A method to enforce stiff constraints in the simulation of articulated multibody systems

Abstract

We propose a novel integrator for implementing bilateral constraints in multibody simulation using variational integrator methods. We first construct a variational penalty method, which is used to enforce a constraint. The penalty term is simulated using an asynchronous variational integrator, allowing the penalty part of the system to be simulated using a smaller time step. We compute the Discrete Euler-Lagrange (DEL) equations for an equivalent penalty term with a larger time step and then use this rescaled system in the aforementioned variational penalty method, thereby enforcing the constraints. This enables us to incorporate some of the behavior of a very stiff system, which would only be stable on the small time scale, into the system on the large time scale. The effect is better adherence to the constraints, at a larger time step. We demonstrate the method with a simulation of a chain of rigid bodies. We then discuss the potential applications of the integrator and highlight how the work can be used to better interpret the tuned values of the coefficients used in penalty formulations.