Efficient path planning for autonomous mobile robots is a critical problem across numerous domains, where optimizing both time and energy consumption is paramount. This paper introduces a novel methodology that considers the dynamic influence of an environmental flow field and considers geometric constraints, including obstacles and forbidden zones, enriching the complexity of the planning problem. We formulate it as a multi-objective optimal control problem, propose a novel transformation called Harmonic Transformation, and apply a semi-Lagrangian scheme to solve it. The set of Pareto efficient solutions is obtained considering two distinct approaches: a deterministic method and an evolutionary-based one, both of which are designed to make use of the proposed Harmonic Transformation. Through an extensive analysis of these approaches, we demonstrate their efficacy in finding optimized paths.

翻译：自主移动机器人的高效路径规划是众多领域中的关键问题，其中同时优化时间与能耗至关重要。本文提出一种新颖方法，该方法考虑了环境流场的动态影响，并纳入了包括障碍物与禁行区在内的几何约束，从而丰富了规划问题的复杂性。我们将其表述为一个多目标最优控制问题，提出了一种称为调和变换的新变换，并应用半拉格朗日格式进行求解。通过考虑两种不同方法——确定性方法与基于进化的方法——获得了帕累托有效解集，这两种方法均设计为利用所提出的调和变换。通过对这些方法的广泛分析，我们证明了它们在寻找优化路径方面的有效性。