In this paper, we survey the field of robotic grasping and the work that has been done in this area over the last two decades, with a slight bias toward the development of the theoretical framework and analytical results in this area.

Robotic grasping and contact: a review

Literature survey of contact dynamics modelling

https://repositorium.sdum.uminho.pt/bitstream/1822/19623/1/6.7.32%202012.pdf

Compliant contact force models in multibody dynamics : evolution of the Hertz contact theory

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.

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

Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs individually. In concert, it is well known that the interaction of such idealized approximations can lead to conflicting and even paradoxical results. As robotics modeling moves from the consideration of isolated behaviors to the analysis of tasks requiring their composition, a mathematically tractable framework for building models that combine these simple approximations yet achieve reliable results is overdue. In this paper we present a formal hybrid dynamical system model that introduces suitably restricted compositions of these familiar abstractions with the guarantee of consistency analogous to global existence and uniqueness in classical dynamical systems. The hybrid system developed here provides a discontinuous but self-consistent approximation to the continuous (though possibly very stiff and fast) dynamics of a physical robot undergoing intermittent impacts. The modeling choices sacrifice some quantitative numerical efficiencies while maintaining qualitatively correct and analytically tractable results with consistency guarantees promoting their use in formal reasoning about mechanism, feedback control, and behavior design in robots that make and break contact with their environment.

A Hybrid Systems Model for Simple Manipulation and Self-Manipulation Systems

In many engineering applications such as assembly of mechanical components, robot manipulation, gripping, fixturing and part feeding, there are situations in which a rigid body is subject to multiple frictional contacts with other bodies. It is proposed to develop a systematic method for the analysis and simulation of such systems. A detailed study is presented on rigid body impact laws, and the assumption of contact compliance is investigated. Comments University of Pennsylvania Department of Computer and Information Sciences Technical Report No. MSCIS-91-48. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/320 Figure 3.3: Cases of collision The final velocities can be obtained as following:

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Yin Tien Wang

Papers

Analysis and simulation of mechanical systems with multiple frictional contacts