Mathematics, Vol. 13, Pages 1847: Inverse Kinematics: Identifying a Functional Model for Closed Trajectories Using a Metaheuristic Approach

Mathematics doi: 10.3390/math13111847

Authors:
Raúl López-Muñoz
Mario A. Lopez-Pacheco
Mario C. Maya-Rodriguez
Eduardo Vega-Alvarado
Leonel G. Corona-Ramírez

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.

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