Prediction of the quasistatic planar motion of a contacted rigid body

Planning the motion of bodies in contact requires a model of contact mechanics in order to predict sliding, rolling, and jamming. Such a model typically assumes that the bodies are rigid and that tangential forces at the contacts obey Coulomb's law. Though, usually assumed to be constant, the static and dynamic coefficients of friction vary in space and time and are difficult to measure accurately. In this paper, we study a quasistatic, multi-rigid-body model for planar systems, in which the coefficients of friction are treated as independent variables. Our analysis yields inequalities defining regions in the space of friction coefficients for which a particular contact mode is feasible. The geometrical interpretation of these inequalities leads to a simple graphical technique to test contact mode feasibility. This technique is then used to generate a nontrivial example in which several contact modes are simultaneously feasible. Despite model ambiguity, there are factors which argue in favor of using a quasistatic, rigid-body model. This point is highlighted by the successful application of our results to the planning of two manipulation tasks