The simplest option for Arobot hardware:

Altera FPGA C4 with Bluetooth interface



The FPGA Altera Cyclone 4  is the main component of the electronic.  Inside FPGA works the custom designed stepper motor controller for 2 axis. Bluetooth module serves as the connection to Android phone. The output pins of FPGA are delivering the PWM signals for the full bridge power drivers of stepper motor's phases. The stepper controller works with 16 micro step pro whole step of stepper motor 

The source in VHDL can be seen in my Github repo

Terasic DE0-Nano Evaluation board with Altera Cyclone C4
Bluetooth Module M-06
Power driver DRV8833
Stepper motors Pololu Bipolar stepper motor, 42 x 38 mm
Robot body  
 Software interface  

The simplest hardware option utilizes the simplest software protocol. The bluetooth messages will be only transferred form controller (Android phone) to actor (robot). The message consist of 6 Bytes:

first Byte = magic Word = 0xA5

second Byte = 0x0

third, fourth Bytes: velocity Left = 16 bits signed short

fifth, sixth Bytes velocity right = 16 bits signed short