Stability of Rigid-body Dynamics with Sliding Frictional Contacts

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Stability of Rigid-body Dynamics with Sliding Frictional ContactsThe use of rigid body models during frictional contact is
often justified by proving the existence of a unique solution
to the forward dynamic equations. The implicit assumption
here is that the contact forces so obtained are stable. In
this paper， the rigid-body assumption is relaxed and body-
to-body contacts are modeled using springs and dampers. A
singular perturbation analysis reveals additional necessary
conditions to ensure contact force stability an the reduced
rigid-body model. Furthermore， the analysis indicates that
stability depends on a damping ratio associated with the
rigid contacts.
1 Introduction
There are many robotic applications which necessitate
the computation of the forward and inverse dynamics of
constrained bodies. These include the automated planning
of mechanical assembly tasks， dextrous manipulation， vir-
tual reality systems， and in some cases， robotic grasping
and parts fixturing as well. For the forward problem of
simulation， the main goals are to compute system motion
accurately and efficiently. In the case of inverse dynamics，
a thorough understanding of the dynamic phenomena is
needed in order to develop motion planning strategies.
Most often rigid body models are used to represent con-
strained systems. Of course， real bodies are compliant.
Rigid bodies are reduced order models introduced for ease
of computation. As such， their use must be justified. The
singular perturbation method presented in this paper is
a rigorous way to provide this justification (assuming， of
course， that the complete order model is correct). This
is in contrast to the common approach of justifying the
rigid-body forward dynamics solution.
rigid model by proving the existence and uniqueness of the