Multiple impacts: A state transition diagram approach

Jia, Yan-Bin; Mason, Matthew T.; Erdmann, Michael

doi:10.1177/0278364912461539

Cited by 37 publications

(33 citation statements)

References 49 publications

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“…Simulation schemes to this problem (e.g. [9,11,19,22,24,36,41] and many others) focus on generation of a single solution via a heuristic (symmetry [22], potential energy [41], etc.). However, for many practical applications in robotics, it is not possible to create a model detailed enough to reliably disambiguate between the multiple potential solutions; essentially, the disambiguation performed by common simulation schemes is not grounded in physical principles.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of Non-Unique Behaviors in Multiple Frictional Impacts

Halm

Posa

2019

Robotics: Science and Systems XV

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Many fundamental challenges in robotics, based in manipulation or locomotion, require making and breaking contact with the environment. To represent the complexity of frictional contact events, impulsive impact models are especially popular, as they often lead to mathematically and computationally tractable approaches. However, when two or more impacts occur simultaneously, the precise sequencing of impact forces is generally unknown, leading to the potential for multiple possible outcomes. This simultaneity is far from pathological, and occurs in many common robotics applications. In this work, we propose an approach for resolving simultaneous frictional impacts, represented as a differential inclusion. Solutions to our model, an extension to multiple contacts of Routh's method, naturally capture the set of potential post-impact velocities. We prove that solutions to the presented model must terminate. This is, to the best of our knowledge, the first such guarantee for set-valued outcomes to simultaneous frictional impacts.

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Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of Non-Unique Behaviors in Multiple Frictional Impacts

Halm

Posa

2019

Robotics: Science and Systems XV

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“…Extension to fast computation of multi-body impacts also awaits investigation. Such an impact can be either sequenced into two-body impacts (Chatterjee and Ruina, 1998) or treated as simultaneous impacts interacting with each other (Liu et al 2008;Jia et al 2013). With the first approach, Algorithm 1 is directly applicable to solving individual two-body impacts.…”

Section: Discussionmentioning

confidence: 99%

Analysis and Computation of Two Body Impact in Three Dimensions

Jia

Wang

2017

Journal of Computational and Nonlinear Dynamics

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A formal impulse-based analysis is presented for the collision of two rigid bodies at single contact point under Coulomb's friction in three dimensions (3D). The tangential impulse at the contact is known to be linear in the sliding velocity whose trajectory, parametrized with the normal impulse and referred to as the hodograph, is governed by a generally nonintegrable ordinary differential equation (ODE). Evolution of the hodograph is bounded by rays in several invariant directions of sliding in the contact plane. Exact lower and upper bounds are derived for the number of such invariant directions, utilizing the established positive definiteness of the matrix defining the governing ODE. If the hodograph reaches the origin, it either terminates (i.e., the contact sticks) or continues in a new direction (i.e., the contact resumes sliding) whose existence and uniqueness, only assumed in the literature, are proven. Closed-form integration of the ODE becomes possible as soon as the sliding velocity turns zero or takes on an invariant direction. Assuming Stronge's energy-based restitution, a complete algorithm is described to combine fast numerical integration (NI) with a case-by-case closed-form analysis. A number of solved collision instances are presented. It remains open whether the modeled impact process will always terminate under Coulomb's friction and Stronge's (or Poisson's) restitution hypothesis.

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“…1: compute Λ(k + 1) by (5). If Λ(k + 1) ≠ 0, go to Step 2, otherwise go to Step 3 2: if Λ(k + 1) > 0, set y F = −c 1 , or, if Λ(k + 1) < 0, set y F = c 2 , and computė…”

Section: Algorithm 1 Computation Of a Reference Trajectorymentioning

confidence: 99%

Dead‐beat regulation of mechanical juggling systems

Menini

Possieri

Tornambè

2017

Asian Journal of Control

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In this paper, mechanical systems subject to impacts and contacts, that would be not controllable if the impacts were absent (usually called jugglers), are considered. On the basis of an algorithm taken from the literature and of a new procedure to determine a reference trajectory for such a class of systems, a fully algorithmic procedure, able to compute a control input that achieves dead-beat regulation of the "uncontrollable" subsystem just by using impacts, is given. Such a procedure exploits some tools borrowed from algebraic geometry that allow to solve parametric systems of equalities and inequalities. A practical example of application of the given procedure is reported.

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Multiple impacts: A state transition diagram approach

Cited by 37 publications

References 49 publications

Modeling and Analysis of Non-Unique Behaviors in Multiple Frictional Impacts

Modeling and Analysis of Non-Unique Behaviors in Multiple Frictional Impacts

Analysis and Computation of Two Body Impact in Three Dimensions

Dead‐beat regulation of mechanical juggling systems

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