This has been a project I've wanted to do for a while, and finally dove into a few weeks ago. I've got a first iteration of the design that is functional.

The basic electrical design consists of an Arduino receiving input from a couple of switches, and driving a Monster Moto Motor Controller board, which is connected to two decent gear motors. Add in the 12V sealed lead acid battery and a 5V regulator and that's all of the electronics needed.

As for the mechanicals, the entire rig connects to the wheelchair via two small brackets mounted to the chair. The main housing slips into the brackets and rotates into place. The drive wheels mounted to the shafts of the gear motors contact the chair's tires. And rubber bands maintain sufficient pressure to ensure the drive wheels are pushed against the tires with sufficient force to avoid undesirably slippage.

The mounting brackets are mostly 3d printed, as are the motor mounts and the drive wheels that mount on the gear motors.