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I have only recently started to understand topology in robotics perspective. I am reading Steve LaValle's book on motion planning. It mentions that a rotating link with a fixed pivot has a configuration space of a unit circle.

Since the configuration space is the set of all possible configurations the link can have, i.e. all possible angles from 0° to 360°, shouldn't the c-space be a line rather than a circle?

harsh
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1 Answers1

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One important quality of a revolute (rotating) joint is the fact that you can loop around configuration values (i.e. 0° = 360°) - otherwise you would reach the end of the line and be unable to continue rotating. A configuration space of a circle is effectively just a line where the two ends are connected so you can do this.

ajshort
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  • But isn't the basic rule of topology that you can't cut or join shapes? – harsh Oct 18 '17 at 08:30
  • I'm not really sure what you're asking - the configuration space of a line segment and a circle wouldn't be topologically equivalent. When you reach the end of a line segment you stop, but if you can keep looping around a circle without ever reaching an end. – ajshort Oct 18 '17 at 12:34
  • Since you said, the 2 ends are "connected", I was bit confused. Yes it is clear now – harsh Oct 18 '17 at 13:54