Efficient leader selection for translation and scale of a bearing-compass formation

The paper considers the efficient selection of leader agents in a swarm running a distributed bearing-compass formation controller. The leaders apply external control which induces translation and scaling of the formation, providing manipulation methods useful to a human operator. The selection algorithm for maximizing translation and scale draws from modularity and submodularity theory. Consequently, the algorithms exhibit guaranteed optimal and suboptimal performance, respectively. For more restricted human-swarm interaction requiring pure translation and scale, a relaxed integer programming algorithm is described to reduce the combinatorial optimization problem to a computationally tractable semidefinite program. The leader selection strategies are supported through demonstration on a swarm testbed.