1. Introduction
The Distributed Drive Electric Vehicle (DDEV) equipped with four hub motors has attracted significant attention in the academic and automotive industries [
1,
2]. Compared to traditional vehicles with centralized traction systems, each motor in a distributed vehicle can independently control torque and facilitates optimal distribution, providing an excellent research platform for improving vehicle maneuverability and lateral stability [
3,
4]. As a crucial component of vehicle active safety systems, the Direct Yaw Control (DYC) system enhances steering characteristics by applying varying torques to the wheels for generating the necessary additional yaw torque, which is widely utilized for improving vehicle handling stability [
5,
6].
Currently, various control strategies have been proposed for the DYC of a DDEV, such as proportional integral derivative (PID) controllers [
6], linear quadratic regulators (LQRs) [
7,
8], and sliding mode control (SMC) [
9,
10] and Model Predictive Control (MPC) [
11]. Each controller has its own specific advantages and disadvantages. Lorenzo Wang [
12] researched yaw angle control strategies using torque vectoring control methods on dual rear-wheel electric vehicles. Hu [
13] proposed a novel hierarchical DYC architecture, and the simulation results indicated that this method significantly improves the yaw rate and sideslip angle of the vehicle under low adhesion road conditions and double-lane change scenarios. Yu [
14] designed a control strategy to enhance vehicle maneuverability, which involves a torque vectoring control strategy based on an optimized reference model for the yaw rate to improve handling sensitivity. Woo [
15] proposed an active differential control system to improve handling and acceleration performance. Ahmadian [
16] proposed a maneuverability control strategy based on estimated information, using a model reference control method to design a controller that can robustly track the reference yaw rate. ZHANG [
17] analyzed the impact of an active yaw moment on vehicle steering characteristics, and proposed a desired yaw motion value considering a transient response to improve vehicle maneuverability. Although these methods can effectively enhance vehicle maneuverability, they do not consider reliable safety constraints, and the vehicle is likely to become unstable under extreme conditions.
To enhance vehicle stability, it is crucial to accurately determine the vehicle operating state. The phase plane method is a widely used graphical stability assessment tool, which primarily includes the
phase plane method, the
phase plane method, and the
phase plane method [
18]. Compared to other types of phase planes, the equilibrium points of the
phase plane always lie on the horizontal axis, making it more suitable for analyzing lateral vehicle dynamics and beneficial for delineating stable trajectory regions. Konghui Guo [
19] used a two-degree-of-freedom vehicle model and a nonlinear tire model to analyze the vehicle state changes in the phase plane, graphically presenting stable and unstable regions. B. Yang [
20] designed a weighting factor to coordinate the coupling effects between differential drive-assisted steering and vehicle motion in phase plane stability analysis. However, stability regions are defined solely based on vehicle speed and tire–road friction, omitting the impact of the front wheel steering angle, which limits the accuracy of stability evaluations [
21]. W. Chen [
22] defined the stability region as an ellipse, but this approach imposes a significant burden on polynomial fitting calibration, which limits its application. Currently, most of the literature still uses the double-line method to establish the stability boundaries of the
phase plane [
19]. However, this stability region still encompasses unstable regions that exceed the vehicle lateral acceleration limits, failing to accurately delineate stability boundaries [
23]. Additionally, part of the stability region defined by the twin-line method falls within the nonlinear range of the tires, where the objectives of maneuverability and stability remain inconsistent [
24]. Therefore, when establishing the
phase plane stability boundaries in this paper, it is necessary to consider yaw rate and maneuverability constraints.
After determining the vehicle state using stability boundaries, maneuverability and stability control can be implemented. Currently, numerous control strategies have been applied to the maneuverability and lateral stability of DDEV. L. Zhang [
25] proposed a torque vectoring controller based on adaptive second-order sliding mode control to improve vehicle maneuverability and stability. H. Alipou [
26] introduced a lateral stability control method for four-wheel-drive vehicles on slippery roads based on improved sliding mode control, which is faster and more robust than classical sliding mode control. Xuewu [
27] presented a vehicle stability control strategy based on adaptive radial basis function network sliding mode theory to enhance dynamic stability under handling limits. Although sliding mode control and its variants have been widely applied and exhibit good performance, they suffer from model errors and high-frequency chattering. S. Ding [
28] designed a second-order sliding mode control strategy for a DYC controller, successfully addressing the chattering issue in traditional SMC and effectively enhancing the robustness of the controller. However, while this method resolves the chattering problem, it cannot handle system control and state constraints. In contrast, MPC is better equipped to handle system input and state constraints. Ningyuan [
29] proposed a fast MPC method for DDEV torque distribution, which minimizes tire slip power loss and enhances vehicle stability. Jalali [
30] introduced an integrated speed estimation and MPC system that maintains a small sideslip angle under various road conditions by tracking the adjusted reference yaw rate.
