Gary D. Hart
ABSTRACT
We present a method for simulating rigid multibody dynamics with joints, contact, and friction. In this work, the nonsmooth contact and frictional constraints are represented by hard constraints. The method requires the solution of only one linear complementarity problem per step and can progress at much larger time steps than explicit penalty methods, which are currently the method of choice for most of these simulations.
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Cross Ref
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Index Terms
- A hard-constraint time-stepping approach for rigid multibody dynamics with joints, contact, and friction
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Reviews
Archana Sangole
This paper discusses a numerical method that formulates the simulation of rigid multibody dynamics, with contact and friction, as a velocity-based linear complementarity problem (LCP). This method deviates from other LCP approaches in one key aspect: constraint stabilization issues. The contact and frictional constraints are represented as inequality constraints, which are treated as hard constraints during computation. The paper is fairly well written. However, the significant highlights of the method (addressed in sections 1 and 2), in comparison to previous and related work, are not very clearly stated. This makes it confusing to follow how the method differs from previous work by the same authors, and how it differs from variants of the same method proposed by other researchers. The paper includes a few things that are worth commenting on individually. In the discussion of differentiability properties (page 35), the method is formulated based on the assumption that the mappings defining the joint and the noninterpenetration constraints are differentiable, indicating that the bodies are smooth and relatively strictly convex. This contradicts the statement made in the abstract: "In this work, the non-smooth contact and frictional constraints are represented by hard constraints." Furthermore, it defers the discussion on doing a similar analysis using nonsmooth, nonconvex shapes to future research. In the numerical results for contact constraints (page 37), the examples discussed-an elliptical body simulation, disk simulation, and Brazil nut simulation-exhibit only contact and friction constraints. There are no joint constraints, as indicated in the title of the paper. On page 37, the authors state: "[O]ur time step compares very favorably with the traditional molecular and time steps on the order of microsceconds." No reference has been cited to substantiate this statement. In summary, the paper is mathematically complete, and clearly demonstrates a positive progression in the development and refinement of the LCP approach for formulating rigid multibody dynamics. This question might be beyond the scope of the paper, but I ask it just out of curiosity: Can this method be generalized or implemented for simulating the dynamics of multiple objects with varying coefficients of friction__?__ In the examples that were discussed, the coefficient of friction was kept the same at all interactions. This may not always be the case when nonsmooth contact surfaces are involved.
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