北京航空航天大学学报 ›› 2007, Vol. 33 ›› Issue (01): 105-109.

• 论文 • 上一篇    下一篇

三连杆平面欠驱动机械臂系统的最优运动规划

刘盛平1, 陆震1, 吴立成2   

  1. 1. 北京航空航天大学 自动化科学与电气工程学院, 北京 100083;
    2. 清华大学 计算机科学与技术系智能技术与系统国家重点实验室, 北京 100084
  • 收稿日期:2005-12-31 出版日期:2007-01-31 发布日期:2010-09-19
  • 作者简介:刘盛平(1978-),男,四川荣县人,博士生,liushengping@asee.buaa.edu.cn.
  • 基金资助:

    国家自然科学基金资助项目(50375007,50405002)

Optimal motion planning of a three-link planar under-actuated manipulator system

Liu Shengping1, Lu Zhen1, Wu Licheng2   

  1. 1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
    2. Tsinghua University, Beijing 100084, China
  • Received:2005-12-31 Online:2007-01-31 Published:2010-09-19

摘要: 研究了在两固定端点之间运动的三连杆平面欠驱动机械臂的最优运动规划问题.该机械臂有两个受驱动的移动关节,而第三个关节是一个既无驱动器又无制动器的被动关节.施加在自由运动连杆上的动力学约束是一个二阶非完整约束.通过坐标和输入变换,系统的状态和输入变量被表示为子状态变量的高阶导数形式;通过这些新的子状态变量,将一个受约束的动力学优化问题变成一个无约束的优化问题.利用变分法原理,推导出满足优化问题的必要条件.给出了PPR型平面欠驱动机械臂最优运动规划的数值算例.

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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