<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This paper proposes and evaluates a novel control approach for trajectory tracking, stability enhancement, and vibration reduction of a flexible joint robot (FJR). The FJR is a 2-degree-of-freedom underactuated nonlinear system that is challenging to control due to vibration, underactuation, uncertainties, and external disturbances. The control objectives are high trajectory tracking performance together with suppressing vibration. The proposed control approach uses integral sliding mode control (ISMC) combined with a barrier function based on back-stepping. This ensures robust and smooth performance by eliminating the reaching phase where sliding mode control (SMC) is typically not robust. Robustness is thus guaranteed from the start. The FJR is modeled as a 4th-order system using Lagrangian mechanics and decomposed into two 2nd-order subsystems for control design. Sliding variables are defined for each subsystem. Using these variables, the proposed control achieves robust trajectory tracking, stability, and vibration reduction. Numerical simulations in MATLAB validate the superior performance of the proposed ISMC-barrier function control compared to conventional ISMC for the FJR. This novel control approach addresses the challenges of controlling this FJR.</p>
</abstract>

This paper proposes and evaluates a novel control approach for trajectory tracking, stability enhancement, and vibration reduction of a flexible joint robot (FJR). The FJR is a 2-degree-of-freedom underactuated nonlinear system that is challenging to control due to vibration, underactuation, uncertainties, and external disturbances. The control objectives are high trajectory tracking performance together with suppressing vibration. The proposed control approach uses integral sliding mode control (ISMC) combined with a barrier function based on back-stepping. This ensures robust and smooth performance by eliminating the reaching phase where sliding mode control (SMC) is typically not robust. Robustness is thus guaranteed from the start. The FJR is modeled as a 4th-order system using Lagrangian mechanics and decomposed into two 2nd-order subsystems for control design. Sliding variables are defined for each subsystem. Using these variables, the proposed control achieves robust trajectory tracking, stability, and vibration reduction. Numerical simulations in MATLAB validate the superior performance of the proposed ISMC-barrier function control compared to conventional ISMC for the FJR. This novel control approach addresses the challenges of controlling this FJR.

Barrier Function-Based Integral Sliding Mode Controller Design for a Single-Link Rotary Flexible Joint Robot

Control and Systems Engineering Department

International Journal on Smart Sensing and Intelligent Systems

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

This paper proposes and evaluates a novel control approach for trajectory tracking, stability enhancement, and vibration reduction of a flexible joint robot...

Symbol	Description	Value
J_eq	Equivalent moment of inertia of servo motor (kg ∙ m²)	0.0018
J_arm	Moment of inertia of the link (kg ∙ m²)	0.0033
B_eq	The viscous friction coefficient of the manipulator (N ∙ m ∙ s /rad)	0.015
K_s	Joint stiffness (N/m)	1.3
K_m	Motor back-EMF constant N/(rad/s)	0.0077
K_g	High gear ratio	70
K_t	Motor torque constant (N ∙ M/A)	0.00767
R_m	Motor torque constant (Ω)	2.6
η_m	Motor efficiency	0.69
η_g	Gearbox efficiency	0.90

Controllers	Design parameters
Unactuated controller (virtual controller)	ε₁ = 0.01, λ₁ = 1, c₁ = 16, c₂ = 8
Actuated controller	ε₂ = 0.01, λ₂ = 0.01, c₃ = 12, c₄ = 7
Observer	K_o = 1000, γ_o = 100, τ_o = 0.0001

Barrier Function-Based Integral Sliding Mode Controller Design for a Single-Link Rotary Flexible Joint Robot

Article Category: Article

Publié en ligne: 04 mai 2024

Pages: -

Reçu: 13 sept. 2023

DOI: https://doi.org/10.2478/ijssis-2024-0015

Mots clés
Flexible Joint Robot, Integral Sliding Mode Control, Barrier Function, Trajectory Tracking, Vibration Reduction

© 2023 Ahmed Mohsen Mohammad et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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Figure 10:

Nominal parameters of the FJR manipulator

Controllers and observer parameters

Barrier Function-Based Integral Sliding Mode Controller Design for a Single-Link Rotary Flexible Joint Robot

Article Category: Article

Publié en ligne: 04 mai 2024

Pages: -

Reçu: 13 sept. 2023

DOI: https://doi.org/10.2478/ijssis-2024-0015

Mots clésFlexible Joint Robot, Integral Sliding Mode Control, Barrier Function, Trajectory Tracking, Vibration Reduction

© 2023 Ahmed Mohsen Mohammad et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1:

Figure 2:

Figure 3:

Figure 3:

Figure 4:

Figure 5:

Figure 6:

Figure 7:

Figure 8:

Figure 9:

Figure 10:

Nominal parameters of the FJR manipulator

Controllers and observer parameters

Mots clés
Flexible Joint Robot, Integral Sliding Mode Control, Barrier Function, Trajectory Tracking, Vibration Reduction