This mechanical engineering project requires electronic controls and sensors. Better try this in collaboration with electronics students.
The concept of an automatic lawn-mower is simple. It is a machine to cut grass automatically without human assistance. Many variety of this machine is already available in the market which have complex electronics parts. They cost around $1000.
Below is a video of a home made automatic lawn mower with a much simpler electronic parts. For your project it is better to try something like this than going for a very complex mechanism.
The main parts of this machine are:
1. Two independent motors preferably servo, if not, try Wiper motors.
2. Sensors at sides and front and the associated control units.
3. A grass cutting mechanism with an independent drive motor.
4. power unit which is a battery (Do not try heavy car batteries, the battery of a two wheeler may be enough).
Lot of information is available in net for this topic, so I am not referring to any particular links.