虚拟非完整约束:一种几何方法

A. Simoes, Efstratios Stratoglou, A. Bloch, L. Colombo
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引用次数: 2

摘要

虚拟约束是通过反馈强加于控制系统的不变关系,与作用于系统的实际物理约束相反。非完整系统是具有速度不可积约束的机械系统。在这项工作中,我们在几何框架中引入了虚拟非完整约束的概念。更准确地说,它是与仿射连接机械控制系统相关联的受控不变分布。我们证明了定义虚拟非完整约束的控制律的存在性和唯一性,并将闭环系统的轨迹表征为与诱导约束连接相关的机械系统的解。此外,我们用虚非完整约束刻画了非完整系统的动力学,即刻画了何时可以从虚非完整约束得到非完整动力学。
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Virtual Nonholonomic Constraints: A Geometric Approach
Virtual constraints are invariant relations imposed on a control system via feedback as opposed to real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the velocities. In this work, we introduce the notion of virtual nonholonomic constraints in a geometric framework. More precisely, it is a controlled invariant distribution associated with an affine connection mechanical control system. We demonstrate the existence and uniqueness of a control law defining a virtual nonholonomic constraint and we characterize the trajectories of the closed-loop system as solutions of a mechanical system associated with an induced constrained connection. Moreover, we characterize the dynamics for nonholonomic systems in terms of virtual nonholonomic constraints, i.e., we characterize when can we obtain nonholonomic dynamics from virtual nonholonomic constraints.
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