Inverse Kinematics: Identifying a Functional Model for Closed Trajectories Using a Metaheuristic Approach

Raúl López-Muñoz, Mario A. Lopez-Pacheco, Mario C. Maya-Rodriguez (), Eduardo Vega-Alvarado and Leonel G. Corona-Ramírez ()
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Raúl López-Muñoz: Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, Mexico City 07340, Mexico
Mario A. Lopez-Pacheco: Escuela Superior de Ingeniería Mecánica y Eléctrica-Unidad Profesional Adolfo López Mateos, Instituto Politécnico Nacional, Mexico City 07738, Mexico
Mario C. Maya-Rodriguez: Escuela Superior de Ingeniería Mecánica y Eléctrica-Unidad Profesional Adolfo López Mateos, Instituto Politécnico Nacional, Mexico City 07738, Mexico
Eduardo Vega-Alvarado: Group of Research and Innovation in Mechatronics (GRIM), Centro de Innovación y Desarrollo Tecnológico en Cómputo (CIDETEC), Instituto Politécnico Nacional, Mexico City 07700, Mexico
Leonel G. Corona-Ramírez: Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, Mexico City 07340, Mexico

Mathematics, 2025, vol. 13, issue 11, 1-18

Abstract: Determining the position values of the effectors in a robot to enable its end effector to perform a specific task is a recurrent challenge in robotics. Diverse methodologies have been explored to address this problem, each with distinct advantages and limitations. This work proposes a metaheuristic-based approach to solve a sequence of optimization problems associated with the discretized trajectory of the end effector. Additionally, a method to identify a functional model that describes the effector trajectories is introduced using the same optimization technique. The key contribution lies in algorithmic adjustments that enhance the metaheuristic solutions by leveraging the behavior of the robot and the influence of the tracking task on the search space. Specifically, two operations are modified in the initialization process of the candidate solution. The proposed biased initialization with variable weights improves positional accuracy (72.5%) in relation to methods without dynamic updates. Additionally, the standard deviation was reduced by (89%). For industrial implementations, modern controllers can directly encode effector positions via parametric functions. The results of this proposal formulate optimization problems whose solutions yield the parameters of a time-dependent mathematical model describing the movement of the effector.

Keywords: optimization; metaheuristic algorithm; inverse kinematics problem; kinematic chain; identification technique (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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