overhead crane using servo-constraints. Multibody System Dynamics42(1): 1–17. https://doi.org/10.1007/s11044-017-9569-4
25.
OuyangHDingX (2019) Decoupled linear model and S-shaped curve motion trajectory for load sway reduction control in overhead cranes with double-pendulum effect. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science233(10): 3511–3522.
26.
OuyangHTianZYuL, et al. (2020a) Motion planning approach for payload swing reduction in tower cranes with double-pendulum effect. Journal of the Franklin Institute357(13): 8299–8320. https://doi.org/10.1016/j.jfranklin.2020.02.001
27.
OuyangHXuXZhangG (2020b) Energy-shaping-based nonlinear controller design for rotary cranes with double-pendulum effect considering actuator saturation. Automation in Construction111: 103054. https://doi.org/10.1016/j.autcon.2019.103054
28.
OuyangHXuXZhangG (2020c) Tracking and load sway reduction for double-pendulum rotary cranes using adaptive nonlinear control approach. International Journal of Robust and Nonlinear Control30(5): 1872–1885. https://doi.org/10.1002/rnc.4854
29.
PengHShiBWangX, et al. (2020a) Interval estimation and optimization for motion trajectory of overhead crane under uncertainty. Nonlinear Dynamics102(3): 1–15.
30.
PengHZhaoHWangX, et al. (2020b) Robust motion trajectory optimization of overhead cranes based on polynomial chaos expansion. ISA Transactions106: 1–11.
31.
RehmanURFasihSMQadirMA, et al. (2022) Input shaping with an adaptive scheme for swing control of an underactuated tower crane under payload hoisting and mass variations. Mechanical Systems and Signal Processing175: 109106. https://doi.org/10.1016/j.ymssp.2022.109106
32.
SatoKOhishiKMiyazakiT (2015) Anti-sway crane control considering wind disturbance and container mass. IEEE Transactions on Industry Applications135(1): 262–271. https://doi.org/10.1541/ieejias.133.262
33.
SorensenKSinghoseWDickersonS (2007) A controller enabling precise positioning and sway reduction in bridge and gantry cranes. Control Engineering Practice15(7): 825–837. https://doi.org/10.1016/j.conengprac.2006.03.005
34.
SteinASinghT (2023) Minimum time control of a gantry crane system with rate constraints. Mechanical Systems and Signal Processing190: 110120. https://doi.org/10.1016/j.ymssp.2023.110120
35.
SunNFangY (2012) New energy analytical results for the regulation of underactuated overhead cranes: an end-effector motion-based approach. IEEE Transactions on Industrial Electronics59(12): 4723–4734. https://doi.org/10.1109/tie.2012.2183837
36.
SunNFangY (2013a) A partially saturated nonlinear controller for overhead cranes with experimental implementation. In: Proceedings of the IEEE international conference on robotics and automation (ICRA 2013), May 6–10,2013, Karlsruhe, Germany. p. 4473–4478.
37.
SunNFangY (2013b) An efficient online trajectory generating method for underactuated crane systems. International Journal of Robust and Nonlinear Control24(7): 1653–1663. https://doi.org/10.1002/rnc.2953
38.
SunNFangYZhangY, et al. (2012) A novel kinematic coupling-based trajectory planning method for overhead cranes. IEEE/ASME Transactions on Mechatronics17(1): 166–173. https://doi.org/10.1109/tmech.2010.2103085
39.
SunNFangYWuX (2014) An enhanced coupling nonlinear control method for bridge cranes. IET Control Theory & Applications8(13): 1215–1223. https://doi.org/10.1049/iet-cta.2013.0584
40.
SunNWuYChenH, et al. (2018) An energy-optimal solution for transportation control of cranes with double pendulum dynamics: design and experiments. Mechanical Systems and Signal Processing102: 87–101. https://doi.org/10.1016/j.ymssp.2017.09.027
41.
