Humans have always been fascinated by autonomous objects like robot. Still, there is not too rapid development in the field of robotics, due to the complex nature of the subject.
As for now, it can be expected that in the coming 2 or 3 decades, autonomous self-driving cars will be reality. The most challenging aspect in developing driverless cars is to avoid accidents. Even if such algorithm is developed, it will still need time and situations for rigorous testing before putting them in market.
Auto-driving will certainly be very beneficial. It is a known fact that most of the accidents happen due to human errors. Self-driving cars will be amazingly safe.
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Google X Lab has been developing driverless car since sometime. Google Driverless Car Project is being led by Sebastian Thrun who is the director of Stanford Artificial Intelligence Laboratory. He is also known for co-inventing Google Street View. He along with other team members developed Stanley, the self-driving car which won the DARPA Grand Challenge (2005).
It seems that soon the self-driving technology will be in our hands. Google expects to completely develop the technology in coming 5 years. Look at this infographic which projects expected future of driving and cars.