  Collaborative multi-agent robotic systems where agents coordinate by
modifying a shared environment often result in undesired dynamical couplings
that complicate the analysis and experiments when solving a specific problem or
task. Simultaneously, biologically-inspired robotics rely on simplifying agents
and increasing their number to obtain more efficient solutions to such
problems, drawing similarities with natural processes. In this work we focus on
the problem of a biologically-inspired multi-agent system solving collaborative
foraging. We show how mean field techniques can be used to re-formulate such a
stochastic multi-agent problem into a deterministic autonomous system. This
de-couples agent dynamics, enabling the computation of limit behaviours and the
analysis of optimality guarantees. Furthermore, we analyse how having finite
number of agents affects the performance when compared to the mean field limit
and we discuss the implications of such limit approximations in this
multi-agent system, which have impact on more general collaborative stochastic
problems.
