I have a robot with four mecanum wheels (blue square) that can move in an open-space room. The position x,y of the robot is measured in a very accurate way by a fixed position sensor (red circle) that is placed in the origin of the place and has coordinates (0,0,0). The position of the robot is updated at 10Hz.
I want to make the robot follow different paths like the one from A to B as showed in the picture (in green color).
What is the best and accurate way to do that? I think I should have to create the path like a series of x,y points and make the robot move towards them but I don't know how to derive the motion equations.
Can you give me some advices or examples, please?