Abstract: Towards the regularity, smoothness and stability problem of existing flock formation control methods, an innovative theory for regulated heterogeneous flock formation control based on geometry-constrained mechanism is proposed. Firstly, geometry Morphing method is utilized to generate a series of intermediate constraint shapes from the initial shapes to the target ones; then capacity constrained centroidal power diagram is introduced to model the internal layouts of groups in the constraint shapes in order to obtain required heterogeneous distributions; finally, the Lloyd’s method for power diagram is presented as a navigation algorithm for smooth and collision-free movement. Experimental results show that the proposed method is stable and reliable to generate smooth and fluent formation transformations, can produce natural formation animations and simulate real scenarios by heterogeneity feature, and is applicable for crowd formation control with different scales and formations.