Machine Learning Feedback Control Approach Based on Symbolic Regression for Robotic Systems

A control system of an autonomous robot produces a control signal based on feedback. This type of control implies the control of an object according to its state that is mathematically the control synthesis problem. Today there are no universal analytical methods for solving the general synthesis problem, and it is solved by certain particular approaches depending on the type of control object. In this paper, we propose a universal numerical approach to solving the problem of optimal control with feedback using machine learning methods based on symbolic regression. The approach is universal and can be applied to various objects. However, the use of machine learning methods imposes two aspects. First, when using them, it is necessary to reduce the requirements for optimality. In machine learning, optimization algorithms are used, but strictly optimal solutions are not sought. Secondly, in machine learning, analytical proofs of the received properties of solutions are not required. In machine methods, a set of tests is carried out and it is shown that this is sufficient to achieve the required properties. Thus, in this article, we initially introduce the fundamentals of machine learning control, introduce the basic concepts, properties and machine criteria for application of this technique. Then, with regard to the introduced notations, the feedback optimal control problem is considered and reformulated in order to add to the problem statement that such a property adjusts both the requirements of stability and optimality. Next, a description of the proposed approach is presented, theoretical formulations are given, and its efficiency is demonstrated on the computational examples in mobile robot control tasks.