Although the aforementioned literature addresses control for maneuverability and stability, most methods use fixed weights for control and rarely consider the coordination between maneuverability and lateral stability. Typically, the yaw rate represents vehicle maneuverability, while the sideslip angle represents vehicle stability. Controlling the sideslip angle when the vehicle is stable can suppress maneuverability, and controlling the yaw rate when the vehicle is unstable can suppress stability. To address this issue, B. Lenzo [
31] proposed a normalized reference yaw rate that combines the yaw rate and sideslip angle for use in Direct Yaw Control (DYC). F. Assadian [
32] used the tracking errors of the yaw rate and sideslip angle to calculate two indicators, and these indicators are controlled by threshold values. When either indicator exceeds its threshold, the DYC (Direct Yaw Control) controller will be activated. However, the simple Boolean activation of DYC can cause motor torque fluctuations, thus affecting driving comfort and motor lifespan. Therefore, to better coordinate vehicle maneuverability and lateral stability, this paper emphasizes the need to establish more comprehensive stability boundaries. Additionally, considering the smooth transition of vehicle torque during control target switching, a smoother control target switching strategy must be developed.
To address the issues mentioned above, this paper proposes a coordinated manipulation stability control framework based on AMPC, as shown in
Figure 1. This framework is mainly divided into three parts: Dynamic Supervision Layer, Online Optimization Layer, and Low-level control Layer. The dynamic supervision layer establishes the
phase plane stability boundary under different conditions and designs variable weight factors based on the stability boundary and vehicle operating status. The online optimization layer constructs an adaptive AMPC strategy for target weights, adjusting the control weights of maneuverability and lateral stability in real time based on the variable weight factors provided by the dynamic supervision layer. The low-level control layer precisely allocates the driver’s required driving force and additional yaw moment using torque distribution error and tire utilization as cost functions. The main contributions of this paper are:
This paper proposes a control framework based on AMPC for coordinating handling stability, consisting of a dynamic supervision layer, online optimization layer, and low-level control layer. This framework uses the AMPC strategy to coordinate maneuverability and lateral stability, enhancing the vehicle handling stability.
In establishing the phase plane stability boundary, the influence of vehicle speed, front wheel steering angle, and road adhesion coefficient on the stability boundary was considered, along with added constraints on the yaw rate and maneuverability to redefine the stability boundary. Based on this, variable weight factors are dynamically quantified in real time, facilitating the coordination of maneuverability and stability control in the online optimization layer.
A target weight-adaptive AMPC strategy was established, which can adjust the control weights for maneuverability and lateral stability in real time based on the vehicle state, thereby enhancing maneuverability under normal conditions and stability under extreme conditions.
The rest of this paper is organized as follows.
Section 2 introduces the vehicle and tire models.
Section 3 elaborates on the design of the hierarchical control architecture.
Section 4 presents the simulation results.
Section 5 provides a summary of the entire paper.
5. Conclusions
This paper proposes a control strategy based on AMPC to coordinate maneuverability and lateral stability, enhancing vehicle handling stability under various conditions. In establishing the phase plane stability boundary, we introduced the yaw rate and maneuverability limits to redefine the stability region. Based on this stability boundary, we dynamically quantified the variable weight factors in real time, thereby constructing the target weight adaptive AMPC strategy. This strategy can adjust the control weights for maneuverability and lateral stability in real time based on the vehicle state, thereby improving the overall handling stability. Simulation results show that, compared to the traditional MPC strategy, under low adhesion double lane change and low adhesion fishhook conditions, the proposed AMPC strategy significantly enhances lateral stability while maintaining maneuverability, and effectively reduces the additional yaw moment. Under the medium adhesion double lane change and high adhesion fishhook conditions, this strategy not only improves maneuverability but also significantly reduces the additional yaw moment requirements.
However, this control strategy has not yet considered longitudinal stability control. Future work will focus on the study of longitudinal stability control, validation on actual vehicles, and improving the robustness of the strategy against parameter uncertainties and external disturbances.