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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

Abstract


Funded by

国家自然科学基金(61773353)

青年科学基金(61903344)

湖北省自然科学基金创新群体(2015CFA010)

高等学校学科创新引智计划(B17040)


References

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  • 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

    ${x_{pd}}~=~x_{pc}^k,{y_{pd}}~=~y_{pc}^k,{\theta~_{pd}}~=~\theta~_{pc}^k,{\theta~_{pdd}}~=~\theta~_{pcd}^k,{q_{4d}}~=~q_{4c}^k$;

    $\bf{{break}}$;

    end if

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