帶有雙球面擺和變繩長(cháng)效應的橋式起重機軌跡規劃

李剛; 馬昕; 李輊; 李貽斌

doi:10.16383/j.aas.c220988

帶有雙球面擺和變繩長(cháng)效應的橋式起重機軌跡規劃

doi: 10.16383/j.aas.c220988

李剛^1,,
馬昕^1,,
李輊^1,,
李貽斌^1,

1.
山東大學(xué)控制科學(xué)與工程學(xué)院機器人研究中心濟南 250061

基金項目: 山東省重點(diǎn)研發(fā)計劃項目 (2021CXGC010701), 山東省中央引導地方科技發(fā)展資金項目 (YDZX2023042), 國家自然科學(xué)基金科學(xué)中心項目 (62188101), 國家自然科學(xué)基金?山東省政府聯(lián)合基金 (U1706228) 資助

詳細信息

作者簡(jiǎn)介:
李剛：山東大學(xué)控制科學(xué)與工程學(xué)院機器人研究中心博士研究生. 主要研究方向為欠驅動(dòng)起重機系統的軌跡規劃與非線(xiàn)性控制. E-mail: ligangsdu@mail.sdu.edu.cn

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

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

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

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- 文章訪(fǎng)問(wèn)數: 555
- HTML全文瀏覽量: 241
- PDF下載量: 144
- 被引次數: 0
出版歷程
- 收稿日期: 2022-12-21
- 錄用日期: 2023-04-13
- 網(wǎng)絡(luò )出版日期: 2023-08-10
- 刊出日期: 2024-05-29

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

LI Gang^1
,,
MA Xin^1
,,
LI Zhi^1
,,
LI Yi-Bin^1
,

1.
Center for Robotics, School of Control Science and Engineering, Shandong University, Jinan 250061

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

摘要: 帶有雙球面擺和變繩長(cháng)效應的橋式起重機具有多輸入多輸出以及欠驅動(dòng)的動(dòng)力學(xué)特性, 目前仍缺乏有效的控制策略. 在臺車(chē)移動(dòng)、橋架移動(dòng)、負載升降同步作業(yè)過(guò)程中, 吊鉤和負載兩級球面擺動(dòng)特性更為復雜, 各狀態(tài)量之間的非線(xiàn)性耦合關(guān)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(wú)法保證橋式起重機系統全狀態(tài)量的暫態(tài)控制性能. 為解決上述問(wèn)題, 提出一種基于多項式的優(yōu)化軌跡規劃方法. 首先, 在未進(jìn)行近似簡(jiǎn)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(cháng)效應的7自由度 (Seven degree-of-freedom, 7-DOF) 橋式起重機的精確動(dòng)力學(xué)模型. 在此基礎上, 構造一組包含各狀態(tài)量的輔助信號, 將施加在臺車(chē)、橋架、繩長(cháng)以及吊鉤、負載擺動(dòng)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(wèn)題轉化為與輔助信號相關(guān)的時(shí)間優(yōu)化問(wèn)題, 并使用二分法求解. 該軌跡規劃方法不僅縮短了吊運時(shí)間, 而且確保了全狀態(tài)量滿(mǎn)足約束條件. 最后, 仿真結果證明了動(dòng)力學(xué)模型的準確性和軌跡規劃方法的有效性.
- 欠驅動(dòng)起重機 /
- 多輸入多輸出系統 /
- 軌跡規劃 /
- 防擺控制
Abstract: Due to the multi-input multi-output and underactuated dynamic characteristics, the overhead crane with double spherical pendulum and varying cable length effect still lacks efficient control approaches. During the simultaneous operation of trolley moving, bridge moving and payload hoisting/lowing, the double spherical pendulum of hook and payload is more complex, and the nonlinear coupling characteristics of various state variables are stronger. It makes anti-swing control of overhead crane much more challenging. Moreover, the existing control methods cannot guarantee the desired transient control performance of the overhead crane system. To address the abovementioned issues, this paper proposes a novel polynomial-based optimal trajectory planning approach. Firstly, an accurate dynamic model for seven degree-of-freedom (7-DOF) overhead crane with double spherical pendulum and varying cable length effects is established by Lagrangian method without any simplifications. Based on this, a group of auxiliary signals containing various states are constructed. Then, the constraints imposed on the trolley/bridge moving, cable length varying, hook/payload swing are equivalently transformed to some new constraints on the auxiliary signals. Therefore, the trajectory planning problem of the overhead crane is transformed into a time optimization problem related to the auxiliary signals and solved by using the bisection method. The proposed trajectory planner not only makes transportation time as short as possible, but also ensures that full-states constraints are satisfied. At last, the simulation results prove the accuracy of the dynamic model and the effectiveness of the trajectory planning method.
- Underactuated crane /
- multi-input multi-output system /
- trajectory planning /
- anti-swing control

HTML全文

圖 1 7自由度橋式起重機系統

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

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圖 2 控制系統框圖

Fig. 2 Block diagram of the proposed control system

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圖 3 雙球面擺動(dòng)力學(xué)響應

Fig. 3 Double spherical pendulum dynamic response

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圖 4 驅動(dòng)狀態(tài)量的仿真結果

Fig. 4 Simulation results of actuated states

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圖 5 非驅動(dòng)狀態(tài)量的仿真結果

Fig. 5 Simulation results of unactuated states

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圖 6 吊鉤和負載軌跡

Fig. 6 Trajectories of the hook and payload

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圖 7 不同索具繩長(cháng)度$ l_2$的仿真結果

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

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圖 8 不同負載質(zhì)量$ m_2$的仿真結果

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

下載: 全尺寸圖片幻燈片

表 1 本文與橋式起重機相關(guān)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(chē)移動(dòng)	橋架移動(dòng)	變繩長(cháng)	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	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$

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表 2 系統參數

Table 2 System parameters

參數	物理意義	單位
$M_1$	臺車(chē)質(zhì)量	kg
$M_2$	臺車(chē)和橋架質(zhì)量之和	kg
$m_1,m_2$	吊鉤、負載質(zhì)量	kg
$x,y$	臺車(chē)、橋架位移	m
$l_1,l_2$	吊繩、索具繩長(cháng)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(chē)、橋架、吊繩驅動(dòng)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	$>15.00$	2.69	0.79	3.63	1.46
光滑器	$>15.00$	2.29	0.23	2.46	0.35
EAB	$>15.00$	3.14	0.22	5.39	1.21
CTP	4.82	3.03	0.01	3.24	0.02
本文方法	4.91	1.92	0	1.97	0

下載: 導出CSV

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