SCIENTIA SINICA Informationis, Volume 50 , Issue 5 : 718-733(2020) https://doi.org/10.1360/SSI-2019-0094

Position and posture control for a planar underactuated manipulator based on model reduction and chained structure

More info
  • ReceivedMay 9, 2019
  • AcceptedOct 8, 2019
  • PublishedApr 23, 2020


Funded by






[1] Lai X Z, Zhang Z, Wu M, et al. Hybrid control strategy for an underactuated three-link manipulator. Sci Sin Inform,2013, 43: 287--302 [赖旭芝, 张镇, 吴敏, 等. 欠驱动三连杆机器人的混杂控制方法. 中国科学: 信息科学, 2013, 43: 287--302]. Google Scholar

[2] Liang D, Sun N, Wu Y. Trajectory planning-based control of underactuated wheeled inverted pendulum robots. Sci China Inf Sci, 2019, 62: 50207 CrossRef Google Scholar

[3] Wang H L, Zhang H, Wang Z P, et al. Exponentially stable periodic walking of under-actuated biped robot. Sci Sin Tech, 2019, 49: 288--300 [王鹤霖, 张皓, 王祝萍, 等. 欠驱动双足机器人的指数稳定周期行走. 中国科学: 技术科学, 2019, 49: 288--300]. Google Scholar

[4] Sun N, Fang Y C. A review for the control of a class of underactuated systems. CAAI Trans Intell Syst, 2011, 6: 200--207. Google Scholar

[5] Huo W, Zheng Z. Planar path following control for stratospheric airship. IET Control Theor Appl, 2013, 7: 185-201 CrossRef Google Scholar

[6] Lai X Z, She J H, Cao W H. Stabilization of underactuated planar acrobot based on motion-state constraints. Int J Non-Linear Mech, 2015, 77: 342-347 CrossRef Google Scholar

[7] 2-XInt J Robust NOnlinear Control 2000, 10: 181--198. Google Scholar

[8] Arai H, Tanie K, Shiroma N. Nonholonomic control of a three-DOF planar underactuated manipulator. IEEE Trans Robot Automat, 1998, 14: 681-695 CrossRef Google Scholar

[9] Mahindrakar * A D, Banavar R N, Reyhanoglu M. Controllability and point-to-point control of 3-DOF planar horizontal underactuated manipulators. Int J Control, 2005, 78: 1-13 CrossRef Google Scholar

[10] Xiong P G, Lai X Z, Wu M. Position control for planar four-link underactuated mechanical system based on model degeneration. Control Decis, 2015, 30: 1277--1283. Google Scholar

[11] Chen G, Zhang L, Jia Q X, et al. Repetitive motion planning for space manipulator based on null space of primary task. J Astronaut, 2013, 34: 1063--1071. Google Scholar

[12] Li Y F, Gao C H, Shen L. Study of vision-based space target capturing strategy for manipulators. Sci Sin Tech, 2015, 45: 31--35 [李宇飞, 高朝辉, 申麟. 基于视觉的机械臂空间目标抓取策略研究. 中国科学: 技术科学, 2015, 45: 31--35]. Google Scholar

[13] Fu D W, Wang J H, Lin M, et al. An Intellectual Robotic Arm Device Controlled by the Head Posture. J Nantong Univ (Nat Sci Ed), 2018, 17: 17--21. Google Scholar

[14] Wang X. Adaptive Real-time Predictive Compensation Control for 6-DOF Serial Arc Welding Manipulator. CJME, 2010, 23: 361-366 CrossRef Google Scholar

[15] Lai X, Zhang P, Wang Y. Position-Posture Control of a Planar Four-Link Underactuated Manipulator Based on Genetic Algorithm. IEEE Trans Ind Electron, 2017, 64: 4781-4791 CrossRef Google Scholar

[16] Oriolo G, Nakamur Y. Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators. In: Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, 1991. 2398--2403. Google Scholar

[17] Lai X, Wang Y, Wu M. Stable Control Strategy for Planar Three-Link Underactuated Mechanical System. IEEE/ASME Trans Mechatron, 2016, 21: 1345-1356 CrossRef Google Scholar

[18] Lin Y, Zhao H, Ding H. Solution of inverse kinematics for general robot manipulators based on multiple population genetic algorithm. J Mech Eng, 2017, 53: 1--8. Google Scholar

[19] Gao J L, Tang Y C, Wang J X, et al. A concurrent trace debugging method for multi-core chip based on genericalgorithm. Sci Sin Inform, 2014, 44: 1253--1263 [高建良, 唐逸晨, 王建新, 等. 基于遗传算法的多核芯片并发追踪调试方法. 中国科学: 信息科学, 2014, 44: 1253--1263]. Google Scholar

[20] Khalil H. Nonlinear Systems. 3rd ed. Englewood Cliffs: Prenice Hall, 2002. Google Scholar

  • Figure 1

    (Color online) The model of the planar AAPA manipulator

  • Figure 2

    (Color online) The model of the planar virtual AAP manipulator

  • Figure 3

    (Color online) The model of the planar Acrobot

  • Figure 4

    Multiple target angles corresponding to a target position-posture

  • Figure 5

    (Color online) Simulation results for case 1. (a) Angles of links; (b) angles velocities of links; (c) coordinate of the passive joint; (d) coordinate of the system endpoint; (e) control torques; (f) posture angles of the passive link and the fourth link

  • Figure 6

    (Color online) Simulation results for case 2. (a) Angles of links; (b) angles velocities of links; (c) coordinate of the passive joint; (d) coordinate of the system endpoint; (e) control torques; (f) posture angles of the passive link and the fourth link

  • Table 1   The model parameters of the planar AAPA manipulator
    Segment $i$ ${m_i}\left(~{{\rm{kg}}}~\right)$ ${l_i}\left(~{\rm{m}}~\right)$ ${l_{ci}}\left(~{\rm{m}}~\right)$ ${J_i}\left(~{{\rm{kg/}}{{\rm{m}}^{\rm{2}}}}~\right)$
    1 1.2 1.2 0.144 0.144
    2 1.2 1.2 0.144 0.144
    3 0.6 0.3 0.144 0.0022
    4 0.6 0.7 0.144 0.0285

    Algorithm 1 Optimization of each target value of the system

    Set up the parameters of GA: ${p_s},{p_c},{p_m},N,G,{N_{{\rm{var}}}}~=~4,\Omega~~\in~\left\{~{~-~2\pi~,2\pi~}~\right\}$;

    Randomly initialize: ${P_k}(g)~=~\left\{~{{x_{pc}},{y_{pc}},{\theta~_{pc}},{q_{4c}}}~\right\}~\in~\Omega,\left(~{k~=~1,2,3,~\ldots~,N}~\right)$;

    for $g=1:G{\rm{~+1~}}$

    Substituting ${q_{4c}}$ and ${\theta~_{pc}}$ into (6), the posture angle ${\theta~_{pcd}}$ of the passive link is obtained;

    Substitute (2), (6) and ${\theta~_{pcd}}$ into (7), and calculate $h$;

    if $h~<~\varepsilon~$ then



    end if

    Update ${x_{pc}},~{y_{pc}},~{\theta~_{pc}},~{\theta~_{pcd}}$ and ${q_{4c}}$ through crossover, mutation, selection operations;