On Dynamic Multi‐Rigid‐Body Contact Problems with Coulomb Friction

Trinkle, Jeff; Pang, Jong Shi; Sudarsky, Sandra; Lo, Grace

doi:10.1002/zamm.19970770411

Cited by 257 publications

(190 citation statements)

References 21 publications

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“…The last few decades have seen an increase in the number of approaches to incorporate impacts in dynamical models (Brogliato, 2000). These developments have been driven largely by animation and gaming applications (Baraff, 1989;Trinkle et al, 1997;Stewart, 2000), which focus on results looking correct. Fortunately, there has also been a recent surge of interest in principled and physically meaningful ways of solving the simulation problem (Marsden and West, 2001;Pandolfi et al, 2002;Fetecau et al, 2003;Lew et al, 2004), with applications in the realms of modeling and control (Pekarek and Marsden, 2008).…”

Section: Introductionmentioning

confidence: 99%

Modeling Forces and Moments at the Base of a Rat Vibrissa during Noncontact Whisking and Whisking against an Object

Quist¹,

Seghete

Huet

et al. 2014

Journal of Neuroscience

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During exploratory behavior, rats brush and tap their whiskers against objects, and the mechanical signals so generated constitute the primary sensory variables upon which these animals base their vibrissotactile perception of the world. To date, however, we lack a general dynamic model of the vibrissa that includes the effects of inertia, damping, and collisions. We simulated vibrissal dynamics to compute the time-varying forces and bending moment at the vibrissa base during both noncontact (free-air) whisking and whisking against an object (collision). Results show the following: (1) during noncontact whisking, mechanical signals contain components at both the whisking frequency and also twice the whisking frequency (the latter could code whisking speed); (2) when rats whisk rhythmically against an object, the intrinsic dynamics of the vibrissa can be as large as many of the mechanical effects of the collision, however, the axial force could still generate responses that reliably indicate collision based on thresholding; and (3) whisking velocity will have only a small effect on the transient response generated during a whisker-object collision. Instead, the transient response will depend in large part on how the rat chooses to decelerate its vibrissae after the collision. The model allows experimentalists to estimate error bounds on quasi-static descriptions of vibrissal shape, and its predictions can be used to bound realistic expectations from neurons that code vibrissal sensing. We discuss the implications of these results under the assumption that primary sensory neurons of the trigeminal ganglion are sensitive to various combinations of mechanical signals.

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Section: Introductionmentioning

confidence: 99%

Modeling Forces and Moments at the Base of a Rat Vibrissa during Noncontact Whisking and Whisking against an Object

Quist¹,

Seghete

Huet

et al. 2014

Journal of Neuroscience

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show abstract

“…Taking into account that the inverses of M obj and M man exist,q obj andθ man can be obtained from the equations (7) and (9). Replacingq obj andθ man in equation (11) and defi ning a α ∈ R n c , with α ∈ {n, t, o}, a linear equation system is obtained   a n a t a o…”

Section: Mathematical Model Of the Contact Problemmentioning

confidence: 99%

“…Section 4, considers a dynamic model for several rigid bodies in contact, the equations that represent it [8,9] and from these, the formulation of MNCP. In section 5 the numerical results for three-fi ngered hand manipulation system holding an object are reported.…”

Section: Introductionmentioning

confidence: 99%

A mixed nonlinear complementarity technique for solving the dynamics of a dexterous manipulation system

Buffo¹,

Maciel²

2006

Mat. apl. comput.

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Abstract. The versatility of a robot to perform a task is limited principally by the flexibility of its end-effector. In the last years, research has been focused on the development of a hand with several fi ngers since these devices are capable of manipulating and grasping objects of different forms. A dexterous manipulation system, composed of a robot hand with several fi ngers and an object that will be held or manipulated, could be modeled as a set of rigid bodies in contact.The dynamics of several rigid bodies in contact tries to predict the accelerations and forces at the contact points of the set of rigid bodies with Coulomb friction. The calculation of such forces allows us to determine if the contact is maintained or disappears and to plan a determined action.The equations that describe the problem form a system of differential algebraic equations. In this contribution the problem is reformulated as a mixed nonlinear complementarity problem (MNCP).Then, an optimization problem with box constraints associated to the MNCP is presented using an adequate merit function. Conditions about the equivalence between the problems are established.Finally, the optimization problem is solved using a robust and effi cient algorithm. Encouraging numerical results are reported.Mathematical subject classification: 49M37, 65C20, 90C30, 90C33.

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“…Before solving the boundary value problem we will first solve the initial value problem to illustrate the benefits of the time-stepping model developed here, comparing it to the solutions obtained by the traditional approach involving a rigid body model with a linear friction-pyramid model for frictional forces [14]. In Figure 3, the ball is launched from the origin with a forward initial velocity with back-spin.…”

Section: A Transitions Between Rolling and Slidingmentioning

confidence: 99%

“…Another approach to overcome the mathematical inconsistencies that are inherent in rigid body models [14] is to consider the impulse and velocity solutions instead of explicitly solving for the forces and accelerations [15], [16]. Timestepping methods, which have their origins in early 80's [17], were developed to overcome some of these difficulties.…”

Section: Introductionmentioning

confidence: 99%

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

Song¹,

Kumar²,

Pang³

2005

Robotics: Science and Systems I

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Abstract-We consider the problem of planning manipulation tasks in which rigid body dynamics are significant and the rigid bodies undergo frictional contacts. We develop a dynamic model with frictional compliant contacts, and a time-stepping algorithm that lends itself to finding trajectories with constraints on the starting and goal conditions. Because we explicitly model the local compliance at the contact points, we can incorporate impacts without resetting the states and reinitializing the dynamic models. The problem of solving for the frictional forces with the Coulomb friction cone law reduces to a convex quadratic program. We show how this formulation can be used to solve boundary value problems that are relevant to process design, design optimization and trajectory planning with practical examples. To our knowledge, this paper is the first time boundary value problems involving changes in contact conditions have been solved in a systematic way.

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On Dynamic Multi‐Rigid‐Body Contact Problems with Coulomb Friction

Cited by 257 publications

References 21 publications

Modeling Forces and Moments at the Base of a Rat Vibrissa during Noncontact Whisking and Whisking against an Object

Modeling Forces and Moments at the Base of a Rat Vibrissa during Noncontact Whisking and Whisking against an Object

A mixed nonlinear complementarity technique for solving the dynamics of a dexterous manipulation system

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

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