Rigid-Body Dynamics with Friction and Impact

By David E. Stewart. SIAM Review, 2000

721 citations recorded by the source corpus.

Rigid-body dynamics with unilateral contact is a good approximation for a wide range of everyday phenomena, from the operation of car brakes to walking to rock slides. It is also of vital importance for simulating robots, virtual reality, and realistic animation. However, correctly modeling rigid-body dynamics with friction is difficult due to a number of discontinuities in the behavior of rigid bodies and the discontinuities inherent in the Coulomb friction law. This is particularly crucial for handling situations with large coefficients of friction, which can result in paradoxical results known at least since Painleve [C. R. Acad. Sci. Paris, 121 (1895), pp. 112--115]. This single example has been a counterexample and cause of controversy ever since, and only recently have there been rigorous mathematical results that show the existence of solutions to his example. The new mathematical developments in rigid-body dynamics have come from several sources: "sweeping processes" and the measure differential inclusions of Moreau in the 1970s and 1980s, the variational inequality approaches of Duvaut and J.-L. Lions in the 1970s, and the use of complementarity problems to formulate frictional contact problems by Lotstedt in the early 1980s. However, it wasn't until much more recently that these tools were finally able to produce rigorous results about rigid-body dynamics with Coulomb friction and impulses.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/b90a3e7d80eeb1f320e2d548cf17e7d17718d1eb

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Citations in the corpus

The bouncing motion appearing in a robotic system with unilateral constraint (2007, background): “For the case of inconsistency M4 s related to the non-existence of solutions, there will be a shock at the contact point [10–13, 18, 19, 23].”
Simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized-α scheme (2014, neutral): “In this case, the aforementioned standard schemes completely fail since the numerical response may artiﬁcially generate energy when a contact occurs, see, e.g., [4].”
A direct method for trajectory optimization of rigid bodies through contact (2014, background): “In the limiting case of purely rigid bodies, the constraint forces, λ( t), are often modeled with Dirac δ functions, as impulsive events, or through measure differential inclusions (Brogliato, 1999; Stewart, 2000; Acary et al., 2004).”
Differential variational inequalities (2008, background): “Yet, as evidenced by the growing literature that has surfaced in recent years on multi-rigid-body dynamics with frictional contacts [3–6,17,18,90,91,94,95,98,101,102] and on hybrid engineering systems [21,49,51,52], ODEs and DAEs are vastly inadequate to deal with many naturally occurring engineerin”
Discontinuous dynamical systems (2008, background): “Consider a brick sliding on a ramp [15].”
Zeno hybrid systems (2001, neutral): “It should be pointed out that modelling of friction and impacts for rigid bodies is, of course, by itself a very active "eld, where advanced mathematical tools are used to handle contacts in a consistent way [27].”
Higher order event capturing time-stepping schemes for nonsmooth multibody systems with unilateral constraints and impacts (2012, neutral): “For more details on the modeling of multibody systems with unilateral constraints, we refer to [3,35,30] and for the mathematical analysis, we refer to [37,26,39,9].”
Rigid Body Dynamics Algorithms (2007, methodology): “For an introduction to the literature, try the review articles by Gilardi and Sharf (Gilardi and Sharf, 2002) and Stewart (Stewart, 2000).”
Bifurcations in Nonsmooth Dynamical Systems (2008, background): “Proving well-posedness is more of a challenge in this context, as one has to avoid situations like the so-called Painlevé paradox [80, 74, 106], which can arise when studying impacts with friction.”
Synthesis and stabilization of complex behaviors through online trajectory optimization (2012, background): “The second type of models are based on time stepping integrators [13], which attempt to model the effects of contact and friction impulses over fixed, relatively large time-steps.”
The scope and limits of simulation in automated reasoning (2016, background): “Within the theory of rigid solid objects, which are the simplest kinds of materials encountered in everyday activities, the analysis of collisions has not been wholly resolved [30,58].”
On the use of simulation in robotics: Opportunities, challenges, and suggestions for moving forward (2020, background): “It is anticipated that embracing compliance in the robotics models will elicit new approaches to handling frictional contact with the potential benefit of alleviating numerical artifacts/ paradoxes brought to the fore by the rigid body model (53).”
Propagation Networks for Model-Based Control Under Partial Observation (2018, background): “2, where ball A’s impact produces a compression wave that propagates through the balls immediately [23].”
A Filippov sliding vector field on an attracting co-dimension 2 discontinuity surface, and a limited loss-of-attractivity analysis☆ (2013, background): “For example, in so-called impact systems, the solution experiences a jump discontinuity; see [24].”