Optimal formation of robots by the continuous-discrete PSO algorithm in three dimensional space

This paper mainly provides and develops a new continuous-discrete PSO algorithm for handling with the optimal formation problem in the three dimensional space. For one class of formation problem with the particular constraints, it is shown that the center of the desired shape is determined and equal to the center of the initial shape by utilizing the Lagrangian method. From the perspective of efficiency, the main task of the continuous-discrete PSO algorithm, short for CDPSO, is to search for some key parameters and to minimize the distance of all robots from the initial shape to the desired shape. To demonstrate the effectiveness of the new CDPSO algorithm, numerical results chiefly concentrate on the optimal helicopters formation from the initial shape to the desired shape in the three dimensional space and the typical shape conversion from the two-dimensional space to the three-dimensional space.