Rolling Based Manipulation under Neighborhood Equilibrium

This paper proposes an idea of Neighborhood Equilibrium (NE) and applies it to the manipulation of an object. Under NE, an object with rolling contact can automatically find another equilibrium state close to the original one even when the current one is broken due to the change of input. For manipulating an object by taking NE into account, all the contact coordinates between the object and the plate are controlled to the desired values. To guarantee NE during the manipulation, we define the contact stable region (CSR) on the object surface. We plan the trajectory of contact coordinates within the CSR. The planned trajectory of contact point on the object surface is composed of multiple equilateral triangles. By using the Gauss-Bonnet theorem, the reachability of the algorithm is shown for a spheroidal object. Numerical examples and experiments are shown to explain our idea.