Advice on a robotic intravenous cart that automatically follows a patient

Hello all! I am new to Arduino and robotics but am trying to create a robot that follows a patient around in a hospital automatically. I am considering using IR, ultrasonic, RF, etc but think that bluetooth may be the best way to go. Bluetooth changes frequencies around 1000 times per second so, considering that there will be many patients and IV carts in a hospital, it will prevent interference between different transmitters and receivers. For bluetooth, I hope to have a transmitter (phone maybe?) on the patient and a receiver (maybe more than one? thinking about ardunio BT shield) on the IV cart. I understand how to establish a connection between the transmitter and receiver but I am not sure how to get the robot to follow the patient using signal strength/proximity detection? I have read through forums and realize that this issue is hard to get across but maybe someone has a novel idea? If it's not possible, do you have any other suggestions for how I should go about making this project? Any help will be greatly appreciated!

It seems unlikely to me that the patient will be very far from the cart, so why not a length of string?

This is a very difficult problem, and I suspect Bluetooth is not anywhere like being part of the correct solution.

What do you mean by "length of string"?

I don't know, maybe enough to go around the patient's waist, and across to the cart and tie-on - a couple of metres?

Why not a vision sensor that track were a person is moving and follows them? The raspberry pi might work better for this project…

Vision sensing seems like a good idea but how do i make sure the robot only tracks it's specific patient and not just any human?

Unique fiducials.
Not really Arduino territory

This might get you started…

http://www.trossenrobotics.com/p/RoboTurret-Vision-Tracking-Starter-Kit.aspx

Also, It looks like it would work with Arduino.

IR may not be the best approach as you will get lots of interference & reflections in a typical hospital environment - plus what happens if there are several of these patients in the same queue etc. I have been involved in projects like this where even $,$$$,$$$+ couldn't deliver a perfect solution.

RF solutions can suffer from interference also - even between floors or through walls. Using RSSI approaches can be unreliable, even with triangulation.

The best approach is likely to be a hybrid approach.

However, there is a campaign running on Kickstarter or Indiegogo using vision technology to have a robot follow colour coded objects, which is quite impressive & interesting. I think they just sell the camera & board with a standard interface. You will still hit some challenges.

Another approach might be to leverage Kinect or WII type gaming devices...but would need some research.

Let me know if you make any progress it's an topic I am interested in.