# Multi-Objective Collaborative Control Method for Multi-Axle Distributed Vehicle Assisted Driving
## 1 Introduction  
Electrification and intelligence are the two major directions for the future development of automobiles [1]. Electric transmission technology not only solves energy and pollution problems but also has more advantages than conventional vehicles. For example, distributed electric drive technology is a new configuration of electric transmission technology, eliminating the need for transmissions and differentials in traditional drive systems, saving chassis space, and improving transmission efficiency. And distributed drive technology enables independent and precise control of the torque of each wheel drive, which helps achieve multi-objective coupling control of vehicle handling, safety, and other aspects [2, 3]. The intelligence level of multi-axle heavy vehicles is relatively low, and their larger body size and higher cockpit increase the difficulty of driver control and also increase driving risks. Assisted driving technology, as an important part of intelligent driving technology, is a compromise solution that involves the driver and the machine completing driving tasks together [4, 5]. It helps to improve the driving safety of multi-axle heavy vehicles before achieving fully automated driving. Assisted driving can be divided into two forms: indirect assisted driving and direct assisted driving [6; 7]. Direct assisted driving is where the control applied by the driver and the assisted system is coupled and applied to the actuator, such as the electric power steering system (EPS). In this mode, the driver can simultaneously perceive the auxiliary torque applied by the system. In contrast to indirect assisted driving, the driver has ultimate control of the vehicle, while the continuous tactile feedback helps maintain the driver's level of presence in the loop and enhances the driver's trust in the system. Of course, inconsistent human-machine intentions in the assisted driving process can lead to control conflicts, and this has been the subject of much research. The authors of [8] first established a driver's two-point preview model, which is combined with the U-shaped function method to characterize the driver's assistance needs. Then, the Takagi-Sugeno multi-model method was used to achieve assisted lane maintenance and obstacle avoidance for the driver. The authors of [9] defined the driver's activity and human-machine cooperation index and used fuzzy logic to adjust assistance weights in real time. It finally used LMI optimization to design an adaptive shared controller, ensuring closed-loop stability while greatly reducing human-machine conflicts during coupled driving processes. Professor [PERSON]'s team has conducted a lot of research on direct assisted driving strategies related to game theory. They first used game theory to analyze human-machine driving rights interactions and established four interaction paradigms: distributed, non-cooperative Nash, non-cooperative Stackelberg, and cooperative Pareto [10]. Many scholars have researched multi-objective optimal control of distributed vehicle dynamics, aiming to improve the safety, stability, handling, and energy economy of the vehicle. Hierarchical control structures are currently the most widely used due to their flexibility in control design, clear division of labor, and efficient operation. Hierarchical control is generally divided into upper and lower layers, where the upper layer tracks or optimizes target variables related to vehicle dynamics, and the lower layer distributes torque. The core of the upper layer controller is direct yaw moment control (DYC), as well as the control forms derived from DYC, such as active front wheel steering (AFS) combined with DYC, active rear wheel steering (RWS) combined with DYC, etc.