I want to create a robot that will navigate on a desired path! That path can be a straight line or a circular path with a given radius.
I will use 3 or 4 omni wheel drive platform and for positioning, I am using this research paper which perform dead-reckoning using mouse sensors.
I've understood that I will get x, y and θ positions, which are actual positions of robot. These can be used to calculate the error and then using PID to compensate the error.
But, to find the error, I must have the desired position of the robot at that moment!
For example, the Robot is at (0,0) and it needs to move in a circular path of equation
$$ x^2 + y^2 - 10y = 0 $$
Now, I want to calculate the position at t = 2 sec, how to do that?
If someone has already done similar stuff, please post the link. I am not able to find any resource on web!