Classical Formation Patterns and Flanking Strategies as a Result of Utility Maximization

In this letter, we show how classical tactical formation patterns and flanking strategies, such as the line formation and the enveloping maneuver, can be seen as the result of maximizing a natural formation utility. The problem of automatic formation keeping is extremely well studied within the areas of control and robotics, but the reasons for choosing a particular formation shape and position is much less so. By analyzing a situation with two adversarial teams of agents facing each other, we show that natural assumptions regarding the target selection of the agents and decreasing weapon efficiency over distance, can be used to optimize a measure of utility over agent positions. This optimization in turn results in formations and positions that are very similar to the ones being used in practice. We present both analytical results for simple examples as well as numerical results for more complex situations.