论文标题
虚拟非道理约束：几何方法
Virtual Nonholonomic Constraints: A Geometric Approach
论文作者
论文摘要
虚拟约束是通过反馈对控制系统强加的不变关系，而不是作用于系统的实际物理约束。非单纯性系统是机械系统，对速度具有不可综合的约束。在这项工作中，我们在几何框架中介绍了虚拟非道理约束的概念。更确切地说，它是与仿射连接机械控制系统相关的受控不变分布。我们证明了对控制定律的存在和唯一性，定义了虚拟的非语言约束，并且我们将闭环系统的轨迹表征为与诱导的约束连接相关的机械系统的解决方案。此外，我们根据虚拟非语言约束来表征非独立系统的动力学，即，我们表征何时可以从虚拟非虚拟约束中获得非实体性动力学。
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.
