Gabriele Trovato is worried about tomorrow. That’s what he confesses to SanTO, a robot. Just shy of 17 inches tall, SanTO resembles the small figurines of saints often found in Catholic homes—except with a computer, microphone, sensors and a facial recognition-enabled camera. As Mr. Trovato speaks to the machine, its deep, echoing voice responds with a Bible quote: “From the Gospel according to Matthew,” it says, “do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own.”

Mr....