I need to construct a Mobile robots preferably circular type of diameter 30 cm, it will be carrying a payload of 5kg. What will be optimal thickness the baseplate considering the material as aluminium? How to calculate these kind of these kind of problems
To be able to select the right material. You will need to estimate the maximum forces that will be applied to it and make sure that it's stronger than that expected maximum.
There's a range of ways to achieve this.
At one extreme, you can create a full model and run finite element analysis on the whole thing and iterate until you have every part of the system to be stronger than the maximum expected load.
In the middle you can do some back of the hand computations to find the worst configuration loads and the weakest points for those loads and make sure that you have a safety margin.
And at the experimental end, you can take a guess, build it and test it in realistic situations and iterate to see if you need stronger or lighter. And iterate on the design.
Each one of these approaches has tradeoffs. More time in the design, more time in fabrication. Or more "optimal" design capabilities. You need to make your own tradeoffs as to what your full optimization function is including design and fabrication time.
Unless the robot is going to have an unusually heavy payload or be subject to excessive forces, you will probably be OK with any reasonable thickness aluminum plate.
It does not provide any real benefit to calculate that you need a plate with a thickness of 1.45657 mm to provide just enough strength for your payload since you cannot purchase aluminum plate with that precise thickness and it would be prohibitively expensive to machine down a plate that precisely.
You would be better off simply checking with your supply house and get what they have already in stock such as 2.6 mm (about 0.1 inch) plate of 6061.