Small projector for affixing to a robot

I’m heading a research project in my robotics lab, and I’m looking for a small projector to affix to the top support structure of a LoCoBot. My plan is to have data/videos/images fed to the projector via the robot’s local machine, so either HDMI or USB connection would work great. It would need to have a relatively small profile to fit comfortably on top of the robot’s support structure, so something less than 7″x4″x5″ (lxwxh). Weight is not as critical and will likely be constrained by the dimensions. One that can be charged would be great, but there is also a battery on the robot to power the robot, so it could also be powered via USB from the battery or the robot’s machine. The battery has four unused USB slots – two providing 2.1A and two providing 1.0A.
Preferred resolution is XGA (1024×768 pixels, 4:3 aspect ratio).

The projector doesn’t need to have a super far projection reach, <= 20 ft or so. Tripod threading would be a plus. The robot is running Ubuntu 16.04, so the projector would need to be compatible with Linux. I wasn’t able to find many examples online of using projectors with ROS, but if anyone knows of any projects or projectors that have been used, that would be helpful!

The project is still in its workshopping phase, and I’m admittedly not much of a projector expert. Unless there exists a type of automatic or remote focusing I can do remotely by ssh-ing into the machine, we would likely have to manually focus the projection. I’m not sure what additional info about the PC would be helpful, let me know and I’ll edit the post to provide that info.