In search of the best fitness function for optimum generation of trajectories for Automated Guided Vehicles

Abstract

This paper presents an offline optimization method designed for use with industrial robots in environments with static obstacles. It is particularly useful in industry where stability and predictability are crucial to meeting expected timelines in automated guided vehicle operations. The main methodological contribution of this work lies in the integral process used to define an effective fitness function that guides the optimization method in the search for optimal solutions. This cost function plays a critical role in the effectiveness of the trajectory tracking algorithm by quantifying path quality and allowing comparisons between solutions. The design of this fitness function poses challenges including accuracy, suitability, minimization of path length, and avoiding or reducing collisions. To achieve the optimization objectives and address some issues such as sensitivity to parameter scaling and the risk of premature convergence, different approaches can be used. This work proposes to incorporate constraints into the fitness function, adjust the optimization parameters to reflect the conditions of the problem, and design a fitness function based on prior knowledge and an accurate representation of the goals. The three relevant contributions for the planning and optimization of routes of automated guided vehicle in industrial environments are the following. Firstly, the development of a mathematical model of trajectories based on Frenet curves that considers the static occupancy map of the environment. Second, an optimization strategy to generate optimal safe paths. Finally, a fitness function that guides the optimization method towards optimal solutions considering the sensitivity to scaling and resolution of the parameters. This study presents an exhaustive analysis of the different fitness functions obtained, each one evaluated based on key metrics such as the length of the trajectory, the average and minimum distance to the occupancy map, and the number of collisions along the path. The results show that the obtained cost function successfully avoids collisions with the environment in all scenarios and consistently remains the fitness function with the largest average distance to obstacles, at least 50% higher than other functions used in this study.