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              帶有雙球面擺和變繩長效應的橋式起重機軌跡規劃

              李剛 馬昕 李輊 李貽斌

              李剛, 馬昕, 李輊, 李貽斌. 帶有雙球面擺和變繩長效應的橋式起重機軌跡規劃. 自動化學報, 2024, 50(5): 911?923 doi: 10.16383/j.aas.c220988
              引用本文: 李剛, 馬昕, 李輊, 李貽斌. 帶有雙球面擺和變繩長效應的橋式起重機軌跡規劃. 自動化學報, 2024, 50(5): 911?923 doi: 10.16383/j.aas.c220988
              Li Gang, Ma Xin, Li Zhi, Li Yi-Bin. Trajectory planning for overhead crane with double spherical pendulum and varying cable length effect. Acta Automatica Sinica, 2024, 50(5): 911?923 doi: 10.16383/j.aas.c220988
              Citation: Li Gang, Ma Xin, Li Zhi, Li Yi-Bin. Trajectory planning for overhead crane with double spherical pendulum and varying cable length effect. Acta Automatica Sinica, 2024, 50(5): 911?923 doi: 10.16383/j.aas.c220988

              帶有雙球面擺和變繩長效應的橋式起重機軌跡規劃

              doi: 10.16383/j.aas.c220988
              基金項目: 山東省重點研發計劃項目 (2021CXGC010701), 山東省中央引導地方科技發展資金項目 (YDZX2023042), 國家自然科學基金科學中心項目 (62188101), 國家自然科學基金?山東省政府聯合基金 (U1706228) 資助
              詳細信息
                作者簡介:

                李剛:山東大學控制科學與工程學院機器人研究中心博士研究生. 主要研究方向為欠驅動起重機系統的軌跡規劃與非線性控制. E-mail: ligangsdu@mail.sdu.edu.cn

                馬昕:山東大學控制科學與工程學院機器人研究中心教授. 主要研究方向為移動機器人, 機器視覺和欠驅動系統控制. 本文通信作者. E-mail: maxin@sdu.edu.cn

                李輊:山東大學控制科學與工程學院機器人研究中心博士后. 主要研究方向為四旋翼無人機系統, 船用起重機系統的非線性控制. E-mail: lizhisucro@sdu.edu.cn

                李貽斌:山東大學控制科學與工程學院機器人研究中心教授. 主要研究方向為智能機器人技術, 智能控制系統. E-mail: liyb@sdu.edu.cn

              Trajectory Planning for Overhead Crane With Double Spherical Pendulum and Varying Cable Length Effect

              Funds: Supported by Key Research and Development Project of Shandong Province (2021CXGC010701), Central Guidance for Local Scientific and Technological Development Funding Projects of Shandong Province (YDZX2023042), Science Center Program of National Natural Science Foundation of China (62188101), and Joint Fund of National Natural Science Foundation of China and Shandong Province (U1706228)
              More Information
                Author Bio:

                LI Gang Ph.D. candidate at the Center for Robotics, School of Control Science and Engineering, Shandong University. His research interest covers trajectory planning and nonlinear control of underactuated crane system

                MA Xin Professor at the Center for Robotics, School of Control Science and Engineering, Shandong University. Her research interest covers mobile robots, machine vision, and control of underactuated system. Corresponding author of this paper

                LI Zhi Postdoctor at the Center for Robotics, School of Control Science and Engineering, Shandong University. His research interest covers quad-rotor unmanned aerial vehicle system and nonlinear control of offshore crane system

                LI Yi-Bin Professor at the Center for Robotics, School of Control Science and Engineering, Shandong University. His research interest covers intelligent robot technology and intelligent control system

