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arXiv 1502.01538cs.RO
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简单操作与自主操作系统的混合系统模型

A Hybrid Systems Model for Simple Manipulation and Self-Manipulation Systems

Robotics Institute, Carnegie Mellon(卡内基梅隆大学机器人研究所)

Aaron M. Johnson, Samuel A. Burden, Daniel E. Koditschek

摘要:

刚体、塑性冲击、持久接触、库仑摩擦和无质量肢体是普遍存在的简化,它们被引入以降低力学模型的复杂性,尽管每个模型都有明显的物理不准确性。众所周知,这种理想化近似的相互作用可能导致相互矛盾甚至自相矛盾的结果。随着机器人建模从考虑孤立的行为转向分析需要其组成的任务,一个数学上易于处理的框架来构建模型,将这些简单的近似值结合起来,但却能获得可靠的结果。在本文中,我们提出了一个正式的混合动力系统模型,介绍了适当限制这些熟悉的抽象成分的一致性保证类似于在经典动力系统的全局存在性和唯一性。这里开发的混合动力系统提供了一个不连续的,但自洽的近似连续(虽然可能非常僵硬和快速)的物理机器人进行间歇性的影响动态。模型的选择牺牲了一些定量的数值效率,同时保持定性正确和分析处理的结果与一致性的保证,促进他们的使用在正式推理机制,反馈控制,行为设计的机器人,使和断开与环境的接触。

英文摘要:

Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs individually. In concert, it is well known that the interaction of such idealized approximations can lead to conflicting and even paradoxical results. As robotics modeling moves from the consideration of isolated behaviors to the analysis of tasks requiring their composition, a mathematically tractable framework for building models that combine these simple approximations yet achieve reliable results is overdue. In this paper we present a formal hybrid dynamical system model that introduces suitably restricted compositions of these familiar abstractions with the guarantee of consistency analogous to global existence and uniqueness in classical dynamical systems. The hybrid system developed here provides a discontinuous but self-consistent approximation to the continuous (though possibly very stiff and fast) dynamics of a physical robot undergoing intermittent impacts. The modeling choices sacrifice some quantitative numerical efficiencies while maintaining qualitatively correct and analytically tractable results with consistency guarantees promoting their use in formal reasoning about mechanism, feedback control, and behavior design in robots that make and break contact with their environment.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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