FIRST-ORDER KINEMATIC CONTROL OF MANIPULATORS WITH AN INACTIVE LAST JOINT

M. Karimi and S.A.A. Moosavian

Keywords

Underactuated manipulators, kinematic control, differential kinematics, dynamic properties, modified transpose effective Jacobian

Abstract

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 velocities is obtained which leads to a mapping between the active and passive joint velocities. This can be considered as a partial integration 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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