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This article presents computationally efficient algorithms for modeling twospecial cases of rigid contact---contact with only viscous friction and contactwithout slip---that have particularly useful applications in robotic locomotionand grasping. Modeling rigid contact with Coulomb friction generally exhibits$O(n^3)$ expected time complexity in the number of contact points and$2^{O(n)}$ worst-case complexity. The special cases we consider exhibit $O(m^3+ m^2n)$ time complexity ($m$ is the number of independent coordinates in themulti rigid body system) in the expected case and polynomial complexity in theworst case; thus, asymptotic complexity is no longer driven by number ofcontact points (which is conceivably limitless) but instead is more dependenton the number of bodies in the system (which is often fixed). These specialcases also require considerably fewer constrained nonlinear optimizationvariables thus yielding substantial improvements in running time. Finally,these special cases also afford one other advantage: the nonlinear optimizationproblems are numerically easier to solve.

Rapidly computable viscous friction and no-slip rigid contact models