Formation Control Algorithm of Agents Based on Earth Mover’s Distance

Algorithm 1

CVT-based method for group sampling.

	Input: collective crowd shape; an error tolerance .
	Output: group sampling points .
	Generate the initial points as the seed;
	Compute the Voronoi region for each seed
	Compute the centroid of each Voronoi region ;
	While do
	L-BFGS
	Compute the energy function in equation (6)
	Compute the gradient w.r.t. x; see equation (7)
	Update x by step search
	end
	return the final centroid points