UAV: Automatic Model Car

Want to develop a model toy car, that will follow a user holding the key or a Bluetooth paired mobile phone. The model toy car should be able to follow or track a user (child) through either a mobile device using Bluetooth signal or through a key (dongle) through radio waves or Bluetooth (open to other suggestions as well). The toy car should be able to avoid obstacles (using sensors and collision avoidance algorithm) to move around them to follow the user. The collision avoidance must be able to prevent collision if multiple cars are operating in the same area. The structure of the car is not important (as long as it has 4 wheels), even a rough model or a basic frame of the car should be sufficient. The focus is on the operating success of the product where it is able to follow a user even though a crowed place by avoiding obstacles. The final deliverable should includes both hardware (car frame including motors for wheels and steering and any sensors/chips used to detect obstacles and any other hardware required for operation) and software. All hardware and software used must be opensource and free to use for both personal and commercial purposes. Documentation in English.