Three-robot minimum-time optimal line formation

Multi-robot formation problem has received increasing attention due to its wide applications like surveillances. To illustrate a novel framework on optimal multi-robot formation given in our previous work, which aims to answer the long-term ignored fundamental problem of describing the formation and clarifying optimal formation rigorously in a mathematical manner, as a preliminary case study, two typical cases of the minimum-time line formation problem for three robots are investigated in this note. In this problem, different robots may move with different speeds and the three-robot team aims to row on a straight line with the minimum formation time. Mathematical results have been established with algebraic and geometric analysis, which are further verified by extensive experimental results.