If you’re looking for a serious answer, how about this one?
“Robot” is not a magic word for a replacement human. A robot is a machine and nothing but a machine. Your question is equivalent to asking whether a refrigerator, a lawnmower, or a vibrator could be Queen of Canada. It’s not clear that such a question has any meaning whatsoever.
In 2008, the Governor-General of Canada, the Queen’s representative, prorogued the Canadian Parliament.
Imagine you have a small town with a speed limit of 30 mph. This town has a police officer who parks his car in the middle of town every day where it’s easily visible. And nobody driving through down ever breaks the speed limit.
You could argue that the police officer isn’t doing anything because he never arrests anyone and he isn’t even necessary because nobody ever speeds anyway. So the town could replace him with plastic police officer who just sits there and also does nothing.
Do you really think people would drive the same way through town?
On the advice of the Prime Minister, just like other prorogations.
Two of HM’s Lieutenant Governors had to use their reserve powers recently, after indecisive provincial elections.
In 2017, BC voters returned a provincial house balancéd on a knife’s edge. The Premier advised the Lt Gov to call another election. The Lt Gov declined to do so, ,rejecting her first minister’s advice.
Last year in New Brunswick, there was a similar minority situation. The Premier who called the election came in second in terms of seats. The leader of the party who came first sought an interview with the Lt Gov and tried to get her to sack the Premier and install him. The Lt Gov refused, saying she would let the Premier have some time to try to reach an agreement with the two smaller parties. However, she also said that there was a time limit: after a certain point, she would insist the Premier advise her to summon the House and prove he had a majority. Implicit in that statement was that if the Premier didn’t make deadline, she might feel compelled to summon the House on her own and require the Premier to show he had a majority.
The word robot has several definitions. I used the word only in the sense of a device that automatically performs complicated tasks.
This is the most interesting (to me) response to my original question that I have seen so far. Can anyone give an example, either historical or theoretical, of where the Queen has a choice of taking more than one action and what factors the Queen would evaluate to determine which action is taken?
Also, of course, examples where the Queen has a choice of taking one or more actions or taking no action at all.
The Queen almost always has a choice between taking an action and not taking an action. The fact that she almost always chooses not to take any action doesn’t change the fact that she does have the choice.
Ynnad, to get an overview, read through with Forsey (linked previously) and also https://www.canadiancrown.com/uploads/3/8/4/1/3841927/the_royal_prerogative.pdf and then dig into Reserve power - Wikipedia and https://www.canada.ca/en/department-national-defence/corporate/reports-publications/military-law/crown-prerogative/introduction.html
You can find further examples from other commonwealth realms, such as Australia.
I thought the provincial house was only “balancéd,” if at all, in Quebec.
And of course read up on the two examples provided by Northern Piper.
My iPhone is erratic in its spell-checker, sometimes substituting French for English, but how “balancéd” got there I have no idea, as it’s misspelt in both of Canada’s official languages. 
équilibré
Balanced by bracketing and by how it rolls off the tongue. A great word.
The Gov Gen may have her work cut out for her in October. The polls are all over the place, but it’s looking like a hung Parliament. Will Justin be able to hold on? Will Andrew push him aside in the race to Rideau? Where will Jugmeet, Elizabeth and Mario end up in all this?
A minority Liberal government might lead to toward proportional representation. A good thing IMHO.