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Volume 33 Issue 01
Jan.  2007
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Journal of Beijing University of Aeronautics and Astronautics  > 2007  >  33(01): 105-109.
Liu Shengping, Lu Zhen, Wu Lichenget al. Optimal motion planning of a three-link planar under-actuated manipulator system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2007, 33(01): 105-109. (in Chinese)
Citation: Liu Shengping, Lu Zhen, Wu Lichenget al. Optimal motion planning of a three-link planar under-actuated manipulator system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2007, 33(01): 105-109. (in Chinese)
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Optimal motion planning of a three-link planar under-actuated manipulator system

  • 1.

    School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

  • 2. Tsinghua University, Beijing 100084, China

  • Received Date: 31 Dec 2005
  • Publish Date: 31 Jan 2007
    Abstract
  • An optimal motion planning scheme for a three-link planar under-actuated manipulator moving between two stationary states was considered. The manipulator has two prismatic joints that are actuated, while the third joint of the manipulator is a revolute passive joint which has neither an actuator nor a holding brake. The dynamic constraint on the free link is shown to be second-order nonholonomic. The states and inputs of the system were expressed in terms of higher order derivatives of a subset of states by using coordinate and input transformations. The explicit expressions for the states and inputs were used to change a constrained dynamic optimization problem into an unconstrained one. The necessary conditions for optimality were derived by calculus of variations.The scheme was applied to a planar PPR under-actuated manipulator and numerical results were reported.

     

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  • [1] Luca A D, Mattone R, Oriolo G. Stabilization of an underactuated planar 2R manipulator[J]. International Journal of Robust and Nonlinear Control, 2000, 24:181-198 [2] Luca A D, Iannitti S, Oriolo G. Stabilization of a PR planar underactuated robot Proceeding of the 2001 IEEE International Conference on Robotics & Automation. Seoul:IEEE Press,2001:2090-2095 [3] Arai H, Tanie K, Shiroma N. Nonholonomic control of a three-dof plarnar underactuated manipulator[J]. IEEE Trans on Robotics and Automation, 1998, 14(5):681-695 [4] Imura J, Kobayashi K, Yoshikawa T. Nonholonomic control of 3 link planar manipulator with a free Joint Pro 35th IEEE Int Conf Decision Control. Kobe:IEEE Press, 1996:1435-1436 [5] Mahindrakar A D, Banavar R N, Reyhanoglu M. Discontinuous feedback control of a 3 link planar PPR underactuated manipulator Proceeding of the 40th IEEE Conference on Decision and Control. Orlando:IEEE Press,2001:2424-2429 [6] 何广平,陆震,王凤翔.欠驱动冗余度空间机器人优化控制[J].控制理论与应用,2004,21(2):305-310 He Guangping, Lu Zhen, Wang Fengxiang. Optimal control of under-actuated redundant space-robot system[J].Control Theory & Application, 2004,21(2):305-310 (in Chinese)
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