Robust Path-Following Control for Autonomous Ground Vehicles Using SNFTSM

By Soham NandiReviewed by Susha Cheriyedath, M.Sc.Feb 16 2024

In an article published in the journal Mathematics, researchers introduced a finite-time robust path-following control strategy for perturbed autonomous ground vehicles (AGVs). This approach featured a self-tuning nonsingular fast-terminal sliding manifold (SNFTSM) to enhance convergence and tracking accuracy. A high-gain disturbance observer (HGDO) estimated uncertain dynamics and disturbances, compensating for control input. Integration of a super-twisting algorithm (STW) reduced chattering in control signals and trajectory.

Background

The rapid progress in artificial intelligence (AI), smart cities, and self-driving vehicles has significantly propelled the application of AGVs across various domains. Path-following control in AGVs is crucial for ensuring safety and efficiency, garnering considerable attention from researchers. While existing approaches effectively address position and orientation errors in path following, system stability is often overlooked, especially in the context of complex multi-input–multi-output nonlinear systems.

Sliding-mode control (SMC) has emerged as a robust choice for controlling AGVs, yet challenges persist, such as the finite-time convergence issue associated with linear sliding surfaces. Terminal sliding mode control (TSMC) and its fast variant (FTSMC) have been introduced to enhance convergence speed, but they may suffer from singularity problems. This paper introduced an SNFTSM to address these limitations, offering robust control with fast convergence, singularity avoidance, and high performance against uncertainties.

Integrating an HGDO and the STW further contributed to reducing chattering and enhancing control accuracy. The proposed framework was theoretically analyzed for global finite-time convergence and stability, addressing gaps in previous approaches. The researchers aimed to provide a comprehensive solution to the challenges in the AGV path following control, offering improved performance and robustness in the presence of uncertainties and disturbances.

The Approach

The research introduced a control approach for the dynamics of a general robot system. The dynamic model was formulated as a set of equations involving position, velocity, and acceleration, considering factors like inertia, centripetal and Coriolis effects, input matrix, kinematic constraints, and disturbances. The proposed approach aimed to achieve fast and precise tracking within a finite time frame.

The control approach involved a novel SNFTSM, designed to ensure fast finite-time convergence and singularity avoidance. The SNFTSM incorporated self-tuning gains to adapt to system errors, promoting faster convergence. Theoretical proofs established the effectiveness of this approach, guaranteeing rapid convergence of the system error within a finite time.

The control framework integrated the SNFTSM with an HGDO and an STW. The HGDO estimated and compensated for lumped uncertainties, enhancing tracking precision. Additionally, the STW was introduced to eliminate chattering in the control system, dynamically adjusting control signals based on the sign of the sliding variable.

The combination of the SNFTSM, HGDO, and STW contributed to a comprehensive control strategy that not only achieved fast and precise tracking but also effectively handled disturbances and minimized chattering. The proposed approach enhanced the overall performance and stability of the robotic system in diverse operational scenarios.

Numerical Examples

The provided numerical example evaluated a proposed control framework for an AGV system. The framework was compared against existing control methods, namely nonlinear fast terminal sliding mode control (NFTSMC) and adaptive fast terminal sliding mode control (AFTSMC), to assess its response speed, accuracy, and efficiency in mitigating chattering. The scenario involved the AGV tracking a lemniscate trajectory on an incline. The controllers were integrated with the STW algorithm and compared with and without incorporating an HGDO.

The parameters and system matrices were specified, considering AGV dynamics, wheel properties, and environmental factors. The trajectories of the AGV under different controllers were presented, showcasing the proposed control scheme's superior efficiency in output response. The tracking errors and cross-track errors were analyzed, revealing the proposed controller's faster convergence rate compared to AFTSMC, which was prone to singularity issues.

The control input signals and chattering phenomenon were illustrated, demonstrating the effectiveness of the proposed approach in eliminating chattering. The HGDO technique's estimation performance was evaluated, showing an accurate estimation of uncertainties. Performance indices, including integral of absolute square values of tracking error and control efforts, confirmed the proposed control framework's effectiveness in achieving minimal errors with optimal control efforts. Overall, the proposed control scheme, integrated with STW and HGDO techniques, proved to be a robust and efficient solution for AGV systems, offering improved tracking performance and disturbance estimation.

Conclusion

In conclusion, the authors introduced a control scheme based on sliding mode control with a nonsingular fast terminal, SNFTSMC, for an AGV. The proposed approach demonstrated noteworthy advantages, including finite-time convergence to the sliding phase equilibrium, effective chattering reduction in trajectory, successful estimation of uncertainties and disturbances using the HGDO technique, and elimination of singularity in the sliding manifold. The system's stability was verified through Lyapunov theory in numerical simulations. Despite the generality of the proposed approach, the sliding surface design can be simplified for specific systems.