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Hybrid Position/Force Control: A Correct Formulation

Fisher, William D.; Mujtaba, M. Shahid

HPL-91-140

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Abstract: This paper will show conclusively that "kinematic instability" is not inherent to the hybrid position/force control scheme of robot manipulators, but is a result of an incomplete and inappropriate formulation. The inverse of the manipulator Jacobian matrix is identified as causing the kinematic instability of the hybrid position/force control scheme. Linear algebra is used to explain clearly the implications of mapping between vector spaces and to reveal why the inverse of the manipulator Jacobian matrix should not be used in hybrid position/force control. A generalized architecture for hybrid position/force control is presented that can influence both joint positions and torques. This generalized formulation also includes the control of redundant manipulators. Some sufficient conditions for kinematic stability are proposed to determine when a system may become unstable without requiriing a complete system analysis. A stable hybrid position/force control scheme is given, and is demonstrated using an example that was previously shown to be unstable.

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