Haar wavelet-based Galerkin method with its feasibility, consistency, and application to unmanned vehicle navigation around moving obstacles

Abstract

In this study, we propose a novel Haar wavelet-based Galerkin method to solve nonlinear optimal control problems with applications to unmanned vehicle navigation. The method addresses the critical challenge of optimizing energy consumption while ensuring safe navigation in dynamic environments with multiple moving obstacles. By leveraging the computational efficiency and scalability of Haar wavelets, combined with the robustness of the Galerkin approach, we demonstrate convergence to the optimal solution under feasibility and consistency conditions. Comprehensive numerical simulations, including diverse and complex obstacle scenarios, validate the method's practicality. Through detailed trajectory, speed, and direction analyses, we highlight the approach's ability to adapt to real-world navigation challenges, making it a promising tool for autonomous system optimization. © 2025 European Control Association