On non-collision flocking and line-shaped spatial configuration for a modified singular Cucker–Smale model

•Sufficient conditions are established for a singular Cucker–Smale model with a general target motion pattern driving force to admit an asymptotic flocking.•A critical value of the exponent in the communication weight is given to lead to global regularity of solutions.•The avoiding collision asymptotic flocking of Cucker–Smale model with a general target motion pattern driving force is obtained for the first time in the literature.•It is the first time to show that the particles finally come to a line-shape formation with collision avoiding by theoretical proof in this paper.