As a child, everyone probably had the experience of playing with a toy called a Spirograph ( https://en.wikipedia.org/wiki/Spirograph ). This geometric drawing toy can create intricate patterns by combining two circular motions. These patterns fall into the class of mathematical curves known as trochoids. The trochoidal motion has been observed in planetary movements, biological spiral waves, electron behaviours and many other naturally occurring phenomena. Engineers have used such patterns for applications including atomic force microscopy, rotary pumps and cam gears, among others. One of the main characteristics of trochoids is that they are contained in a limited area, which is finely swept through by the curves. Suppose that a team of mobile robots wants to trace these patterns, for example, for surveying an area. What kind of control laws will ensure that the robots trace trochoidal patterns? Would it be possible to design such a control law only using locally exchanged information? In this chapter, we use the distributed consensus law to achieve a coordinated trochoidal formation among a team of mobile agents. The mobile agents are either modelled as single or double integrators, and a general communication topology is considered. We modified the standard consensus protocol and design the gains to create trochoidal motion through local information exchange. Several examples are presented that show complex trochoidal patterns. We discuss our current results and the potential application of our findings across various civilian and military applications.

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Trochoids

  • Jerome Moses Monsingh,
  • Hoam Chung,
  • Arpita Sinha

摘要

As a child, everyone probably had the experience of playing with a toy called a Spirograph ( https://en.wikipedia.org/wiki/Spirograph ). This geometric drawing toy can create intricate patterns by combining two circular motions. These patterns fall into the class of mathematical curves known as trochoids. The trochoidal motion has been observed in planetary movements, biological spiral waves, electron behaviours and many other naturally occurring phenomena. Engineers have used such patterns for applications including atomic force microscopy, rotary pumps and cam gears, among others. One of the main characteristics of trochoids is that they are contained in a limited area, which is finely swept through by the curves. Suppose that a team of mobile robots wants to trace these patterns, for example, for surveying an area. What kind of control laws will ensure that the robots trace trochoidal patterns? Would it be possible to design such a control law only using locally exchanged information? In this chapter, we use the distributed consensus law to achieve a coordinated trochoidal formation among a team of mobile agents. The mobile agents are either modelled as single or double integrators, and a general communication topology is considered. We modified the standard consensus protocol and design the gains to create trochoidal motion through local information exchange. Several examples are presented that show complex trochoidal patterns. We discuss our current results and the potential application of our findings across various civilian and military applications.