Abstract
In this paper, the motion recovery methodologies are proposed to recover as many components of the manipulator twist as possible while minimizing the 2-norm of the joint velocity vector. If any component of the joint velocity vector after the recovery violates the corresponding limits, the joints with velocities exceeding the limits are treated as failed and their velocities are set to their limits. When the Jacobian matrix of the failed manipulator is full row-rank and the joint velocities remain within their limits, the full recovery is achieved using the inverse or generalized inverse of the reduced Jacobian matrix. If the Jacobian matrix of the failed manipulator is full row-rank, but the minimum 2-norm of the joint velocities violate their limits so as the full recovery is not achieved, an optimization method followed by partitioning the reduced Jacobian matrix is proposed. Also, when the Jacobian matrix is full column-rank and the joint velocities remain within their limits, the partial recovery is obtained using partitioning the reduced Jacobian matrix. As examples, planar serial and parallel manipulators are investigated to show the effectiveness of the methodologies.
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