ThoHDKaneshigeATerashimaK (2020) Minimum-time S-curve commands for vibration-free transportation of an overhead crane with actuator limits. Control Engineering Practice98: 104390. https://doi.org/10.1016/j.conengprac.2020.104390
42.
TomczykJCinkJKosuckiA (2014) Dynamics of an overhead crane under a wind disturbance condition. Automation in Construction42(1): 100–111. https://doi.org/10.1016/j.autcon.2014.02.013
43.
TuanLALeeSGMoonSC (2012) Partial feedback linearization control of overhead cranes with varying cable lengths. International Journal of Precision Engineering and Manufacturing13(8): 1455–1460.
44.
WangYSunNWuY (2021) Real-time motion planning of deep sea-oriented flexible crane systems. Acta Automatica Sinica47(12): 2761–2770.
45.
WangTLinCLiR, et al. (2023) Nonlinear enhanced coupled feedback control for bridge crane with uncertain disturbances: theoretical and experimental investigations. Nonlinear Dynamics111(20): 19021–19032. https://doi.org/10.1007/s11071-023-08881-1
WuQWangXHuaL, et al. (2020a) Dynamic analysis and time optimal anti-swing control of double pendulum bridge crane with distributed mass beams. Mechanical Systems and Signal Processing144: 106968. https://doi.org/10.1016/j.ymssp.2020.106968
48.
WuXXuKHeX (2020b) Disturbance-observer-based nonlinear control for overhead cranes subject to uncertain disturbances. Mechanical Systems and Signal Processing139: 106631. https://doi.org/10.1016/j.ymssp.2020.106631
49.
WuXXuKLeiM, et al. (2020c) Disturbance-compensation-based continuous sliding mode control for overhead cranes with disturbances. IEEE Transactions on Automation Science and Engineering17(4): 2182–2189. https://doi.org/10.1109/tase.2020.3015870
YangTSunNChenH, et al. (2018) Motion trajectory-based transportation control for 3-D boom cranes: analysis, design, and experiments. IEEE Transactions on Industrial Electronics66(1): 308–318. https://doi.org/10.1109/tie.2018.2853604
52.
YouCHanJ (2007) Trajectory planning of manipulator for a hitting task with autonomous incremental learning. In: Proceedings of the IEEE international conference on robotics and biomimetics. China, Sanya, 15-18 December 2007, pp. 1446–1450.
53.
ZhangXFangYSunN (2014) Minimum-time trajectory planning for underactuated overhead crane systems with state and control constraints. IEEE Transactions on Industrial Electronics61(12): 6915–6925. https://doi.org/10.1109/tie.2014.2320231
54.
ZhangMMaXChaiH, et al. (2016a) A novel online motion planning method for double-pendulum overhead cranes. Nonlinear Dynamics85(2): 1–13. https://doi.org/10.1007/s11071-016-2745-x
55.
ZhangMMaXRongX, et al. (2016b) Adaptive tracking control for double-pendulum overhead cranes subject to tracking error limitation, parametric uncertainties and external disturbances. Mechanical Systems and Signal Processing76: 15–32. https://doi.org/10.1016/j.ymssp.2016.02.013
56.
ZhangMZhangYChengX (2019) An enhanced coupling PD with sliding mode control method for underactuated double-pendulum overhead crane systems. International Journal of Control, Automation and Systems17(6): 1579–1588. https://doi.org/10.1007/s12555-018-0646-0
57.
ZhangSHeXZhuH, et al. (2022) PID-Like coupling control of underactuated overhead cranes with input constraints. Mechanical Systems and Signal Processing178: 109274. https://doi.org/10.1016/j.ymssp.2022.109274
58.
ZhuHOuyangHXiH (2023) Neural network-based time optimal trajectory planning method for rotary cranes with obstacle avoidance. Mechanical Systems and Signal Processing185: 109777. https://doi.org/10.1016/j.ymssp.2022.109777
