A new framework of optimal multi-robot formation problem

In the past decade, cooperation of swarm of mobile robots has been extensively studied for its high error tolerance, efficiency, scalar extendibility and wide applications in various services and surveillances. Among most of these applications, the robots are required to formate into certain shape or positions so as to accomplish tasks with satisfied overall performance, hence multi-robot formation problem has received increasing attention in the research community and has been studied from different aspects. This contribution aims at one long-term ignored fundamental problem of describing the formation rigorously in a mathematical manner and establishing one general framework of optimal multi-robot formation problem, which can serve as a theoretical basis for later studies on robot formation. Within the proposed framework, the preliminary case studies to three-robot optimal formation problem have shown that the formulated optimal formation problems are generally non-trivial and challenging even for the most simple three-robot optimal line formation problems.