HP Labs Technical Reports

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A Kinematically Stable Hybrid Position/Force Control Scheme

Fisher, William D.; Mujtaba, M. Shahid



Abstract: A correction to the position formulation of the hybrid position/force control scheme is presented. In the original position formulation, the derivation that uses the inverse of the Jacobian matrix to map from Cartesian space to joint space is shown to be algebraically incorrect. This incorrect derivation causes the kinematic instability attributed to the hybrid position/force control scheme. The correct derivation shows that the transformation between joint space and Cartesian space involves both the selection matrix and the Jocobian matrix; making the inverse mapping more complex since the two matrix transformations can no longer be treated independently. A sufficient condition for system stability using only the kinematic information is defined. With the corrected position formulation, the hybrid position/force control scheme demonstrates kinematically stable behavior and is applied to an example that was previously shown to be unstable. This correction generalizes the applicability of the hybrid position/force control scheme by providing system robustness for all robot manipulators.

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