The integration of motion planning and control within a unified architecture based on reachability theory provides an effective approach to extending the autonomous motion capability boundaries of distributed drive electric vehicles (DDEVs). This architecture is further enhanced by embedding forward set propagation methods into the dynamics analysis of DDEVs. The analytical expression of forward reachable sets (FRSs), the real-time processing of reachability constraints, and the design of integrated planning-control frameworks remain challenging. To address these challenges, this paper proposes a reachability-constrained motion planning and control integration framework (RC-MPCI) for DDEVs. The proposed RC-MPCI features strong interpretability, rigorous safety guarantees, and computational efficiency. First, a maneuver-oriented vehicle motion model is established to construct the closed-loop system dynamics. Subsequently, an FRS computation method based on sum-of-squares programming (SOSP) is proposed. It formulates an analytical expression of dynamic reachable boundaries that accounts for multi-actuator coordination, and tracking error models are introduced to ensure the reachability of the closed- loop system. Then, a constraint optimization strategy based on collision-free tunnels (CFTs) is designed, within which online motion planning and control methods are developed under a receding horizon optimization framework. Finally, the effectiveness and robustness of the proposed RC-MPCI are confirmed through virtual simulations and hardware-in-the-loop (HIL) tests. This framework, based on reachability theory, provides both theoretical and technical foundations that enable safe and efficient autonomous motion of DDEVs in highly dynamic environments.

The stability region is an important criterion in the active safety system of vehicle. Extensive literatures have developed various stability regions for the centralized driving vehicle (CDV). However, seldom of them make a thorough analysis of the stability for distributed driving electric vehicle (DDEV). Especially when the direct yaw moment control (DYC) intervenes, the stability region of DDEV shows a huge difference compared with CDV. So far, most researches on the stability control of DDEV are still based on the traditional CDV stability region, which leads to the conservation of controller design. To this end, a dynamic and analytical stability region of DDEV is firstly developed in this paper. By employing sum of square programming (SOSP) algorithm, we choose a high-order Lyapunov function to make a precise estimation of the stability region. A novel DC shape function is proposed to reduce the conservation of estimation when DYC involves. To ensure the real-time performance for control application, Long Short Term Memory (LSTM) neural network is employed to fit the coefficients of Lyapunov function, as well as enable the dynamic shifting with driving conditions. Based on the aforementioned stability region, we develop a MPC controller to ensure the stability and tracking performance during handling limit. Both simulations and road tests demonstrate that the developed stability region could effectively restraint the vehicle states from diverging, which enhances vehicle maneuverability while ensuring vehicle stability.Note to Practitioners—Handling stability is a crucial factor which concerns the safety of vehicle. Almost all vehicles should be equipped with active safety system, such as Electronic Stability Program (ESP) of Bosch and Electronic Stability Controller (ESC) of GM. They collect the real-time vehicle states by the Built-in sensors. Meanwhile, they calculate the current stability margin according to the driver’s control input and analyze the deviation of the vehicle states to decide whether the active control is needed to maintain the stability of vehicle. This system is established well in CDV. However, for DDEV, it has another input of DYC in addition to wheel steering angle, which changes the dynamic characteristic of vehicle. This means that the stability margin of traditional ESP is inaccurate when the DYC intervenes, which will lead to the misjudgment of instability or the unsafety of vehicle. This paper develops an analytic stability region of DDEV and describes the stability margin with different values of DYC, which could adapt to varying conditions. This technology fills the gap of the stability determination of DDEV and has a good application prospect in the active safety system of DDEV.

