Key Takeaways & Executive Findings
- •• Proposes a robust Tube-MPC trajectory tracking control method for 4WIS vehicles on intermittent icy and snowy roads, addressing time-varying adhesion coefficients and cornering stiffness uncertainties. • Integrates a Bi-directional LSTM neural network for online estimation of tire cornering stiffness, enhancing the accuracy of the nominal MPC model under varying road conditions. • Combines Tube-MPC with robust Sliding Mode Control to handle road irregularities, improving trajectory tracking accuracy and robustness compared to standard Tube-MPC. • Experimental results demonstrate superior trajectory tracking performance under challenging road conditions, providing a theoretical foundation for future vehicle stability and control studies.
Abstract
Four-Wheel Independent Steering (4WIS) Vehicles can independently control the angle of each wheel, demonstrating superior trajectory tracking performance under normal conditions. However, on intermittent icy and snowy roads, the presence of time-varying adhesion coefficients, time-varying cornering stiffness, and the irregularities due to ice and snow accumulation introduce multiple uncertainties into the steering system, significantly degrading the trajectory tracking performance of 4WIS vehicles. In response, this paper proposes a robust Tube Model Predictive Control (Tube-MPC) trajectory tracking control method for 4WIS. In this method, a Bi-directional Long Short-Term Memory neural network is established for online estimation of tire cornering stiffness under different road adhesion coefficients, providing accurate estimation of time-varying cornering stiffness for each wheel to mitigate the uncertainties of time-varying adhesion coefficients and cornering stiffness. Additionally, considering the road irregularities caused by snow accumulation on intermittent icy and snowy roads, a trajectory tracking controller that integrates Tube-MPC and robust Sliding Mode Control is proposed. The nominal MPC model, developed from the estimated tire cornering stiffness, utilizes the sliding surface and the optimal auxiliary control unit law for the tube is derived from the reaching law in Tube-MPC, aiming to minimize the trajectory tracking error while enhancing the controller’s robustness against road uncertainties. The experiments show that the proposed method outperforms the Tube-MPC algorithm in terms of trajectory accuracy and robustness. This method demonstrates excellent trajectory tracking accuracy under intermittent icy and snowy road conditions, and it lays a theoretical foundation for future studies on vehicle stability and trajectory tracking under such road conditions.
1. Introduction
4WIS vehicles can independently control the angle of each wheel through electrical signals, providing an optimal steering platform for intelligent driving [1, 2]. On conventional road surfaces, 4WIS vehicles can fully exploit their structural advantages, particularly in trajectory tracking control, where they often exhibit more precise tracking performance compared to traditional vehicles [3, 4]. However, on intermittent icy and snowy roads, uncertainties in road conditions, including variations in adhesion coefficients and differences in snow depth, lead to a decline in the trajectory tracking performance of 4WIS vehicles. Therefore, it is urgent to study trajectory tracking control for 4WIS vehicles under intermittent icy and snowy roads [5].
Addressing the multiple uncertainties of road conditions to achieve trajectory tracking control for 4WIS vehicles on intermittent icy and snowy roads is of paramount importance. Ensuring that these systems function optimally under various conditions plays a critical role in enhancing both performance and security.
Research on trajectory tracking control for vehicle uncertainties is divided into two main directions: trajectory tracking considering external environmental uncertainties and vehicle system modeling parameter uncertainties [6]. In studies based on modeling parameter uncertainties, Ref. [7] incorporates adaptive switching supervisory control with Lyapunov-based nonlinear tracking laws to tackle trajectory tracking issues in underactuated autonomous vehicles facing substantial modeling parameter uncertainties. In Ref. [8] state feedback control (RSC) method for trajectory tracking is proposed, comparing the performance of the MPC and RSC controllers in tracking predefined trajectories under different scenarios, and evaluating the trajectory tracking performance under uncertain road conditions. Reference [9] proposes a nonlinear model predi...
Loading authentic research manuscript (Pages 1–5)...
Xiaochuan Zhou, Ruiqi Liu, Jinyu Zhou, Ziyu Zhang, Chunyan Wang, Wanzhong Zhao (2025). Robust Tube-MPC Trajectory Tracking Control for Four-Wheel Independent Steering Vehicles on Intermittent Snowy and Icy Roads. Chinese Journal of Mechanical Engineering. https://doi.org/10.1186/s10033-025-01232-8
Research & Educational Purpose Only:The translations, structured abstracts, analytical annotations, and data reports provided by SinoTechIntel are intended exclusively for academic research, internal corporate R&D, and educational benchmarking. They do not constitute formal engineering, chemical safety, legal, or professional advice.
Copyright & Intellectual Property Notice: Original copyright of the underlying source articles and experimental data remains with the respective authors, institutions, and original publishing journals. SinoTechIntel claims intellectual property only over its proprietary translations, analytical syntheses, and AEO structured enhancements in accordance with international fair use and academic citation principles.
