guidance for making a mini robot

Hello there. I have just begun to introduce myself to Arduino and so am a complete beginner with no making experience. I’ve been working my way through the Arduino projects book, but not yet had the confidence to go straight into making my robot. So figured I’d seek help first before jumping in…

For my first project my idea is to build a miniature robot that will navigate itself around a structure. I’ve attached a sketch of it. The picture illustrates the intended layout for the structure but not the scale because this will be dependant upon how small I can make the robot which is to navigate the space.
The idea is for the robot to keep moving until it encounters a wall at which point it will turn either left or right and continue in an alternate direction. I would like to be able to build several (3-4) of the robots and have them all navigating the same space simultaneously. So cost is as much a consideration for the build of the robot as well as the level of difficulty of putting it together.

I’ve been looking around at robots others have made and the example attached shows what I am trying to achieve. In terms of size, aesthetic and function. The only difference is that the robot only turns left when it encounters an obstacle.

Guidance and tips on where or how to start would be very appreciated! Thanks