Benefited from the advantage of four-wheel independent driving, Distributed Driving Electric Vehicle (DDEV) can precisely generate direct yaw moment (DYC) to influence lateral motion. In coordination with Active Front Steering (AFS), this allows for decoupled control under normal driving condition. However, DYC is fundamentally generated through the longitudinal forces of the tires, so its impact on dynamic stability under handling limit cannot be ignored. Particularly, the intervention of DYC changes the vehicle’s safety boundary, a factor seldom addressed in existing research. Extension literatures use the safety boundaries of traditional Centralized Driving Vehicle (CDV) to design stability controller for DDEV, resulting in conservative or aggressive performance. To this end, we propose a hierarchical safety-critical controller for DDEV during handling limit. A feedback control law based on high-order polynomials is constructed, and the closed-loop stability boundary is expanded using the Sum of Square Programming (SOSP) algorithm. Additionally, DYC is included in the stability margin assessment, and a safety envelope boundary suitable for DDEV is reconstructed. This safety boundary is used as a state constraint to design a safety-critical controller based on ODCBF. Simulation and experiments show that the proposed algorithm can widen the stable yaw rate boundary by 15% under high-speed continuous steering condition, enhancing the vehicle’s maneuverability while ensuring safety.

Accurately obtaining motion states of surrounding vehicles (SVs) plays a pivotal role in achieving the safety and closed-loop optimality of intelligent vehicles (IVs) for motion control, where the connected environment serves as the hardware foundation. To mitigate data collisions and alleviate communication burdens, this paper introduces a novel protocol-based fusion estimator (PBFE) for estimating the motion states of SVs. Based on the time-varying nonlinear system models, RRP-based cubature Kalman filter (CKF) and WTODP-based CKF are designed, which embed communication protocols, i.e., round-robin protocol (RRP) and weighted try-once-discard protocol (WTODP), into the variable-structure CKF framework. Then, mathematical definitions and descriptions of RRP and WTODP are provided, which are utilized to adjust the data transmission mechanism from sensors to estimators, leading to the establishment of a novel protocol-based measurement model. Subsequently, to preemptively quantify the performance impact of communication protocols on PBFE from a theoretical perspective, the boundedness analysis of the estimation error is rigorously derived. Conclusively, virtual simulations (VSs) based on high-fidelity models from CarSim and Matlab/Simulink, covering diverse real-world driving scenarios, are conducted to compare the protocol-based CKF method with the protocol-based unscented Kalman filter (UKF) method. Furthermore, the robustness and stability of the proposed approach are verified through practical on-road tests (ORTs).

Abstract The variational level set model has been widely used in image segmentation. However, its performance is significantly hindered by bias fields and noise within the images. To address these limitations, we introduce a novel hybrid variational level set model based on dual Gaussian distribution fitting (DGDF) energy in this paper. The DGDF energy integrates both local and global Gaussian distributions. The local energy is derived from the original image, while the global energy employs the corrected image, enabling effective segmentation of images with intensity inhomogeneity. Furthermore, the model demonstrates low sensitivity to weighting parameters and robust performance for noisy images. We develop an alternating iteration algorithm that combines variational methods with gradient descent to efficiently solve the proposed model. Experimental results validate the effectiveness of the model and the algorithm. In addition, the proposed model shows competitiveness on test images and three datasets compared to several state‐of‐the‐art models, including other variational level set models and deep learning‐based techniques.

Abstract Active contour based methods are effective models for image segmentation. However, they always suffer from the limited performance due to the presence of noise and intensity inhomogeneity. To solve this problem, a kernel metric induced local image fitting (KLIF) variational model is proposed in this paper. Firstly, a kernel metric induced local fitting image (KLFI) is introduced by minimising a kernel metric based energy. The combination of the kernel metric and the local fitting image enables the model to be more robust to the noise and intensity inhomogeneity. And then, using the KLFI, a variational level set model that is a squared l 2 distance between the KLFI and the original image is constructed. Two regularisation terms are employed in the model to keep the level set function to be stable during the evolution. At last, an alternating iterative algorithm combining with fixed‐point iteration and gradient descent of three‐step time‐splitting is introduced to solve the proposed model. The experimental results show the effectiveness of the proposed model for image segmentation in the presence of noise and intensity inhomogeneity, and demonstrate the competitive performance over several state‐of‐the‐art variational models in term of accuracy and robustness.