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In multi-agent systems, limited resources must be shared by individuals during missions to maximize the group utility of the system in the field. In this paper, we present a generalized adaptive self-organization process for multi-agent systems featuring fast and efficient distribution of a consumable and refillable on-board resource throughout the group. An adaptive inter-agent spacing (AIS) controller based on individual resource levels is proposed that spaces out high resource bearing agents throughout the group including the group boundary extrema, and allows low resource bearing agents to adaptively occupy the in-between spaces receiving resource from the high resource bearing agents without over-crowding. Experimental results for cases with and without the proposed AIS controller validate faster convergence of individual resource levels to the group mean resource level using the proposed AIS controller. The generalized approach of the self-organizing process allows flexibility in adapting the proposed AIS controller for various multi-agent applications.