Modern Methods and Algorithms of Path Planning for Autonomous Mobile Robots, Their Objective Functions

The current situation in the world of research algorithms for path planning by autonomous robots shows that there are a large number of algorithms and their modifications that require researchers and engineers of autonomous robotics to have a fine understanding of the fundamental aspects of their functioning. The general goal of the research is to conduct an analysis of existing algorithms, methods and their modifications from the point of view of the component of the mathematical apparatus, namely their target functions. The research examines 38 modern algorithms and methods of path planning by autonomous robots. Considered the importance and criticality of understanding the objective function for the field of robotics. Examples illustrating the importance of this aspect are given. In the process of research, algorithms are presented in the form of formalized generalized mathematical formulas taking into account possible minimization/maximization, their improvements and improvements. For each considered algorithm and method, a conclusion is given regarding its target function. In the study, the methods of "Dynamic games" are separately highlighted and the application of the fundamental "Method of solving functions of A.O. Chikryi" for path planning is considered. In general, information on the advantages and importance of understanding the mathematical apparatus of pathfinding algorithms by autonomous robots for solving scientific problems is provided. The generalized results are summarized in a single comparative table, which provides the main formalized function of the algorithms, reveals the main idea, advantages/disadvantages, the scope of application and an example of use. The comparative table is presented in the form of a generalized auxiliary reference element of the study.