# Multi-Objective Collaborative Control Method for Multi-Axle Distributed Vehicle Assisted Driving
## 1 Introduction
A robust sliding mode predictive control (SMPC) strategy was proposed to solve a multi-objective multi-constraint optimization problem, which first determined the current vehicle stability based on a phase plane analysis method and combined the driver's future driving state prediction with a fuzzy control algorithm to obtain weight coefficients to coordinate AFS and DYC [11]. [PERSON] et al. [12; 13] proposed a real-time nonlinear model predictive control (NMPC) strategy to solve the direct yaw moment control problem, and for the first time, an extended/generalized minimum residual (C/GMRES) algorithm was used for nonlinear optimization and real-time solution. A real-time nonlinear model predictive control strategy combining DYC and RWS was proposed in the literature [14], using [PERSON]'s principle of minimum (PMP)-based algorithm for fast solution of nonlinear optimization problems, which has better handling stability compared to the pure DYC method. For the lower-layer torque allocation problem, the literature [15] realized the reconfiguration distribution of the lower layer motor torque by adjusting the quadratic form distribution matrix and used the sliding mode control (SMC) algorithm to calculate the modified torque to keep each tire within the optimal slip ratio. [PERSON] et al. [16] proposed a dynamic programming algorithm (DP) to solve the economical problem of torque distribution. Current research on human-machine co-driving has focused only on the allocation of human-machine driving privileges, ignoring the optimal control of vehicle dynamics. For the multi-axe heavy vehicle studied in this paper, due to the large inertia of the vehicle itself, if only the front wheel steering is used for assisted driving motion control, its handling will inevitably be poor. At the same time, when the tires enter the nonlinear region, the vehicle is also more prone to instability. Therefore, it is necessary to comprehensively consider the allocation of human-machine driving permissions and the collaborative optimization of the handling and stability performance of multi-axe vehicles in the control of assisted driving. The chassis control performance of human-machine collaborative driving conditions is also inseparable from the reasonable allocation of torque for distributed electric drive vehicles. In the study of lower-layer torque allocation, efficient torque distribution with multiple objectives such as energy saving and tire loading is still one of the difficulties in research due to the nonlinearity of the energy consumption relationship of the drive system and the redundancy of the execution components of distributed multi-axle vehicles. Therefore, a multi-objective collaborative control method for multi-axle distributed vehicle assisted driving chassis is proposed in this article, and the overall control framework is shown in Figure 1. The control method includes the fuzzy cooperative control strategy based on LTV-MPC at the upper layer and the torque distribution strategy at the lower layer. In the upper-layer controller, the LTV system control model is established first, which combines the steering model, the two-degree-of-freedom (2 DOF), model and the path tracking model. Secondly, using the phase plane analysis method, the critical conditions of vehicle stability and the linear operation of vehicle tires are analyzed. Finally, the critical stable steering angle \(\delta_{1c}\) and linear critical steering angle \(\delta_{1I}\) of the vehicle under different conditions are calibrated, and the state region of the vehicle is defined. In the fuzzy cooperative control strategy, the human-machine cooperation index \(CI\) is defined, and the assisted driving weight adjustment coefficient \(\lambda_{r}\) is obtained by fuzzy rule mapping. The stability weight adjustment coefficient \(\lambda_{\beta}\) is obtained by mapping the steering angle and the rate of the steering angle, where the membership function of the steering angle is designed based on the obtained vehicle state region.