Here is another educational robot kit that you can build and control from your iOS or Android device. The UBTECH Jimu Inventor Robot has Bluetooth. It comes with 675 interlocking parts, 16 digital servos, and step by step instructions in an app with 360 degree pan, tilt, and zoom capability.
You can build various characters with this kit. Additional servos can be added to expand this robot. This kit is available for under $400 at this time.