、。
What on earth makes anyone think I know anything about robotics?
Literal
Where [obj-を] how think-[if-たら], I [subject-が] robotics [on-に] bright [emphatic-など] [quotative-と] think [probably-のだろうか].
A rhetorical self-questioning. どこをどう考えたら ('if you think where and how') is a fixed rhetorical expression meaning 'what could possibly lead one to think?' — essentially 'I have no idea how this conclusion was reached.' ロボット工学 ('robot engineering / robotics') is a technical compound. ~に明るい is an idiom: 明るい ('bright') here means 'well-versed in, knowledgeable about.' など in negative/rhetorical contexts is dismissive — 'the mere thought of.' のだろうか is the reflective speculative 'I wonder why.'