OTIMIZAÇÃO CINEMÁTICA INVERSA ALGORITMOS COM A.G., SEGURANÇA DE TRAJETÓRIAS EM MANIPULADORES ROBÓTICOS EDUCACIONAIS E INDUSTRIAIS: COM LSPB X POLINÔMIO DE 5ª ORDEM

• DOI: https://doi.org/10.22533/at.ed.080112613012

• Palavras-chave: Manipulador Robótico; Segurança Robótica; Algoritmo Genético; LSPB; Polinômio De Quinta Ordem.

• Keywords: Robotic Manipulator; Robotic Safety; Genetic Algorithm; LSPB; Fifth-Order Polynomial.

• Abstract: This article analyses the optimization of inverse kinematics using a Genetic Algorithm (GA) and trajectory safety in a four-degree-of-freedom serial robotic manipulator, developed on an educational scale but with potential conceptual transfer to industrial applications. The study integrates the inverse kinematics solution, based on minimizing the Cartesian error between the target point and the point reached by the end effector, with temporal motion planning using LSPB (Linear Segment with Parabolic Blends), comparing this profile with classical fifth-order polynomial planning. The methodology is analytical-computational and combines approximate geometric modelling, Denavit-Hartenberg representation, interpretation of inverse kinematics through Conformal Geometric Algebra, a fitness function with penalties associated with positioning error, joint limits, and kinematic constraints, as well as the evaluation of safety criteria related to velocity, acceleration, jerk, motion smoothness, repeatability, mechanical integrity, and the need for experimental validation. The preliminary results indicate a planar error of 0.0028 cm, equivalent to 0.028 mm, between the target point and the point obtained by the computational solution. This value should be interpreted as numerical validation in a simulation environment, not as guaranteed physical accuracy of the prototype. The comparison between the methods shows that the GA + LSPB association favors computational simplicity, predictability of the acceleration, constant-velocity, and deceleration phases, as well as adequate application in educational benches and low-cost prototypes. On the other hand, the fifth-order polynomial provides greater smoothness in boundary conditions, with continuity of position, velocity, and acceleration, reducing the tendency toward mechanical shocks and becoming more appropriate when dynamic smoothness is a priority requirement. It is concluded that the GA + LSPB-based approach is suitable for teaching, prototyping, numerical validation, and initial trajectory analysis, whereas industrial applications require kinematic model calibration, repeatability tests, formal risk assessment, real actuator limits, emergency stop systems, safe control, and compliance with applicable standards for robots and robotic cells. As future work, experimental validation of the simulated results, comparison of different trajectory profiles, and incorporation of quantitative safety, accuracy, and dynamic performance metrics are recommended.