Still working out some of the details, but I think...

You are a:

>! Twist (ie, a plot twist)

I can keep you grounded, or I can rile you up.
>! You can be tied down, or twisted in knots

I can facilitate your travel, or I can discourage you from going.
>!As in to spin, or to change course

a cyborg, a professor, and a statue, schizophrenic mind, and a sled.
>! All are the main focus of famous movie twists:  Blade Runner, ? , Planet of the Apes, Fight Club, Citizen Kane