Analysis of Rigid-Body Dynamic Models for Simulation of Systems With Frictional Contacts

Abstract

The use of Coulomb’s friction law with the principles of classical rigid-body dynamics introduces mathematical inconsistencies. Specifically, the forward dynamics problem can have no solutions or multiple solutions. In these situations, compliant contact models, while increasing the dimensionality of the state vector, can resolve these problems. The simplicity and efficiency of rigid-body models, however, provide strong motivation for their use during those portions of a simulation when the rigid-body solution is unique and stable. In this paper, we use singular perturbation analysis in conjunction with linear complementarity theory to establish conditions under which the solution predicted by the rigid-body dynamic model is stable. We employ a general model of contact compliance to derive stability criteria for planar mechanical systems. In particular, we show that for cases with one sliding contact, there is always at most one stable solution. Our approach is not directly applicable to transitions between rolling and sliding where the Coulomb friction law is discontinuous. To overcome this difficulty, we introduce a smooth nonlinear friction law, which approximates Coulomb friction. Such a friction model can also increase the efficiency of both rigid-body and compliant contact simulation. Numerical simulations for the different models and comparison with experimental results are also presented.

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

“…Nowadays, friction is well recognized: frictional effects in multibody systems are commonly taken into consideration in engineering practice, and some aspects of modeling of friction are taught during multibody dynamics courses at various universities [3,41]. On the other hand, friction in multibody systems is extensively investigated by 21st century researchers (e.g., [7,8,[16][17][18]28]). This paper was aimed at pointing the attention to some important properties of various approaches to friction modeling that manifest themselves in the stiction regime.…”

“…1a), various functions of the velocity of sliding are used. Some of them, for example, saturation [8,17], hyperbolic tangent [7,18], or arctangent [27] do not differ static and kinetic friction coefficients (Fig. 1b).…”

“…The problems with friction discontinuity at zero relative velocity are often alleviated by smoothing the Coulomb friction law. Models of this kind are frequently used in both theoretical considerations and practical applications; see, for example, [7][8][9][10]. Some drawbacks of smoothed Coulomb models are well known: the set of differential equations of motion is usually stiff, and a drift is observed instead of stiction since the friction force equals zero at zero relative joint velocity.…”

A Two-Point Boundary-Value Approach for Planning Manipulation Tasks

“…The use of dynamic models and design based on dynamic analysis is particularly difficult because of two main reasons. First, the use of non-smooth frictional contact models with the principles of classical rigid body dynamics introduces mathematical inconsistencies that can be hard to resolve [10]. Second, there are no accepted models for rigid body impacts.…”

GPU-Based Parallel Computing for the Simulation of Complex Multibody Systems with Unilateral and Bilateral Constraints: An Overview

“…In terms of the former, sequential computing appears to lose momentum at a time when the microprocessor industry ushers in commodity many-core hardware. In terms of internal factors, contributions made in understanding and handling frictional contact [1][2][3][4][5][6][7][8][9][10][11], have led to robust numerical algorithms that can tackle sizeable granular dynamics problems. This paper discusses how the interplay of these two factors will enable in the near future a discrete approach to investigating the dynamics of systems with hundreds of millions of rigid bodies.…”