Frequently Asked Questions
What is the main contribution of this paper?
The paper proposes a robust Tube-MPC trajectory tracking control method for 4WIS vehicles on intermittent icy and snowy roads, integrating a Bi-directional LSTM for cornering stiffness estimation and Sliding Mode Control to handle road uncertainties, improving tracking accuracy and robustness.
How does the proposed method handle time-varying cornering stiffness?
It uses a Bi-directional Long Short-Term Memory (LSTM) neural network to estimate tire cornering stiffness online under different road adhesion coefficients, providing accurate real-time estimates for each wheel.
What are the key advantages of the proposed Tube-MPC approach?
The approach combines Tube-MPC with robust Sliding Mode Control, which enhances robustness against road irregularities and uncertainties, leading to superior trajectory tracking performance compared to standard Tube-MPC.
What are the experimental results?
Experiments show that the proposed method outperforms the Tube-MPC algorithm in terms of trajectory accuracy and robustness under intermittent icy and snowy road conditions.
What is the significance of this research for future studies?
The method lays a theoretical foundation for future studies on vehicle stability and trajectory tracking under challenging road conditions, potentially improving safety and performance of intelligent vehicles.
Related Technical Papers & Translations
Direct Repair of the Crystal Structure and Coating Surface of Spent LiFePO4 Materials Enables Superfast Li-Ion Migration
The rapid accumulation of spent LiFePO4 (LFP) cathodes from retired lithium-ion batteries necessitates the development of effective and environmental-friendly recycling strategies. In this context, direct regeneration has emerged as a promising approach for reclaiming LFP cathode materials, offering a streamlined pathway to restore their electrochemical functionality. We report an integrated regeneration protocol that simultaneously repairs the degraded crystal structure and reconstructs the damaged carbon coating in spent LFP. The regenerated cathode material had superfast lithium-ion diffusion kinetics and a stable cathode–electrolyte interface, giving a remarkable rate capability with specific capacities of 122 mAh g−1 at 5C and 106 mAh g−1 at 10C (1C = 170 mA g−1). It also maintained capacities of 110.7 mAh g−1 (5C) and 84.1 mAh g−1 (10C) after 400 cycles. It could be used in harsh environments and could be stably cycled at subzero temperatures (−10 and −20 °C) and in solid-state electrolyte batteries. Life cycle assessment combined with economic evaluation using the EverBatt model reveals that this direct regeneration approach has high economic and environmental benefits.
Oxide Semiconductor for Advanced Memory Architectures: Atomic Layer Deposition, Key Requirement and Challenges
Oxide semiconductors (OSs), introduced by the Hosono group in the early 2000s, have evolved from display backplane materials to promising candidates for advanced memory and logic devices. The exceptionally low leakage current of OSs and compatibility with three-dimensional (3D) architectures have recently sparked renewed interest in their use in semiconductor applications. This review begins by exploring the unique material properties of OSs, which fundamentally originate from their distinct electronic band structure. Subsequently, we focus on atomic layer deposition (ALD), a core technique for growing excellent OS films, covering both basic and advanced processes compatible with 3D scaling. The basic surface reaction mechanisms—adsorption and reaction—and their roles in film growth are introduced. Furthermore, material design strategies, such as cation selection, crystallinity control, anion doping, and heterostructure engineering, are discussed. We also highlight challenges in memory applications, including contact resistance, hydrogen instability, and lack of p-type materials, and discuss the feasibility of ALD-grown OSs as potential solutions. Lastly, we provide an outlook on the role of ALD-grown OSs in memory technologies. This review bridges material fundamentals and device-level requirements, offering a comprehensive perspective on the potential of ALD-driven OSs for next-generation semiconductor memory devices.
Laser powder bed fusion of biodegradable Zn-4Cu alloy: Processing, microstructure and properties
Zn's natural degradability and biocompatibility make it a promising candidate for implants, however, its mechanical properties remain insufficient for bone applications. In this study, the performance of Zn was enhanced by developing Zn-Cu alloys via laser powder bed fusion (LPBF). Optimal LPBF parameters for forming stable tracks were achieved by adjusting laser power and scanning speed. Under optimized conditions of 100 W and 100 mm/s, high-density (99.58%) Zn-Cu alloys with improved hardness (68.2HV) and yield strength (160 MPa) were achieved. These improvements are attributed to solid solution strengthening, segregation strengthening, and grain refinement. The Zn-Cu alloys also demonstrated favorable degradation behavior, with a rate of 0.16 mm/year. This degradation is primarily driven by micro-galvanic corrosion between the CuZn5 phase and Zn matrix, along with refined grains and increased grain boundary density. This work demonstrates a viable strategy for fabricating Zn-based implants with enhanced structural integrity and mechanical performance via LPBF.