Formation Distance Problem in Multi-Agents Control

A new problem named formation distance problem (FDP) in multi-agents formation control is presented, with the aim to minimize the sum of distance all the agents traveled during every formation rebuilding process. By defining the formation distance matrix (FDM), we prove the FDP is an NP-hard problem. A recursion algorithm is described to exact solve the FDP, whose time complexity and space complexity are too large. In order to simplify the calculation, a so-called intelligent ant colony optimization (ACO) algorithm is used to solve this problem. The FDP is converted to modified traveling salesman problem (TSP) using topology knowledge firstly. Then the distance each agent traveled in the formation process is changed to the length between two nodes in the graph. Finally, the problem is converted to graph traversal problem, and a modified ACO algorithm is proposed to solve the FDP. Numerical Simulation results show the effectiveness of the presented algorithm.