Research on Algorithms for Local Robot Positioning Using Methods of Discrete Optimization

Introduction. The use of robots is becoming increasingly prevalent each year. Simultaneously, there is a gradual shift from using individual robots to deploying collective robots, as this approach proves to be more efficient for various tasks such as agricultural surveys and irrigation. However, there are specific challenges, particularly the lack of access to global satellite navigation systems for collective robots, which can be jammed for security reasons. The purpose of the article study is to develop an algorithm for the local positioning system of a small collective of robots to maintain a stable structure during group movement while executing tasks in three-dimensional conditions. It is assumed that the collective is controlled by an artificial intelligence single operator, regardless of the number of robots in the group. Results. An algorithm for local positioning based on solving the problem of discrete optimization has been developed. By anchoring one object to the origin point and fixing the position of the second object on the horizontal axis, the problem of ambiguity in the solution, manifested in the symmetrical reflection of points and their displacement relative to real positions, has been resolved. Conclusions. Improvements to the existing local positioning system robot group based on an enhanced discreet optimization algorithm are discussed. The study formulated the task of forming and maintaining the structure of three robots in a two-dimensional space. For constructing the relative coordinate system, a method of forming a base triangle using a nonlinear discrete optimization method was proposed. An algorithm for building a local positioning system for a robot group was developed to ensure the stable configuration of the group in the absence of access to global or cellular navigation systems while performing tasks in two-dimensional spaces. The proposed algorithm serves as a foundation for developing software applications for controlling a small robot group by artificial intelligence or a single operator and avoiding collisions between UAVs. The optimization problem is solved using the SLSQP method, which is suitable for solving problems with nonlinear constraints. It allows for optimizing the coordinates of three objects, minimizing distance and angle errors considering physical constraints, such as fixing the coordinates of certain points and ensuring the minimum distance between objects is not exceeded. The algorithm from the scipy.optimize.minimize library numerically finds the solution to the discrete optimization problem with a combined objective function considering the specified constraints, ensuring coordinate recovery accuracy of approximately 10 % and acceptable program execution speed for fixed-wing UAVs. Keywords: UAV group, local positioning, nonlinear discrete optimization.