Interesting, shouldn't you be using a TI-84 calculator for
school (or do you want it to take math classes for you).
First of all, you need to find a way to connect outside electronics to the calculator (motors, servos, sensors, etc.) and find a way to send/receive data to/from them. The USB port could be used, but that may be complicated. The I/O port could also be used, but it seems like it could only work for only one attached electronic. Other than that, there is no places to connect outside electronics
directly to the calculator. What you can do is use a "USB interface", such as a Phidget board. Link:
http://www.phidgets.com/ . You could plug this to the USB port and then connect outside electronics to that interface. The next part is sending/receiving data from the "Phidget" to the TI-84. I have heard TI-BASIC is a fairly comprehensive language, so creating a script for the USB interface shouldn't be difficult. After this is done, you're free to start making the 'bot do stuff.
I would suggest speaking to people more familiar to the TI-84's abilities; such as the official TI forums (or any other forum dedicated to modifying TI calculators). Once you've mastered programming it and controlling outside electronics with it; come back and ask us about the "getting the bot to do stuff" part.