M. Karimi and S.A.A. Moosavian
Underactuated manipulators, kinematic control, differential kine-matics, dynamic properties, modified transpose effective Jacobian
Differential kinematics and control of manipulators with an inactive last joint will be studied in this paper. A relationship between the active joint velocities and the corresponding end-effector output ve- locities is obtained which leads to a mapping between the active and passive joint velocities. This can be considered as a partial integra- tion of the second-order non-holonomic constraint. In other words, without requiring the passive joint velocity, end-effector trajectory can be computed using the active joints input vector. Then, the modified transpose effective Jacobian (MTEJ) algorithm is proposed as a first-order kinematic control of underactuated manipulators for trajectory tracking task in operational space. Various case studies of an underactuated three-link robot manipulator reveal the merits of the proposed methodology even in the presence of substantial disturbances.
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