How to send a vector with Service Client Communication?

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Yes this is possible.

You can define a variable in a service or message definition as a vector by adding empty square brackets after the type, eg:

int32[] myVectorOfInts

So in your case to send a vector of values to a service provider from the client your service definition could look something like this:

string singleVariable
int32[] vectorOfIntegers
std_msgs/ColorRGBA[] vectorOfAnotherMessage
---
int32 variableReturnedToClient

Hope this helps.