Prediction of equilibria of lifted logarithmic radial potential fields

Many distributed manipulation systems are capable of generating planar force fields which act over the entire surface of an object to manipulate it to a stable equilibrium within the field. Passive air flow and other physical phenomena naturally generate force fields through the linear superposition of logarithmically varying radial potential fields. The main advantage of these fields is that they are realizable through very simple actuation. However, they do not lend themselves to analytical prediction of net forces or equilibria. In this paper we present an efficient means of numerically computing the net force and moment exerted by such fields on objects composed of multiple simple shapes, as well as efficient means of finding equilibrium points on these fields with experimental verification. Existence conditions of stable equilibria are investigated in analytic forms and incremental searching algorithms are proposed based on existence conditions.