Pumendu,
You need naturally need some processing capability on your robot. Image processing can be quite complex and generally requires a powerful processor. I tend to prefer FPGA's for this type of application. With an FPGA you can include an embedded processor, and also include some custom processing components, in this case the processing needed to analyze the images. I am not saying that this is the easiest way to approach this, but it is a great application for an FPGA.
Another possibility is to use a nice 32bit microprocessor. I'm not sure an 8-bitter would be up to the task, at least it would be quite slow. Atmel makes some nice 32bit processors, as does Pic. You will need a development kit, cables, etc. You will probably end up paying around $100, maybe up to $200 for this, depending on what you purchase. Look for 3rd parter programmers, they can often be less expensive than the manufacturers versions. I prefer the Atmel devices because you can use GNU C compilers, and the toolchain is free. I am not very familiar with the Pic offerings, but there are many PIC fans out there, so it should not be difficult to get help with these.
Find a CMOS image sensor, these have various methods of capturing data, so find one that would integrate easily with the processor you chose. I can't help you with types or features.. but you will probably need some sort of lens as well.
With the CMOS sensor attached to your processor, you can now write code to capture data. Many sensors return data in a scan, top to bottom, left to right. As you capture a frame of data, keep track of the lines, and the columns. Lets assume that your camera is oriented so that the "top" of the image is pointing forward for your vehicle. So, as you read scan lines left to right, you are scanning across the floor left to right in relation to the vehicle. A simple approach is to bin the columns into a small number of bins. What i mean is that if the sensor has 1024 columns, combine all of the data in groups of 102 columns, thus getting 10 "bins". You probably do not need more resolution than this, and the fewer bins you have the easier it is to process. Calculate the average "color" of each bin. Then, look for the patterns that indicate your line. white, white,white, gray,gray,gray,white,white,white...
The color data from the sensor can easily be converted to "black and white". If you check the sensor, it might even have the ability to do this automatically. Sensors have many settings, and so look for an option to return the data in "gray level", then just set a threshold. You will have to do the research on the image sensor to find one that does what you need, but doing that in the sensor is best to minimize the processing needed.
From there, just track the location of the white/colored edges.. and build your control system to follow.
Good luck.
Ed
