What they need is emotional intimacy, but they can't get that because of crippling anxiety. You're not going to get emotional intimacy from a robot, and if you try, you run the very real risk of really adverse effects, like this or this.
That's why I suggested separating concerns. Keep the bot physical, and encourage real personal relationships in a low risk environment. There's always a chance a personal relationship develops into something more, whereas there's a lot of risk expecting a bot to fill that gap.