Please let me know if you have any suggestions on where else to look for visual references to the design, or how best to explore its origins. Also, would it be accurate to assume that a coat of arms would have been given or awarded or authorized for a service that had been performed, or would there be another reason? As noted in an earlier post, I am very new to all this.
Given the likely Swiss origins of the coat of arms, I've tried looking through Rietstap's
Armorial Général, with some 120,000 coats of arms from all over Europe, but while he lists a number of Robert's, none of them match your coat of arms here. Of the closest ones, one (from Languedoc) has a single chevron with
two stars above it and a rose beneath it, while the other (to a Roberti from Flanders, dated 1652) has two chevrons with two stars above it and a lion's head beneath it. (And the colors in both instances are different from yours.)
I'm not sure of the best places to continue the search from here. There are very few Swiss armorials available in any form for us to look in.
As for the reason for having the coat of arms, while in many countries they are granted for various kinds of service, in many other instances they are simply self-assumed; that is to say, the person using the arms just started using them. This can be especially true in countries, like Switzerland, where there was no granting authority (such as the English College of Arms) or crowned head to give such coats. In other instances, as still happens today unfortunately, a person may go to a painter or artist and ask for a drawing of their "family coat of arms," and receive a drawing of a coat of arm with their surname attached to it, but which may not belong to their family line at all, but only to another family with the same (or a similar) surname). This sort of "bucket shop heraldry" has been going on for centuries. (I've researched instances of this in early 18th Century New England, for example.)
So the bottom line, I'm afraid, is that until we can know more about the origins of the coat of arms itself, it's very difficult to say why, or even whether, it was granted or awarded.
I'm sorry that I haven't been of greater help to you in tracking down this coat of arms. If you have any additional questions, or if I can be of further assistance to you, please don't hesitate to ask here.
David