# Multi-Objective Collaborative Control Method for Multi-Axle Distributed Vehicle Assisted Driving
## 2 Fuzzy Cooperative Control Strategy Based on LTV-MPC
### Fuzzy Collaborative Control Strategy  
The fuzzy collaborative control strategy includes four input parameters, namely the human-machine cooperation index \(CI\) and the assisted driving weight adjustment coefficient at the previous moment \(\lambda_{r,last}\), the vehicle's steering angle \(\delta_{1}\) and angle change rate \(\hat{\delta}_{1}\). The input variables are inferred through two fuzzy rule bases, namely human-machine conflict and handling stability, to obtain the assisted driving weight adjustment coefficient \(\lambda_{r}\) and the stability weight adjustment coefficient \(\lambda_{\beta}\), in order to achieve human-machine collaborative control and handling stability collaborative control. The following are introductions to two fuzzy control strategies. (1) **Fuzzy strategy for human-machine collaboration**  
The human-machine cooperation index \(CI\) consists of three parts, namely the steering torque index \(CI_{M}\), the steering torque change rate index \(CI_{\Delta M}\), and the human-machine target path consistency index \(CI_{path}\), expressed as follows:  
\[CI=CI_{M}\cdot CI_{\Delta M}\cdot CI_{path} \tag{19}\]  
The definition of \(CI_{M}\) is related to the torque difference between humans and machines. Under cooperative driving, the torque direction is the same, while on the contrary, the torque is opposite and conflicting. The definition of \(CI_{M}\) is as follows:  
\[CI_{M}=1-\frac{|\overline{T}_{a2}-(k_{b}+1)\cdot\overline{T}_{b}|\cdot| \overline{T}_{b}|}{\left(|\overline{T}_{a2}|+(k_{b}+1)\cdot|\overline{T}_{b}| \right)\cdot|\overline{T}_{b}|} \tag{20}\]  
where \(\overline{T}_{a2}\) is the average value of the torque auxiliary component, and \(\overline{T}_{b}\) is the average value of the driver's output torque range. At the same time, the direction of change in human-machine torque also reflects the cooperative state of the human-machine. The steering torque change rate index \(CI_{\Delta M}\) is used to supplement the lack of the human-machine conflict description in \(CI_{M}\), defined as:  
\[CI_{\Delta M}=1-\frac{\left|\hat{\mathbf{r}}_{a2}-(k_{b}+1)\cdot\hat{\mathbf{T}}_{b} \right|\cdot|\overline{T}_{b}|}{\left(|\overline{T}_{a2}|+(k_{b}+1)\cdot| \overline{T}_{b}|\right)\cdot|\overline{T}_{b}|} \tag{21}\]  
In the formula, \(\hat{T}_{a2}\) and \(\hat{T}_{b}\) are the rate of change of the torque auxiliary component and the rate of change of the driver's output torque, while \(\overline{\hat{T}}_{a2}\) and \(\overline{\hat{T}}\) are the average values of the range of torque change rates. The human-machine target path consistency index \(CI_{path}\) in the future can be used as one of the evaluation factors for its cooperation possibility, and the specific definition of \(CI_{path}\) is:  
\[CI_{path}=1-\frac{\sum_{i=1}^{N_{m}}(\mathcal{Y}_{i}-y_{i})}{(N_{w}\cdot v)} \tag{22}\]  
where \(Y_{i}\) and \(y_{i}\) are the intelligent assistance system and the driver's intended path point, \(N_{n}\) is the length of the path point, and \(v\) is the normalization coefficient. The range of variation for \(CI_{M}\), \(CI_{AM}\), \(CI_{path}\), and \(CI\) is \([0,1]\). When \(CI\) approaches 0, it indicates a significant conflict in the willingness of human-machine behavior, while on the contrary, it indicates that the human-machine is in a highly cooperative state. The universe of the human-machine cooperation index \(CI\) is \([0,1]\). The set of fuzzy language values is defined as \(I_{1}\in\{\text{LC},\text{MLC},\text{MC},\text{MHC},\text{HC}\}\), corresponding to low, medium-low, medium, medium-high, and high cooperation, respectively. The specific membership function design is shown in Figure 7a. The input variable \(\lambda_{r,last}\) is the assisted driving weight adjustment coefficient at the previous moment, and the assisted driving weight adjustment coefficient \(\lambda_{r}\) of the current moment needs to be determined based on the human-machine cooperation index \(CI\) of the current moment in \(\lambda_{r,last}\).