An Unconditionally Stable First-Order Constraint Solver for Multibody Systems
This work addresses the need for stable and efficient constraint solving in multibody dynamics simulations, particularly for applications requiring coarse accuracy and moderate constraint complexity.
The paper presents a first-order constraint solver for multibody systems that is unconditionally stable and handles various constraints without numerical issues. The solver is computationally efficient, especially for systems with coarse accuracy and moderate constraint numbers, outperforming other implicit integration methods.
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.