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Yes, it's fine to reuse the TransformBroadcaster to send multiple different transforms, irrespective of their relationship. Based on your above content you may want to send them simultaneously using a vector of transforms.

A nan_input almost always means an unnormalized quaternion. The other option is that you're passing in a nan value to the vector. But based on the above snippet that does not look possible and as such I'd suggest checking your normalization logic.