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Originally Posted by omalleyj
I think you need explain that more clearly. The robot will go at its maximum speed in the direction any pair is going in for the omni@45 arrangement. And .7071 of that speed in the regular front-back side-side directions. The ratio is 1.4, but you give the impression that it will go faster than its wheels are turning, which is impossible in any direction.
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I have found that Ether is better at explaining this than me. You can look at the gif that he attached on this
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There are several research papers published on this (mostly for robocup).
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Thus, the addition of angled omni-wheels can result in a net body velocity that is greater than the maximum radial velocity of the wheel (Ashmore and Barnes, pg. 7).
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That paper goes on to say that by traveling with rotation and in an arch a holonomic robot can travel even faster. We have thought about creating a control scheme that takes advantage of this but it would be very difficult, in the context of a FIRST robot.