Two Interpretations of Rigidity in Rigid-Body Collisions

Chatterjee, Anindya; Ruina, Andy

doi:10.1115/1.2791929

Cited by 49 publications

(31 citation statements)

References 26 publications

(33 reference statements)

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“…Incremental laws start with the differential form of Eq. 1 (thus requiring stronger rigidity, see Chatterjee and Ruina, 1998a), and then hypothesize specific types of incremental contact behavior that vary from law to law; integration of the resulting differential equations up to a hypothesized termination criterion then determines the outcome of the collision. When needed, we assume that at least one of the objects is geometrically smooth at the contact point so a well defined tangent plane exists with normal n directed out from the reference object in the n or 1 direction.…”

Section: Preliminariesmentioning

confidence: 99%

“…Algebraic laws attempt to describe the net collisional interaction by algebraic equations that relate pre-collision and post-collision quantities. Thus, algebraic laws are generally based on less stringent rigidity requirements than incremental laws (see e.g., Chatterjee and Ruina, 1998a). One interpretation of incremental calculations is that they are a means to calculate a reasonable net impulse and not a literal description of the true contact mechanics.…”

Section: Introductionmentioning

confidence: 99%

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A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations

Chatterjee

Ruina

1998

Journal of Applied Mechanics

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174

167

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We present a geometric representation of the set of 3D rigid body collisional impulses that are reasonably permissible by the combination of non-negative post-collision separation rate, non-negative collisional compression impulse, non-negative energy dissipation and the Coulomb friction inequality. The construction is presented for a variety of special collisional situations involving special symmetry or extremes in the mass distribution, the friction coefficient, or the initial conditions. We review a variety of known friction laws and show how they do and do not fit in the permissible region in impulse space as well as comment on other attributes of these laws. We present a few parameterizations of the full permissible region of impulse space. We present a simple generalization to arbitrary 3D point contact collisions of a simple law previously only applicable to objects with contact-inertia eigenvectors aligned with the surface normal and initial relative tangent velocity component (e.g. spheres and disks). This new algebraic collision law has two restitution parameters for general 3D frictional single-point rigidbody collisions. The new law generates a collisional impulse that is a weighted sum of the impulses from a frictionless but non-rebounding collision and from a perfectly sticking, non-rebounding collision. We describe useful properties of our law; show geometrically the set of impulses it can predict for several collisional situations; and compare it with existing laws. For simultaneous collisions we propose that the new algebraic law be used by recursively breaking these collisions into a sequence ordered by the normal approach velocities of potential contact pairs.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations

Chatterjee

Ruina

1998

Journal of Applied Mechanics

Self Cite

174

167

View full text Add to dashboard Cite

show abstract

“…Linear and angular momentum conservation generally demand that mechanical energy be lost in plastic collisions; where the energy goes depends on detailed non-rigid-body mechanics that do not effect the post-collisional rigid-body motions e.g. (Chatterjee and Ruina, Dec 1998). However, if the colliding points on two objects have the same velocity when they make plastic contact, then no energy is lost in that "collision" even though it is a plastic or sticking collision.…”

Section: Modeling Approachmentioning

confidence: 99%

A five-link 2D brachiating ape model with life-like zero-energy-cost motions

Gomes

Ruina

2005

Journal of Theoretical Biology

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We have found periodic life-like brachiating motions of a rigid-body ape model that use no muscle or gravitational energy to move steadily forward. The most complicated of these models has 5 links (a body and two arms each with 2 links) and 7 degrees of freedom in flight. The defining feature of all our periodic solutions is that all collisions are at zero relative velocity. These motions are found using numerical integration and root-finding that is sufficiently precise so as to imply that the solutions found correspond to mathematical solutions with exactly zero energy cost. The only actuation and control in the model is for maintaining contact with and releasing handholds which requires no mechanical work. The similarity of these energy-free simulations to the motions of apes suggests that muscle-use minimization at least partially characterizes the coordination strategies of brachiating apes.

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“…The concept of rigidity assumes a perfectly non-deformable body. Rigidity is an idealized view and per se not found in real nature [22,74]. On a microscopic level, even extremely hard bodies, such as diamonds, deform slightly when they collide with each other.…”

Section: Rigid Body Physicsmentioning

confidence: 99%

Optimization-based animation

Milenkovic

Schmidl

2001

Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques

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of a doctoral dissertation at the University of Miami.Dissertation supervised by Professor Victor J. Milenkovic. No. of pages in text: 162A new paradigm for rigid body simulation is presented and analyzed. Current techniques for rigid body simulation run slowly on scenes with many bodies in close proximity. Each time two bodies collide or make or break a static contact, the simulator must interrupt the numerical integration of velocities and accelerations. Even for simple scenes, the number of discontinuities per frame time can rise to the millions. An efficient optimization-based animation (OBA) algorithm is presented which can simulate scenes with many convex threedimensional bodies settling into stacks and other "crowded" arrangements. This algorithm simulates Newtonian (second order) physics and Coulomb friction, and it uses quadratic programming (QP) to calculate new positions, momenta, and accelerations strictly at frame times. The extremely small integration steps inherent to traditional simulation techniques are avoided.Contact points are synchronized at the end of each frame. Resolving contacts with friction is known to be a difficult problem. Analytic force calculation can have ambiguous or non-existing solutions. Purely impulsive techniques avoid these ambiguous cases, but still require an excessive and computationally expensive number of updates in the case of many simultaneous contacts. It is shown informally that even taking into account advances in stiff integration techniques, penalty force methods cannot overcome this issue of running time in highly crowded scenes. New algorithms are presented that calculate simultaneous impulses to resolve collisions and static contacts under the Coulomb friction model. The simultaneous impulses are the solution to a QP.In addition, the algorithms apply "bouncing at distance" and "freezing of bodies" to further speed up the simulation. These new QP algorithms are hybridized with a traditional priority queue momentum update scheme to allow sequential impulses when they are required for realism, such as in the office toy pendulum. When added to the implementation of OBA, these new algorithms increase the speed of the simulation by a factor of up to 30.The position update has been hybridized with retroactive detection (RD) to prevent fast and thin bodies from passing through each other. Due to the modular design of the OBA simulator, the described techniques can be used as components in any existing simulator that follows a modular design of position update, finding contacts, and resolving contacts. Non-convex bodies are simulated as unions of convex bodies. Links and joints are simulated with bi-directional constraints. Analysis of the algorithm and discussion of example simulations are provided. DedicationIn loving memory of my father.iii

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Two Interpretations of Rigidity in Rigid-Body Collisions

Cited by 49 publications

References 26 publications

A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations

A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations

A five-link 2D brachiating ape model with life-like zero-energy-cost motions

Optimization-based animation

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