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，其中优化时间和能耗至关重要。本文提出了一种新颖的方法，综合考虑环境流场的动态影响以及几何约束（包括障碍物和禁行区域），从而增加了规划问题的复杂性。我们将该问题形式化为多目标最优控制问题，提出了一种名为“调和变换”（Harmonic Transformation）的创新变换，并采用半拉格朗日格式进行求解。通过两种不同方法——确定性方法和基于进化算法的方法——获得帕累托有效解集，这两种方法均设计为充分利用所提出的调和变换。通过对这些方法的深入分析，我们验证了其在寻找优化路径方面的有效性。