A Riemannian-Geometry Approach for Modeling and Control of Dynamics of Object Manipulation under Constraints

<table>The pressing
force to the object at <math id="M757" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>P</mi><mn>1</mn></msub></mrow></math> in the
direction <math id="M758" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>n</mi><mn>1</mn></msub></mrow></math> induces a
rotational moment around <math id="M759" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>P</mi><mn>2</mn></msub></mrow></math> and vice versa.</table>

Journal of Robotics

fig9

Figure 9

Figure 9: A Riemannian-Geometry Approach for Modeling and Control of Dynamics of Object Manipulation under Constraints 