ABSTRACT

A spherical pendulum is a 2 degree-of-freedom mechanism consisting on a rod whose tip moves on the surface of a sphere. It is common to use two angular coordinates to describe such a system. This paper proposes the use of a non-minimal set of coordinates for modelling and controlling a fully-actuated torque-driven spherical pendulum. These coordinates is merely for the purpose of showing the application of unit quaternions as a useful tool for dealing with the orientation of rigid bodies. First, we recall the properties of unit quaternions, and explain how they can be employed for the definition of such non-minimal pendulum coordinates. Later, the control objective for orientation regulation is established and an inverse-dynamics controller, which uses joint displacement and velocity measurements but also some non-minimal states for the orientation error, is proposed. The stability analysis shows the fulfilment of the control objective and is validated through simulations.

摘要

球形摆是一种2自由度的机构，其机制是在杆的尖端在球体表面上移动的杆上。通常使用两个角坐标来描述这样的系统。本文提出了使用一组非最小坐标来建模和控制完全驱动的扭矩驱动球形摆的方法。这些坐标仅是为了显示单位四元数作为处理刚体方向的有用工具的目的。首先，我们回顾一下单元四元数的性质，并解释如何将它们用于定义这样的非最小摆坐标。后来，确定了方向调整的控制目标，并建立了逆动力学控制器，提出了使用关节位移和速度测量值以及一些非最小状态的定向误差的方法。稳定性分析显示了控制目标的实现，并通过仿真进行了验证。