Dynamic modeling and robust control of cable-driven cleaning robot for marine multi-curvature bulkhead
LI Jian1,2, WANG Shenghai1,2, LIU Jiang1,2, GAO Yufu1,2, HAN Guangdong1,2, SUN Yuqing1,2
1. Marine Engineering College, Dalian Maritime University, Dalian 116026, China; 2. Ministry of Science and Technology for International Research Center of Subsea Engineering Technology and Equipment, Dalian Maritime University, Dalian 116026, China
Abstract：[Objective] Cleaning operations for ships become challenging due to the irregular hull surface and ship motion. Thus, to achieve efficient and automated cleaning operations, this study proposes a variable-structure spatial cable-driven cleaning robot. Existing research is mainly based on fixed-base conditions and has not considered the influence of base motion on modeling accuracy. The cleaning robot is mounted on ships, and the 6 degrees of freedom ship motion will inevitably affect the tracking accuracy of the motion platform, eventually causing closed-loop instability of the system. Moreover, most research simplifies the external disturbances acting on the motion platform, which cannot accurately comprehend the influence of external disturbances on tracking accuracy. The cleaning robot is affected by external disturbances such as wind, waves, and currents during operation, and existing dynamic models are inapplicable. [Methods] To address the aforementioned issues, this study proposes the use of the Newton-Euler method to establish a dynamic model including ship motion and external disturbances. Fluid simulation is used to verify that water flow can be sprayed onto the operating surface, and to determine the reaction force acting on the motion platform. Furthermore, given the influence of sea wind on cleaning operations, the wind pressure projection method is used to calculate the wind’s disturbing force and combine it with the reaction force of water flow as an external disturbance. Furthermore, given the uncertainty of the dynamic model, it is decomposed into the modeled part and model error, and separate control laws are designed for these two parts. A proportional-integral sliding mode controller (PI-SMC) is further proposed. To improve the response speed and tracking accuracy of the control system, a fuzzy adaptive PI sliding mode controller (FAPI-SMC) is proposed based on the PI-SMC with an adaptive law and a fuzzy control strategy. Finally, the stability of the control system is proven by the Lyapunov theory, and the effectiveness of the controller is verified through simulations. [Results] The numerical analysis results showed that: (1) Under the set operating conditions, water flow could be sprayed onto the operating surface, and the mean value of the reaction force was approximately 9 N. (2) Under different forms of wave excitations and operating conditions, the position steady-state error of the motion platform under FAPI-SMC was maintained at ±0.02 m, and the angle steady-state error was maintained at ±0.02°. (3) When the operating conditions change, the steady-state error under proportional-integral-differential controller (PID) changed by approximately 0.16 m, the steady-state error under PI-SMC changed by approximately 0.19 m, and a smaller steady-state error under FAPI-SMC changed by approximately 0.01 m. (4) Compared with PI-SMC and PID, the maximum error of FAPI-SMC was reduced by 8% and 6%, respectively, the response speed was improved by 18% and 57%, respectively, and the steady-state performance was improved by 2% and 3%, respectively. [Conclusions] The proposed control strategy has high precision and rapid response under ship motion and external disturbances. Moreover, the cleaning robot has excellent operating stability for different wave excitations and operating conditions. Thus, the dynamic model and control strategy proposed in this study can provide theoretical guidance for applying cable-driven mechanisms in ships.
李建, 王生海, 刘将, 高钰富, 韩广冬, 孙玉清. 绳驱动船舱清洗机器人动力学建模及鲁棒控制[J]. 清华大学学报（自然科学版）, 2024, 64(3): 562-577.
LI Jian, WANG Shenghai, LIU Jiang, GAO Yufu, HAN Guangdong, SUN Yuqing. Dynamic modeling and robust control of cable-driven cleaning robot for marine multi-curvature bulkhead. Journal of Tsinghua University(Science and Technology), 2024, 64(3): 562-577.
