Abstract
Torque loss values resulting from friction in mechanical arm joints and their actuators were identified. Then, using the LuGre friction model and applying the nonlinear least square error estimation method, a more precise model is presented to model its effect. To investigate more efficiently, the general LuGre friction model was used in three forms for modeling the system’s friction. The first model was the common LuGre model, while in the two other extended models, the parameters were considered time-varying that are estimated online. Of note is that the third model also includes the nonlinear viscous term. Then, by utilizing a nonlinear sliding mode controller, simulations were performed for both point-to-point and linear path of the system’s state, and the efficiency of designed algorithm was examined. The results show the advantage of the identified models with time-varying parameters over the constant parameters model. Eventually, a 6R laboratory robot was employed for validation of the proposed algorithm, subsequently validating the simulation results, and as it showed, the final friction model presented better performance.
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Abbreviations
- T (t):
-
Vector of motors torque
- \({u_{FJ}}\left({\dot q\left(t \right)} \right)\) :
-
Vector of the joint friction
- \({u_{FM}}\left({\dot q\left(t \right)} \right)\) :
-
Vector of the motor friction
- Ĉ :
-
Nominal values of coriolis acceleration effects
- Ĝ :
-
Nominal values of gravity force vector
- \({\hat M}\) :
-
Nominal values of inertia matrix
- K n×n & λ n×n :
-
Control gain coefficients matrix
- \({u_{{F_{M,ID}}}}\left({\dot q\left(t \right),z} \right)\) :
-
Values of motor estimated friction model
- σ 0 :
-
Stiffness coefficient
- σ 1 :
-
Dumping coefficient
- σ v :
-
Viscous coefficient
- F s :
-
Stribeck coefficient
- F c :
-
Coulomb coefficient
- v s :
-
Stribeck velocity
- z :
-
Internal variable of friction model
- f (x,θ):
-
Considered model in estimation algorithm
- J :
-
Jacobian matrix
- \({u_{{F_{J,ID}}}}\left({\dot q\left(t \right),z} \right)\) :
-
Values of joint estimated friction model
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Paria Moradi received the B.S. in Mechanical Engineering from Razi University, Kermanshah, Iran, in 2018. She is currently an M.S. student of Mechanical Engineering at the Iran University of Science and Technology. Her research interests include robotics, robust control of nonlinear system.
Moharram Habibnejad Korayem received his B.Sc. (Hon) and M.Sc. in Mechanical Engi-neering from the Amirkabir University of Technology in 1985 and 1987, respectively. He obtained his Ph.D. in Mechanical Engineering from the University of Wollongong, Australia, in 1994. He is a Professor of Mechanical Engineering at the Iran University of Science and Technology. His research interests include dynamics of elastic mechanical manipulators, trajectory optimization, symbolic modeling, robotic multimedia software, mobile robots, industrial robotics standard, robot vision, soccer robot, and the analysis of mechanical manipulator with maximum load carrying capacity.
Naeim Yousefi Lademakhi received the Associate of Automotive Technology from Enghelabe Eslami Technical College of Tehran in 2010, the B.Sc. in Automotive Technology Engineering from the Shahid Rajaee Teacher Training University of Tehran in 2013 and M.Sc. in Mechatronic Engineering from Iran University of Science and Technology in 2016. He is currently a Ph.D. candidate at IUST. His current research and interests include robotics, nonlinear and optimal control, identification systems and observers, model predictive control.
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Moradi, P., Korayem, M.H. & Lademakhi, N.Y. Online identification and robust compensation of extended nonlinear time-varying friction model in robotic arms. J Mech Sci Technol 37, 367–373 (2023). https://doi.org/10.1007/s12206-022-1235-y
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DOI: https://doi.org/10.1007/s12206-022-1235-y