This may not be as "simple" as it first appears, because (apart from the most basic playing technique) the piano pedal action is not just an "on-off switch". You need to control the speed of movement, and not necessarily depress the pedal fully. Also the pedals need quite a lot of force to operate them, which is no problem for normal human feet, but would require some "serious engineering" to do accurately (and safely, reliably, and silently) with an electric motor
Unless you really can't bear to part with the actual gifted piano, you might consider a Yamaha Disklavier, which is a conventional piano plus the mechanics for full MIDI control (of everything, not just the pedals). They aren't cheap, but presumably your existing piano would offset some of the cost. You could then use almost any sort of MIDI controller to operate the pedals - possibly even a set of "digital piano pedals", perhaps mechanically modified to work with the foot movement that you have.
There are plenty of companies who sell kits for the opposite purpose - i.e. to convert an acoustic piano into a source of MIDI data, to record a live performance - but that is not what you want. I don't know of anybody (apart from the Disklavier) selling something that would convert an acoustic piano to be played by MIDI.
Incidentally, even the Disklavier mechanism is quite "wimpy" compared with the old-style pneumatically operated "player pianos" controlled by piano rolls.
This http://www.soundonsound.com/sos/aug00/articles/ballet.htm is the saga of some of the problems recreating an avant-garde piece written for 16 synchronized player pianos (!!!) using a stage full of Disklaviers.