  We consider the problem of determining the optimal composition of a
heterogeneous multi-agent team for coverage problems by including costs
associated with different agents and subject to an upper bound on the maximal
allowable number of agents. We formulate a resource allocation problem without
introducing additional non-convexities to the original problem. We develop a
distributed Projected Gradient Ascent (PGA) algorithm to solve the optimal team
composition problem. To deal with non-convexity, we initialize the algorithm
using a greedy method and exploit the submodularity and curvature properties of
the coverage objective function to derive novel tighter performance bound
guarantees on the optimization problem solution. Numerical examples are
included to validate the effectiveness of this approach in diverse mission
space configurations and different heterogeneous multi-agent collections.
Comparative results obtained using a commercial mixed-integer nonlinear
programming problem solver demonstrate both the accuracy and computational
efficiency of the distributed PGA algorithm.
