Research on Finite-Time Adaptive Robust Trajectory Tracking Control for Dual-Arm Space Robots

Research Background and Problem

With the rapid development of space technology, space robots are playing an increasingly important role in on-orbit servicing, satellite assembly, spacecraft refueling, and other tasks. However, space robot systems face numerous challenges when performing tasks, particularly the friction nonlinearity of the base actuator and the uncertainty of external time-varying disturbances, which severely affect the system’s trajectory tracking performance. Traditional control methods often fall short in addressing these issues, especially in tasks requiring high precision and high dynamic performance. Therefore, effectively compensating for these nonlinear frictions and external disturbances to enhance the trajectory tracking capability of space robots has become a hot research topic.

This study focuses on the Dual-Arm Space Robot (DSR) system and proposes a Finite-Time Adaptive Robust Control (FTARC) method based on Single Gimbaled Control Moment Gyroscopes (SGCMGs). The aim is to address the impact of SGCMGs friction nonlinearity and external disturbances on system performance, thereby achieving high-precision joint angle trajectory tracking.

Paper Source and Author Information

This paper is co-authored by Lu Wang, Liaoxue Liu, and Zhengrong Xiang, all from the School of Automation at Nanjing University of Science and Technology, China. The research was accepted on February 24, 2025, and published in the journal Nonlinear Dynamics, with the DOI number 10.1007/s11071-025-11055-w. The study was supported by the National Natural Science Foundation of China, the Natural Science Foundation of Jiangsu Province, and the Fundamental Research Funds for the Central Universities.

Research Process and Detailed Methodology

1. System Modeling and Problem Description

The study first conducted dynamic modeling of the DSR system, with particular attention to the friction characteristics of SGCMGs. SGCMGs, as the base actuator, have their friction nonlinearity described by the LuGre friction model. Unknown parameters in the friction model are estimated through adaptive update laws, while the upper bound of external disturbances is also estimated and used for compensation to reduce their adverse effects on the system. The system’s dynamic equation can be expressed as:

$$ D(q)\ddot{q} + H(q, \dot{q})\dot{q} = \tau + d $$

where $D(q)$ is the inertia matrix, $H(q, \dot{q})$ is the centripetal and Coriolis force matrix, $\tau$ is the control torque, and $d$ is the external disturbance.

2. Controller Design

To address the aforementioned issues, the study proposes a Finite-Time Adaptive Robust Controller (FTARC). The controller design is based on Lyapunov stability theory, and by introducing an auxiliary vector $r$, a finite-time convergence control law is designed. The control law includes a convergence term $u_r$ and a model compensation term $u_c$, with the specific form as follows:

$$ u = u_c + u_r $$

Here, the convergence term is used to accelerate error convergence, while the model compensation term is used to reduce the effects of friction nonlinearity and external disturbances. Adaptive update laws are employed to estimate unknown parameters and the upper bound of disturbances, ensuring the system’s robustness.

3. Stability Analysis

Using a Lyapunov function, the study proves that the proposed controller can achieve practical finite-time stability for the system. Specifically, the system’s trajectory tracking error can converge to an arbitrarily small neighborhood containing the origin within a finite time. This conclusion is verified through rigorous mathematical derivation and theorem proof.

4. Numerical Simulation Validation

To validate the performance of the proposed controller, the study conducted numerical simulations in two scenarios. The simulations compared the proposed FTARC method with the existing Non-Singular Fast Terminal Sliding Mode Control (NFTSMC) method. The results show that FTARC outperforms NFTSMC in both dynamic and steady-state performance, particularly in trajectory tracking accuracy and error convergence speed.

Main Results and Conclusions

1. Simulation Results

In the first simulation scenario, the system’s initial attitude angles were $[-0.5, 0.65, 0.25, 0.55, 0.35]$ rad, and the initial angular velocities were $[0, 0, 0, 0, 0]$ rad/s. The simulation results show that the FTARC method can converge the system’s attitude error to within $\pm3 \times 10^{-3}$ rad in 10 seconds, while the NFTSMC method’s convergence error range is $\pm7 \times 10^{-3}$ rad. Additionally, the joint trajectory tracking error of the FTARC method can reach as low as $\pm7 \times 10^{-4}$ rad, significantly better than the $\pm5 \times 10^{-3}$ rad of NFTSMC.

In the second simulation scenario, the system’s initial attitude angles were $[0, 3\pi/4, -\pi/4, \pi/4, \pi/4]$ rad, and the initial angular velocities were $[0, 0, 0, 0, 0]$ rad/s. The simulation results show that the FTARC method can converge the system’s attitude error to within $\pm7 \times 10^{-4}$ rad in 2.5 seconds, while the NFTSMC method’s convergence error range is $\pm3 \times 10^{-4}$ rad.

2. Conclusions

This study proposes a Finite-Time Adaptive Robust Control method based on SGCMGs, effectively addressing the friction nonlinearity and external disturbance issues in the DSR system. Through theoretical analysis and numerical simulations, the study demonstrates the superiority of the proposed controller in trajectory tracking accuracy and error convergence speed. This research provides new ideas and methods for the control of space robot systems, offering significant theoretical and practical value.

Research Highlights

1. Innovative Control Method: For the first time, the Finite-Time Adaptive Robust Control method is applied to the DSR system, proposing a controller design based on SGCMGs.
2. Friction Nonlinearity Compensation: Friction parameters are estimated through adaptive update laws, effectively compensating for the impact of SGCMGs friction nonlinearity on system performance.
3. External Disturbance Suppression: A method for estimating the upper bound of disturbances is designed, successfully suppressing the interference of external time-varying disturbances on the system.
4. High-Performance Simulation Validation: Numerical simulations validate the superiority of the proposed controller in both dynamic and steady-state performance, particularly in trajectory tracking accuracy and error convergence speed.

Research Significance and Value

The findings of this study not only provide new theoretical support for the control of DSR systems but also have broad application prospects. The proposed control method can be applied to space tasks such as on-orbit servicing, satellite assembly, and spacecraft refueling, enhancing the operational accuracy and reliability of space robot systems. Furthermore, the proposed adaptive robust control framework can be extended to the control of other complex nonlinear systems, offering significant academic and engineering application value.