  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.
