I'm not sure that I've understood you and also this is my first answer, but I'll try my best.
Two years ago, I've faced the exact same challenge. Is there a way of building budget friendly mapping robot? Unfortunately, the answer to this question is not binary. There are so many variables that should be accounted such as movement of robot, movements in the environment, sensor sensivity, encoder sensivity, friction etc. Perhaps there are better questions. What is the ratio of accuracy to budget? Do we need a 3D or 2D map? How can we map an environment in 3D? What are the sources of error?
I've looked for an answer and tried many things along the way. Some of them was cheaper and some of them was more convenient.
1) IR/Sonar Sensor + Servo
Most basic or "primitive" type of solution, also the first one I've tried. It consists of a simple wheeled platform, a servo (two if you want 3D) and an IR/Sonar sensor. You calculate the movement of robot by measuring distance from the front to the next obstacle, and you map the room/house by doing a sweeping motion with the servo + sensor.
- Budget friendly
- Extremely simple
- Highly inaccurate
- Algorithm wise not scalable
If you want to implement this way, pick Sonar sensors. The good ones are a little bit more expensive then most IR sensors but they won't get scrambled when you bump into a reflective surface. Also, make sure that you sweep few times to estimate distance with smaller errors.
2) IR/Sonar Sensor + Encoders
A little bit more expensive this way, but a little bit more accurate so to say. The only change is that now the encoders define the position of the robot. Since we are getting the measurements from two seperate sources, we can calculate an error value more precisely. Unfortunately more problems start to occur this way. The encoders give accurate values, but can we really trust that? What if our robot slips during a movement? What if it gets stuck while moving to a carpet? Now we have to calculate different errors for different situations.
- Little bit expensive but still manageable
- Still simple enough
- Two sources of information
- Two sources of error
Use rubber tires with small wheels, so that you can get a more precise value from encoders since needed wheel rotation for distance increases and minimize the slipping since rubber has greater friction.
3) Xbox Kinect (or equivalent)
In my opinion the best choice for mapping, but not for robotics. Fairly cheap, can be found everywhere, very accurate and tons of tutorials exist. The key phrase is "Point Cloud Map". The Kinect device sends many IR rays and then collects them. By combining this mechanic with the Kinect camera, you can attach every distance point a pixel. Thus it's called Point Cloud.
- Best accuracy/budget ration
- Many resources available
- It's not very robotics friendly due to its size
- Another computating device (such as a notebook) is needed to process the data
- Not very easy to tinker with
A wider robot with a small device to buffer the data (such as Raspberry Pi) would be ideal. You could connect the Kinect to Raspberry Pi and with a wifi dongle you can buffer mapping data to your computer to process, but since you would need an external usb hub too I wouldn't recommend this way.
4) Laser Scanners / Radar Modules
Even though I think this is not suitable to your concept of mapping, I will mention this just as a reference. The industrial solution to mapping because of best precision. Many unmanned vehicles, even the ones owned by the military use these devices. But of course they come with a price.
- Best precision
- Highly durable and reliable
- Extremely expensive
- Most of the time require a high power source
Although this might be out of your league, you may still find inspiration in them. They more or less work with the same principle as IR Sensor + Servo combos.
I've tried my best to mention all current trends in SLAM technology even though you've mentioned that you only have a single IR sensor because I wanted this to be a source for future projects. I hope it helps to you and the others.