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Rolling Spheres, BB-8, and Holonomy

oliver oreilly's picture

Dear Colleague,

Imagine rolling a tennis ball on a table top so that the center of the ball returns to its original location. Surprisingly, the orientation of the ball will have changed - something you can notice by looking at the branding markings on the ball. This phenomenon is known as a holonomy. Holonomy is also exhibited by the BB-8 robot: as it moves around a room and returns to its original location, the orientation of its spherical part will have changed albeit camouflaged by the ingenious magnetic mechanism used to orient its head.

In a recent work with Theresa Honein, the holonomy of a rolling sphere is explored:

Explorations of the Holonomy of a Rolling Sphere [Open Access]

We find that it is possible to prescribe a rectangular path to achieve any desired reorientation (holonomy) but it is often easier to prescribe a set of three rectangular paths to achieve the desired holonomy. Our work uses quaternions and Euler angle parameterizations of a rotation. The paths for a given holonomy are not unique.

Video summaries of the paper can be found on threads: [Video summary] and the site formerly known as twitter: [Video summary]. An article on the paper can be found here: [Link to Article]. 

The work has application to motion planning for spherical robots and may prove useful in courses on rigid body dynamics.

Best wishes,

Oliver

 

 

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