How to specify a desired trajectory for a group of robots?

Please check the image attached.

Say I have a vector for N robots where we can say N to be 5 as an example. They are at random initial positions with random theta angle. So I have a random x coordinate and a random y coordinate for 5 robots in two different column vectors. Now I have to define a desired trajectory for all the robots to follow.

I want that desired trajectory to be a sinusoidal and want to generate an error vector which I have to minimize. how do I define my desired trajectory such that I can get an error Vector generated from all the coordinates of individual robots.