This paper considers task allocation problems where a group of agents must discover and allocate themselves to tasks. Task allocation is particularly difficult when agents can only exchange information over a limited communication range and when the agents are initialized from a single departure point. To address these constraints, we present a novel approach that incorporates computational models of motivation into a guaranteed convergence particle swarm optimization algorithm. We introduce an incentive function and three motive profiles to guaranteed convergence particle swarm optimization. Our new algorithm is compared to existing approaches with and without motivation under conditions of limited communication. It is tested in the case where the agents are initialized from a single point and random points. Results show that our approach increases the number of tasks discovered by a group of agents under these conditions. Furthermore, it significantly outperforms benchmark PSO algorithms in the number of tasks discovered and allocated when the agents are initialized from a single point.