| Description |
Models of swarming behavior aid in disaster planning, direct the actions of ware- house robots, and can map the foraging characteristics of insects. These mod- els use the optimal behavior of individual agents to determine the behavior of the larger population. Optimal transportation is one such model that has been used to successfully describe the behavior of swarming agents[3]. The Monge- Kantorovich formulation of the optimal transportation problem models the best direct route for individual agents in a swarm. The presented work investigates op- timal transportation and duality in a Monge-Kantorovich formulation. We reduce the Monge-Kantorovich formulation to the linear programming problem which can be e#14;ciently solved numerically. However this formulation is not applicable in the case where the domain of travel is restricted, so that agents must travel along a particular network of paths. For instance, robots traveling throughout a ware- house must navigate through a network of aisles, and foraging bugs may prefer to travel along premade routes. We extend the Monge-Kantorovich formulation to a network of paths which di#11;ers from transfer over a direct route. We show that this extended formulation can also be reduced to the linear programming problem. Finally, we investigate various applications of both the direct and network transfer using numerical simulations. |
