Nowadays, mobile robotics is one of the most important fields of robotics. Due to the popularity of mobile robots, finding a feasible path that allows a robot to move from a starting point to a target point in a certain environment has become one of the most researched problems in this field of robotics. This problem is known as path planning (PP). PP is categorized as an NP-Hard problem and, for this reason, Multi-Objective Evolutionary Algorithms (MOEAs) could be used to efficiently solve this problem. In this work, a Multi-Objective approach based on the Shuffled Frog-Leaping Algorithm (MOSFLA) has been proposed to solve the PP problem. This algorithm is inspired on the frogs' behavior in nature. In our problem definition we considered three different objectives: the path safety, the path length, and the path smoothness. The last one is a very important objective in mobile robotics since it is directly related to the energy consumption. Furthermore, and unlike other authors, eight realistic scenarios have been used for the paths calculation and the assessment of our proposal. In order to compare the obtained results, we also used the well-known Non-dominated Sorting Genetic Algorithm II (NSGA-II), which is the most commonly used algorithm by other authors who tackled the PP problem in a multi-objective way. With respect to the results evaluation, on the one hand, we used specific quality metrics. On the other hand, to demonstrate the statistical relevance of the obtained results we performed an in-depth statistical analysis. Finally, the study shows that the proposed MOSFLA is a good alternative to solve the PP problem.