Decentralized Bioinspired Non-Discrete Model for Autonomous Swarm Aggregation Dynamics

In this paper a microscopic, non-discrete, mathematical model based on stigmergy for predicting the nodal aggregation dynamics of decentralized, autonomous robotic swarms is proposed. The model departs from conventional applications of stigmergy in bioinspired path-finding optimization, serving as a dynamic aggregation algorithm for nodes with limited or no ability to perform discrete logical operations, aiding in agent miniaturization. Time-continuous simulations were developed and carried out where nodal aggregation efficiency was evaluated using the following metrics: time to aggregation equilibrium, agent spatial distribution within aggregate (including average inter-nodal distance, center of mass of aggregate deviation from target), and deviation from target agent number. The system was optimized using cost minimization of the above factors through generating a random set of cost datapoints with varying initial conditions (number of aggregates, agents, field dimensions, and other specific agent parameters) where the best-fit scalar field was obtained using a random forest ensemble learning strategy and polynomial regression. The scalar cost field global minimum was obtained through basin-hopping with L-BFGS-B local minimization on the scalar fields obtained through both methods. The proposed optimized model describes the physical properties that non-digital agents must possess so that the proposed aggregation behavior emerges, in order to avoid discrete state algorithms aiming towards developing agents independent of digital components aiding to their miniaturization.