Trajectory tracking control based on non-singular fractional derivatives for the PUMA 560 robot arm
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Trajectory tracking control based on non-singular fractional derivatives for the PUMA 560 robot arm J.E. Lavín-Delgado1 · J.E. Solís-Pérez1 · J.F. Gómez-Aguilar2 · R.F. Escobar-Jiménez1
Received: 15 December 2019 / Accepted: 16 June 2020 © Springer Nature B.V. 2020
Abstract In this paper, a novel hybrid fractional-order control strategy for the PUMA-560 robot manipulator is developed and presented, which combines the derivative of Caputo– Fabrizio and the integral of Atangana–Baleanu, both in the Caputo sense. The fractionalorder dynamic model of the system (FODM) is also considered which consists of two models, the robot manipulator model, and the model of the induction motors which are the actuators that drive their joints. The fractional model of the manipulator is obtained using the Euler–Lagrange formulation. On the other hand, for controlling each one of the induction motors, fractional-order controllers PIϑ based on Atangana–Baleanu in the Caputo sense integral were developed. And for the trajectory tracking control, fractional-order controllers PDξ were developed based on the fractional derivative of Caputo–Fabrizio in the Caputo sense. Also, ordinary PI and PD controllers were developed for the PUMA robot control to compare their performance with the fractional-order controllers. The results obtained demonstrated that the fractional-order controllers have a better capability for tracking trajectory tasks than the integer-order controllers, even when changes of the desired trajectory and external disturbances are considered. Additionally, an end-effector trajectory tracking task for manufacturing applications is also considered. All numerical simulations were performed by using the same orders and gains, demonstrating that the proposed fractional-order PIϑ and PDξ controllers are robust, under different operating conditions, for tracking trajectory tasks. The fractional-order controllers and the integer-order controllers were tuned applying the cuckoo search optimization algorithm where the root-mean-square error (RMSE) was chosen as the cost function to minimize. Keywords Fractional calculus · Puma 560 arm robotic manipulator · Induction motor · Fractional-order PI controller · Fractional-order PD controller · External disturbances · Cuckoo search optimization algorithm
B J.F. Gómez-Aguilar
[email protected]
1
Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México
2
CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México
J.E. Lavín-Delgado et al.
1 Introduction Robot manipulators are extensively used in the industrial manufacturing sector to perform several tasks like materials handling, welding, assembly, spray painting, and other applications. These applications require path planning, trajectory generation, and control strategies implementation. Actuators are usually not considered in the dynamic model of the robot for the position control of
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