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�������պ����ѧѧ�� 2007, Vol. 33 Issue (01) :105-109    DOI:
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��ʢƽ1, ½��1, ������2*
1. �������պ����ѧ �Զ�����ѧ���������ѧԺ, ���� 100083;
2. �廪��ѧ �������ѧ�뼼��ϵ���ܼ�����ϵͳ�����ص�ʵ����, ���� 100084
Optimal motion planning of a three-link planar under-actuated manipulator system
Liu Shengping1, Lu Zhen1, Wu Licheng2*
1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. Tsinghua University, Beijing 100084, China

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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.
Keywords�� robot   under-actuated   planar manipulator   nonholonomic system   motion planning     
Received 2005-12-31;
Fund:

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About author: ��ʢƽ(1978��),��,�Ĵ�������,��ʿ��,liushengping@asee.buaa.edu.cn.
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��ʢƽ, ½��, ������.������ƽ��Ƿ������е��ϵͳ�������˶��滮[J]  �������պ����ѧѧ��, 2007,V33(01): 105-109
Liu Shengping, Lu Zhen, Wu Licheng.Optimal motion planning of a three-link planar under-actuated manipulator system[J]  JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2007,V33(01): 105-109
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