An Unconditionally Stable First-Order Constraint Solver for Multibody Systems

TL;DR

This paper introduces an unconditionally stable, first-order constraint solver for multibody systems that efficiently handles various constraints, including friction, without numerical issues, and is suitable for coarse simulations with potential stiffness.

Contribution

The paper presents a novel, absolutely stable first-order constraint solver capable of handling complex constraints without regularization or numerical problems, improving efficiency for multibody dynamics simulations.

Findings

Solver is unconditionally stable and L-stable.

Handles diverse constraints including friction without regularization.

Computational complexity varies with constraint types, often polynomial time.

Abstract

This article describes an absolutely stable, first-order constraint solverfor multi-rigid body systems that calculates (predicts) constraint forces for typical bilateral and unilateral constraints, contact constraints with friction, and many other constraint types. Redundant constraints do not pose numerical problems or require regularization. Coulomb friction for contact is modeled using a true friction cone, rather than a linearized approximation. The computational expense of the solver is dependent upon the types of constraints present in the input. The hardest (in a computational complexity sense) inputs are reducible to solving convex optimization problems, i.e., polynomial time solvable. The simplest inputs require only solving a linear system. The solver is L-stable, which will imply that the forces due to constraints induce no computational stiffness into the multi-body dynamics differential equations. This approach is targeted to multibodies simulated with coarse accuracy, subject to computational stiffness arising from constraints, and where the number of constraint equations is not large compared to the number of multibody position and velocity state variables. For such applications, the approach should prove far faster than using other implicit integration approaches. I assess the approach on some fundamental multibody dynamics problems.