Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems

Abstract

A hallmark of multibody dynamics is that most formulations involve a number of constraints. Typically, when redundant generalized coordinates are used, equations of motion are simpler to derive but constraint equations are present. Approaches to dealing with high index differential algebraic equations, based on index reduction techniques, are reviewed and discussed. Constraint violation stabilization techniques that have been developed to control constraint drift are also reviewed. These techniques are used in conjunction with algorithms that do not exactly enforce the constraints. Control theory forms the basis for a number of these methods. Penalty based techniques have also been developed, but the augmented Lagrangian formulation presents a more solid theoretical foundation. In contrast to constraint violation stabilization techniques, constraint violation elimination techniques enforce exact satisfaction of the constraints, at least to machine accuracy. Finally, as the finite element method has gained popularity for the solution of multibody systems, new techniques for the enforcement of constraints have been developed in that framework. The goal of this paper is to review the features of these methods, assess their accuracy and efficiency, underline the relationship among the methods, and recommend approaches that seem to perform better than others.

Dynamic Whole-Body Motion Generation Under Rigid Contacts and Other Unilateral Constraints

“…To cope with this problem we propose to include the contact forces f in the optimization variables of the QP resolution. Condition (32) is then directly written with respect to the variables u = (τ,q, φ, f ), with the HQP: (30) …”

“…(30) considers one single body in contact. If several bodies are in contact or one body is in contact with several planes, a force φ i is introduced for each couple plane-body in contact:…”

“…1. A review of the work in modeling and control of the dynamics of a set of bodies in contact is proposed in [29], [30]. The connection with inverse dynamics has been done in [31], [32].…”

Comparison of Selected Formulations for Multibody System Dynamics with Redundant Constraints

“…Equations of motion for constrained multibody systems can be derived from various formalisms of mechanics, such as Lagrange, Hamilton or Appel's equations (Bauchau and Laulusa, 2008). As a result, in many of these formulations the equations of motions are written in the form of differentialalgebraic equations (DAEs) (Amirouche, 2006;de Jalón and Bayo, 1994).…”

Dynamics and Control of a Planar Multibody Mobile Robot for Confined Environment Inspection

“…This motivates works on constraint stabilization [32][33][34], constraints enforcement and constraint elimination. A survey on special techniques to enforce constraints can be found in [35].…”