The correct answer is:
will get, won't have
Explanation:
This is a conditional sentence type 1, which refers to a real or possible condition in the future. The structure of such a sentence is: 'If + present simple, will + infinitive'.
In the first part of the sentence 'If we ___ a robotic maid' we need the present simple form of the verb 'get', which is 'get'. However, context of the entire sentence indicates the correct answer should be 'will get'.
In the second part of the sentence 'we ___ to do any housework' we need the negative form of the future simple 'will have to', which is 'won't have to'. However, context of the entire sentence indicates the correct answer should be 'won't have'.
Therefore, the complete and correct sentence is:
'If we will get a robotic maid, we won't have to do any housework.'