  Many fundamental challenges in robotics, based in manipulation or locomotion,
require making and breaking contact with the environment. To represent the
complexity of frictional contact events, impulsive impact models are especially
popular, as they often lead to mathematically and computationally tractable
approaches. However, when two or more impacts occur simultaneously, the precise
sequencing of impact forces is generally unknown, leading to the potential for
multiple possible outcomes. This simultaneity is far from pathological, and
occurs in many common robotics applications. In this work, we propose an
approach for resolving simultaneous frictional impacts, represented as a
differential inclusion. Solutions to our model, an extension to multiple
contacts of Routh's method, naturally capture the set of potential post-impact
velocities.We prove that solutions to the presented model must terminate. This
is, to the best of our knowledge, the first such guarantee for set-valued
outcomes to simultaneous frictional impacts.
