A more compact expression of relative Jacobian based on individual manipulator Jacobians

This work presents a re-derivation of relative Jacobian matrix for parallel (dual-arm) manipulators, expressed in terms of the individual manipulator Jacobians and multiplied by their corresponding transformation matrices. This is particularly useful when the individual manipulator Jacobians are given, such that one would not need to derive an entirely new expression of a relative Jacobian but will only use the existing manipulator Jacobians and perform the necessary transformations. In this work, the final result reveals a wrench transformation matrix which was not present in previous derivations, or was not explicitly expressed. The proposed Jacobian expression results in a simplified, more compact and intuitive form. It will be shown that the wrench transformation matrix is present in stationary as well as mobile combined manipulators. Simulation results show that at high angular end-effector velocities, the contribution of the wrench transformation matrix cannot be ignored. We present a relative Jacobian for dual-arm manipulators expressed in terms of the individual manipulator Jacobians.In this new expression, each manipulator Jacobian is multiplied with a rotation and/or wrench transformation matrices.The relative Jacobians for both stationary and mobile dual-arm manipulators are presented.The effect of wrench transformation matrix is analyzed in both analytical approach and numerical simulation.At high angular end-effector velocities, the contribution of the wrench transformation matrix cannot be ignored.

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