[1] HUA J, CHIU Y S, TSAI C Y. En-route operated hydroblasting system for counteracting biofouling on ship hull[J]. Ocean Engineering, 2018, 152:249-256. [2] SHI X T, XU L, XU H B, et al. A 6-DOF humanoid wall-climbing robot with flexible adsorption feet based on negative pressure suction[J]. Mechatronics, 2022, 87:102889. [3] WANG B, NI Z F, SHEN Y, et al. Design and analysis of a wheel-leg compound variable curvature ship hull cleaning robot[J]. Ocean Engineering, 2022, 266:112755. [4] BOSTELMAN R, ALBUS J, DAGALAKIS N, et al. Applications of the NIST robocrane[C]//Proceedings of the 5th International Symposium on Robotics and Manufacturing. Maui, USA:NLST, 1994:403-410. [5] NAN R D. Five hundred meter aperture spherical radio telescope (FAST)[J]. Science in China Series G, 2006, 49(2):129-148. [6] EL-GHAZALY G, GOUTTEFARDE M, CREUZE V. Adaptive terminal sliding mode control of a redundantly-actuated cable-driven parallel manipulator:CoGiRo[C]//Proceedings of the Second International Conference on Cable-Driven Parallel Robots. Cham, Germany:Springer, 2015:179-200. [7] 李政清, 侯森浩, 韦金昊, 等. 面向仓储物流的平面索并联机器人视觉自标定方法[J]. 清华大学学报(自然科学版), 2022, 62(9):1508-1515. LI Z Q, HOU S H, WEI J H, et al. Vision-based auto-calibration method for planar cable-driven parallel robot for warehouse and logistics tasks[J]. Journal of Tsinghua University (Science and Technology), 2022, 62(9):1508-1515. (in Chinese) [8] 王晓光, 吴军, 林麒. 欠约束绳牵引并联支撑系统运动学分析与鲁棒控制[J]. 清华大学学报(自然科学版), 2021, 61(3):193-201. WANG X G, WU J, LIN Q. Kinematics analysis and control of under-constrained cable-driven parallel suspension systems[J]. Journal of Tsinghua University (Science and Technology), 2021, 61(3):193-201. (in Chinese) [9] WU Y L, CHENG H H, FINGRUT A, et al. CU-brick cable-driven robot for automated construction of complex brick structures:From simulation to hardware realisation[C]//2018 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR). Brisbane, Australia:IEEE, 2018:166-173. [10] MOON S M, SHIN C Y, HUH J, et al. Window cleaning system with water circulation for building façade maintenance robot and its efficiency analysis[J]. International Journal of Precision Engineering and Manufacturing-Green Technology, 2015, 2(1):65-72. [11] 李建, 陈羿宗, 王生海, 等. 绳驱动并联清洗机器人绳索张力优化[J]. 科学技术与工程, 2022, 22(35):15667-15674. LI J, CHEN Y Z, WANG S H, et al. Cable tension optimization of cable-driven parallel cleaning robots[J]. Science Technology and Engineering, 2022, 22(35):15667-15674. (in Chinese) [12] [JP+2]赵雅聪, 王启明. FAST索牵引并联机器人的动力学建模与仿真[J]. 清华大学学报(自然科学版), 2022, 62(11):1772-1779. ZHAO Y C, WANG Q M. Dynamic modeling of the FAST cable-driven parallel robots[J]. Journal of Tsinghua University (Science and Technology), 2022, 62(11):1772-1779. (in Chinese) [13] CAVERLY R J, FORBES J R. Dynamic modeling and noncollocated control of a flexible planar cable-driven manipulator[J]. IEEE Transactions on Robotics, 2014, 30(6):1386-1397. [14] ABDALLAH F B, AZOUZ N, BEJI L, et al. Modeling of a heavy-lift airship carrying a payload by a cable-driven parallel manipulator[J]. International Journal of Advanced Robotic Systems, 2019, 16(4):1729881419861769. [15] KINO H, YOSHITAKE T, WADA R, et al. 3-DOF planar parallel-wire driven robot with an active balancer and its model-based adaptive control[J]. Advanced Robotics, 2018, 32(14):766-777. [16] WANG Y Y, ZHU K W, YAN F, et al. Adaptive super-twisting nonsingular fast terminal sliding mode control for cable-driven manipulators using time-delay estimation[J]. Advances in Engineering Software, 2019, 128:113-124. [17] JIA H Y, SHANG W W, XIE F, et al. Second-order sliding-mode-based synchronization control of cable-driven parallel robots[J]. IEEE/ASME Transactions on Mechatronics, 2020, 25(1):383-394. [18] CAVERLY R J, FORBES J R. Flexible cable-driven parallel manipulator control:Maintaining positive cable tensions[J]. IEEE Transactions on Control Systems Technology, 2018, 26(5):1874-1883. [19] 韦慧玲, 仇原鹰, 盛英. 一种绳牵引摄像机器人的运动控制策略与稳定性研究[J]. 振动与冲击, 2017, 36(9):93-100, 171. WEI H L, QIU Y Y, SHENG Y. Motion control strategy and stability of a cable-based camera robot[J]. Journal of Vibration and Shock, 2017, 36(9):93-100, 171. (in Chinese) [20] CHEN Y Z, LI J, WANG S H, et al. Dynamic modeling and robust adaptive sliding mode controller for marine cable-driven parallel derusting robot[J]. Applied Sciences, 2022, 12(12):6137. [21] BORGSTROM P H, JORDAN B L, BORGSTROM B J, et al. NIMS-PL:A cable-driven robot with self-calibration capabilities[J]. IEEE Transactions on Robotics, 2009, 25(5):1005-1015. [22] CHEN Z Y. LaSalle-Yoshizawa theorem for nonlinear systems with external inputs:A counter-example[J]. Automatica, 2023, 147:110636. [23] FENG Y, YU X H, MAN Z H. Non-singular terminal sliding mode control of rigid manipulators[J]. Automatica, 2002, 38(12):2159-2167. [24] 王六平. PID控制系统设计:使用MATLAB和Simulink仿真与分析[M]. 北京:清华大学出版社, 2023. WANG L P. PID control system design and automatic tuning using MATLAB/Simulink[M]. Beijing:Tsinghua University Press, 2023. (in Chinese) [25] BHAT S P, BERNSTEIN D S. Finite-time stability of continuous autonomous systems[J]. SIAM Journal on Control and Optimization, 2000, 38(3):751-766. [26] MONDAL S, MAHANTA C. Adaptive second order terminal sliding mode controller for robotic manipulators[J]. Journal of the Franklin Institute, 2014, 351(4):2356-2377. [27] FOSSEN T I. Handbook of marine craft hydrodynamics and motion control[M]. Hoboken:John Wiley & Sons, 2011. [28] DNV. Environmental conditions and environmental loads:DNV-RP-C205[S]. Oslo:DNV, 2007.
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