Study of the robotic manipulators' kinematic manipulability

The series robotic manipulator's operation space is studied, the conclusion that the greater of the robotic manipulator's operation space volume, the better of the robotic manipulator's manipulability is drawn, volume element based on redundant robotic manipulator's kinematics is proposed as an operational performance index.
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-DOF serial robotic manipulator's operation space is
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-dimensional Riemannian manifold, the
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-dimensional Riemannian manifold volume is calculated using the moving coordinate system and the exterior product definition in differential geometry, and get the robotic manipulator's operation space volume, and compared the obtained results with the operation space volume using inner product determinant in the literature, it shows that the volume element as a kinematic operational performance index is feasible.