Problem of Control Synthesis of Stabilization System for a Nonholonomic Mobile Robot: An Autonomous Solution via Modified Synthesized Genetic Programming Method

Solving the synthesis problem for a stabilization system by the application of a symbolic regression technique is presented and analyzed. The objective is to automatically determine a multi-dimension feedback control function with the aid of a computer in order for the control object to transition from any initial condition in any region to a terminal one where the quality criterion has the desired value. Traditionally, control synthesis problems are addressed through analytical or technical methodologies that depend on the specific characteristics of the mathematical model. However, we propose that contemporary numerical techniques, specifically symbolic regression, can automate the process of finding control solutions without direct reliance on the model’s explicit equations. The study utilizes modified Cartesian genetic programming (MCGP) and modified synthesized genetic programming method (MSGP), which is utilized for the inaugural time to tackle automatically the issue of general control synthesis. The methods have been adapted using the small variations principle to decrease the searching space. The successful application of these approaches is illustrated through solving issues related to the general synthesis of a stabilization control system numerically for a nonholonomic mobile robot. Experimental tests show that modified synthesized genetic programming (MSGP) was, on average, 2.24 times quicker at finding solutions for control synthesis compared to modified Cartesian genetic programming (MCGP). Furthermore, a Wilcoxon signed-rank test was conducted and illustrated that the MSGP can be considered the more time-efficient method without compromising solution quality. © 2025 Elsevier B.V., All rights reserved.