Do getParamCached() and dynamic_reconfigure have the same functions?

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The way I understand it, they are totally different.

getParamCached provides local caching of values and gets notified once the parameter on the master changed somehow. However, you still have to call getParamCached regularly to get the notifications. I.e., you don't call it once in your constructor, e.g., and get all updates to the respective parameter.

dynamic_reconfigure however really provides the ability to change parameters dynamically via a callback based mechanism. So you don't have to call something regularly yourself, you just register the callback and this handles notifying you once a parameter changed.

Thus, I'd say dynamic_reconfigure is the way to go. getParamCached would probably work if this is really for a single parameter.