论文标题
代数拓扑和差异几何形状可以教会我们有关机器人的内在动态和全球行为的什么？
What Can Algebraic Topology and Differential Geometry Teach Us About Intrinsic Dynamics and Global Behavior of Robots?
论文作者
论文摘要
传统上，机器人被视为通用运动机器。它们主要是由运动学方面的考虑因素设计的，而所需的动力学是由强大的执行器和高速控制回路施加的。作为替代方案，可以首先考虑机器人的内在动力学，并根据所需的任务进行优化。因此，人们需要更好地理解机器人系统的内在，不受控制的动力学。在本文中，我们专注于周期性轨道，作为具有许多实际应用的基本动态属性。代数拓扑和差异几何形状提供了一些有关周期轨道存在的基本陈述。例如，我们提出了最简单的多体系统的周期性轨道：重力中的双铅。这个简单的系统已经显示出各种各样的周期性轨道。我们将它们分为三类：环形轨道，磁盘轨道和非线性正常模式。我们其中一些是通过几何见解发现的，有些是通过数值模拟和采样的。
Traditionally, robots are regarded as universal motion generation machines. They are designed mainly by kinematics considerations while the desired dynamics is imposed by strong actuators and high-rate control loops. As an alternative, one can first consider the robot's intrinsic dynamics and optimize it in accordance with the desired tasks. Therefore, one needs to better understand intrinsic, uncontrolled dynamics of robotic systems. In this paper we focus on periodic orbits, as fundamental dynamic properties with many practical applications. Algebraic topology and differential geometry provide some fundamental statements about existence of periodic orbits. As an example, we present periodic orbits of the simplest multi-body system: the double-pendulum in gravity. This simple system already displays a rich variety of periodic orbits. We classify these into three classes: toroidal orbits, disk orbits and nonlinear normal modes. Some of these we found by geometrical insights and some by numerical simulation and sampling.
