That sounds like an interesting project! You can power your 3pi+ through an external supply, like a solar panel, through the VBAT and GND pins near the back right corner of the control board. (Make sure you do not have batteries installed at the same time though.) The minimum to maximum operating voltage for the 32U4 control board is 2.7V to 6.5V.
None of us here have made a solar powered 3pi+ ourselves, so I do not have any other specific suggestions. However, designing around the turtle edition seems like the easiest starting point since that version uses low power motors, which means you are probably more likely to find suitable solar panels.
If you get something working I would be interested to hear more about it!