Control problem of shortest square distance for a multi-agents formation

A new control problem named shortest square distance (SSD) for multi-agents formations is proposed. The control aim is to minimize the square sum of distances all the agents traveled during reformation process, in order to save total energy and balanced energy consumption as far as possible. The SSD problem is first proved an NP-hard problem through recursion algorithm. Then by defining square distance matrix, the SSD problem is converted to solving shortest path problem. Finally a dynamic programming algorithm is given to solve the SSD problem. Simulation results demonstrate the effectiveness of the presented algorithm.