              • 摘要: 帶有雙球面擺和變繩長效應的橋式起重機具有多輸入多輸出以及欠驅動的動力學特性, 目前仍缺乏有效的控制策略. 在臺車移動、橋架移動、負載升降同步作業過程中, 吊鉤和負載兩級球面擺動特性更為復雜, 各狀態量之間的非線性耦合關系更強, 橋式起重機的防擺控制更具挑戰性. 不僅如此, 現有方法無法保證橋式起重機系統全狀態量的暫態控制性能. 為解決上述問題, 提出一種基于多項式的優化軌跡規劃方法. 首先, 在未進行近似簡化的前提下, 使用拉格朗日方法建立帶有雙球面擺和變繩長效應的7自由度 (Seven degree-of-freedom, 7-DOF) 橋式起重機的精確動力學模型. 在此基礎上, 構造一組包含各狀態量的輔助信號, 將施加在臺車、橋架、繩長以及吊鉤、負載擺動上的約束轉化為對輔助信號的約束, 從而將橋式起重機的軌跡規劃問題轉化為與輔助信號相關的時間優化問題, 并使用二分法求解. 該軌跡規劃方法不僅縮短了吊運時間, 而且確保了全狀態量滿足約束條件. 最后, 仿真結果證明了動力學模型的準確性和軌跡規劃方法的有效性.
              • 圖  1  7自由度橋式起重機系統

                Fig.  1  Seven degree-of-freedom overhead crane system

                圖  2  控制系統框圖

                Fig.  2  Block diagram of the proposed control system

                圖  3  雙球面擺動力學響應

                Fig.  3  Double spherical pendulum dynamic response

                圖  4  驅動狀態量的仿真結果

                Fig.  4  Simulation results of actuated states

                圖  5  非驅動狀態量的仿真結果

                Fig.  5  Simulation results of unactuated states

                圖  6  吊鉤和負載軌跡

                Fig.  6  Trajectories of the hook and payload

                圖  7  不同索具繩長度$ l_2$的仿真結果

                Fig.  7  Simulation results of different rigging cable lengths $ l_2$

                圖  8  不同負載質量$ m_2$的仿真結果

                Fig.  8  Simulation results of different payload masses $ m_2$

                表  1  本文與橋式起重機相關工作的比較

                Table  1  Comparison between our work and the relevant work about overhead crane

                自由度參考文獻臺車移動橋架移動變繩長吊鉤搖擺負載搖擺
                2[7?8]$\checkmark$$\times$$\times$$\times$$\checkmark$
                3[9?11]$\checkmark$$\times$$\times$$\checkmark$$\checkmark$
                3[12?14]$\checkmark$$\times$$\checkmark$$\times$$\checkmark$
                4[15?17]$\checkmark$$\times$$\checkmark$$\checkmark$$\checkmark$
                4[18?19]$\checkmark$$\checkmark$$\times$$\times$$\checkmark$
                5[20?21] $\checkmark$$\checkmark$$\checkmark$$\times$$\checkmark$
                6[22?24]$\checkmark$$\checkmark$$\times$$\checkmark$$\checkmark$
                7本文$\checkmark$$\checkmark$$\checkmark$$\checkmark$$\checkmark$
                下載: 導出CSV

                表  2  系統參數

                Table  2  System parameters

                參數物理意義單位
                $M_1$臺車質量kg
                $M_2$臺車和橋架質量之和kg
                $m_1,m_2$吊鉤、負載質量kg
                $x,y$臺車、橋架位移m
                $l_1,l_2$吊繩、索具繩長度m
                $\theta_1,\theta_2,\theta_3,\theta_4$吊鉤、負載三維空間擺角 °
                $F_x,F_y,F_z$臺車、橋架、吊繩驅動力N
                $g$重力加速度m/s2
                下載: 導出CSV

                表  3  量化指標對比結果

                Table  3  Comparison results of quantitative indices

                控制方法$t_s\;({\rm{s}})$ ${\theta _{1\max }}\; (^\circ)$${\theta _{1\,{\rm{res} } } } \;(^\circ )$${\theta _{3\max }}\;(^\circ)$${\theta _{3\,{\rm{res} } } }\;(^\circ )$
                EI$>15.00$2.690.793.631.46
                光滑器$>15.00$2.290.232.460.35
                EAB$>15.00$3.140.225.391.21
                CTP4.823.030.013.240.02
                本文方法4.911.9201.970
                下載: 導出CSV
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