Functional-voxel modeling of robot collision areas

The problem of avoiding collision between agents in motion constantly arises in multi-agent systems with decentralized control. As the number of moving agents increases, the amount of computation increases, which makes it difficult to adapt these algorithms for implementation on mobile platforms. The solution of this problem requires using simpler computational schemes and suitable models. The classical collision avoidance algorithm ORCA is based on mutual computation of half-planes of possible collision for each pair of agents, which is the most computationally expensive stage of the algorithm. The functional-voxel modelling will make it possible to store in graphical images the required local geometrical characteristics of the required geometrical region, as well as to perform most of the calculations in advance, thus simplifying the calculations and speeding up the algorithm. The paper presents a functional-voxel model of geometric region of possible collisions of agents by interpolation of the region's contour using Bezier curves. The local geometric modeling of Bezier curves is performed via a zero segment on the positive domain. A four-dimensional graphical model is proposed to simulate the dynamic case of the developed model. This model carries out the distribution of the results of static case modeling in space-time characteristics.