You may want to narrow down your thesis a bit. What you are trying to do is near the state of the art for small robots. The robot you are talking about will also need expensive hardware capabilities and a lot of processing. Think about all the things that you have implied your robot will do:
1) Search for an object -- this involves recording how much you have moved from your starting point and the location of any obstacles that obscure the line of sight or block your path. You will need obstacle detection sensors, or you could use a simple motion base like the iRobot Create where you can just bump into obstacles and record their location.
2) Detect a specific object -- this can be done but may require expensive sensors. Your best bet is to pick a simple shape like a soda can that is a single contrasting color to your environment and use CMUCam to find it in relation to your robot.
3) Move to the object -- this involves estimating the location of the desired object repeatedly and using it to plan to motion commands. You will have to figure out what to do when you hit an obstacle on the way.
4) Grab the object -- How do you position your gripper so that it is exactly positioned around the object, without bumping the object out of place in the process?
5) Lift the object
6) Search for the "trash bin". Even if you knew where this was in relation to your starting point, most navigation sensors are inaccurate enough that you will need to do a little "search" to relocate the trash bin.
7) Move to the trash bin. If you don't locate the object correctly with respect to the bin, it may fall on the floor.
Release the object into the trash bin. That part was easy!
So depending on what hardware you have in your lab, you might want to work on just on piece of this problem rather than the whole thing.