Being a little more serious
What is needed is not a robot, but an automatic system (it has after all only one function.)
If this involves hot-desking, the problems are going to be:
NVH (to avoid spillage and annoying other people).
Spillage is going to be the most difficult because the feedback mechanism to stabilise the beer is going to be really difficult - people come with three axis visually and mechanically sensed stabilisation. I don't think mobile phone sensors would cut it for the accelerometers, and the actuators would be expensive.
Therefore I suggest that the pickup tray have locating holes for the glasses, and a simple actuator causes silicone rubber discs to descend on top of them to act as a seal. The discs need to have a dip in the middle so that as they are lifted any drops are centralised.
However, having (say) 4 full pint glasses at counter level will cause other problems, such as easily being knocked over, so the pickup tray needs to be capable of going up and down. Since we will want desk and people sensors at a height of around 600mm as well as closer to ground level, this could be done with a pair of vertical struts on which the pickup tray slides, operated with a polymer chain or belt for quietness, with a sensor ring at the top and another one at about 100mm above ground.
The base unit would then be roughly rectangular with the struts to one side, so that in use the tray will rise to a convenient height for loading and unloading, and in carrying position descend to the middle of the base unit, giving a low CoG. Interlocks would ensure that the base unit only moves when the tray is down and the glass covers are in the actuated position. Interlocks are needed because software is written by people (says the person who once boiled away a litre of fluorinert for lack of a thermal switch).
The tray could hold a convenient clip for the order, and whatever payment means is being used.
Navigation is interesting. Presumably you aren't allowed to lay white tape on the floor, which gives rise to a very easy solution involving simple photosensors. But GPS isn't going to work well in a building and isn't accurate enough anyway. One option might be to borrow an idea from WW2 and use a simple infrared beam. The beam of course would need to operate from a point high enough to avoid obstacles. The conveyor would have a rotating sensor at the top. The rule would be that on the outward trip the beam is behind and on the return journey it is in front. If obstacles have to be avoided, the conveyor will deflect suitably but try to ensure it is at least on the beam fringes. The sensor head will need to be wide enough that it can detect the variation in strength across the received beam width and so work out the orientation of the centre of the beam. When following the beam exactly, the signal will be strongest in the centre and weakest at the periphery. If people block the beam, the thing just stops until it is visible again. A simple semiconductor IR LED should do it.
I hope this helps. It's a pity I can't post pictures.