The problem of avoiding a collision between moving agents constantly arises in multi-agent systems with decentralized control. The various algorithms for solving this problem are accompanied by computational complexity and increasing computational power requirements as the number of agents in question increases. There are difficulties in adapting these algorithms to practical applications on mobile platforms. It is necessary to develop simpler computational schemes and to apply appropriate models. The most computationally expensive step in the classical collision avoidance algorithm ORCA is to calculate the mutual half-planes of possible collision for each pair of robots and use linear programming to calculate the new velocity from them. The application of the functional-voxel method will simplify the necessary calculations by storing in graphical images the local geometric characteristics of the searched domain. Moreover, the application of such models will make it possible to perform most of the necessary calculations in advance, which will accelerate the work of the algorithm. This paper proposes the construction of a functional-voxel model of a required geometric domain by interpolating the contour of the domain using Bézier curves. The local geometric modelling by means of local zeroing function is used as a tool for functional-voxel curve modelling. The obtained functional-voxel model represents a static case of possible mutual positioning of two agents. A four-dimensional graphical model is proposed to solve the dynamic case. This model performs the distribution of the static case modelling results in the space-time characteristics