Modeling and Control of 2D Grasping under Rolling Contact Constraints between Arbitrary Shapes: A Riemannian-Geometry Approach

Figure 3

Rolling contact constraint is expressed by equalizing the velocity of contact point $P_{1A}(=P_1)$ in the direction of the unit tangent vector ${\mathit{b}}_0$ with that of $P_{1B}(=P_1)$ in the same direction of ${\mathit{b}}_1$. The velocity of $P_{1A}$ in the direction of the normal ${\mathit{n}}_1$ should be equal to that of $P_{1B}$ in the same direction. It is therefore assumed that ${\mathit{b}}_0={\mathit{b}}_1$.