# Vehicle Motion Control for Overactuated Vehicles to Enhance Controllability and Path Tracking
## 2 Control Architecture  
The integrated control of all actuators, while simultaneously tracking a reference path for autonomous path following, can be achieved using a single controller. However, employing a single controller in this manner imposes limitations on the modularity and increases the computational demands [18]. Therefore, in this paper, a modular control architecture is proposed that separates CA from the path tracking task. Additionally, it enables manual vehicle control without modifying the control architecture. However, CA for manual driving is not within the scope of this work. This approach utilizes 4 WS and wheel-independent 4 WD  
* to optimally allocate TV and rear-wheel steering (RWS) to track the (linear) reference vehicle behavior with respect to handling using MF and CA, and
* to utilize this reference vehicle behavior within the MPC framework to create a fast and robust path tracking controller. The architecture in this paper follows an upstream control approach with layered vehicle control [3; 23], as shown in Figure 2. Global demands are refined into actuator commands in lower control layers. Key layers include the supervision strategy, high-level control, and the CA layer. Detailed views of the high-level control and CA are provided in Figure 3.  
The control objective is to follow a reference path described by the path length \(s\), curvature \(\rho(s)\) and reference vehicle velocity \(V_{\text{ref}}(s)\) given the current vehicle state, heading error \(\theta\) and lateral error \(e\). The high-level control comprises the LTV-MPC and MF. Unlike nonlinear MPC, this approach results in a convex quadratic program (QP) with linear constraints, allowing for efficient and robust solvers and long prediction horizons in the MPC. Consequently, the high-level control does not account for nonlinearities such as tyre saturations and overactuation. These aspects are accounted for in the CA, which is formulated as a nonlinear optimization problem without preview, being less computationally expensive than MPC. Both layers are connected through global demands for the longitudinal force \(\overline{\Sigma F}_{x}\), lateral force \(\overline{\Sigma F}_{y}\) and yaw moment \(\overline{\Sigma M}_{z}\) generated by the MF, aiming to align the generated vehicle response with the expected reference vehicle response in the MPC. Considering the desired linear reference vehicle behavior, a two-wheel vehicle model with linear tyre characteristics is sufficient to design the MPC and MF; see Figure 4a. The planned trajectories of the MPC are constrained within a stability envelope (SE) to address vehicle stability concerns related to tyre staturations [12]. Leveraging the results of [19], which demonstrated the improved controllability of overactuated vehicles with 4 WS and TV, and phase plane studies presented in later sections, this work extends the SE limits to accommodate overactuation capabilities. The MPC outputs are the front wheel steering (FWS) speed \(\dot{\delta}_{f}\) and drive force \(F_{d}\) to maintain the vehicle velocity given the vehicle state, current path errors \(\theta\) and \(e\) and a segment of the reference path by \(V_{\text{ref}}\) and \(\rho\) comprising sampled points originating from the current vehicle position and extending until a look-ahead distance; see Figure 3.  
In the subsequent CA layer, an optimal CA problem is employed to optimize the tyre force utilization with RWS and TV and trim the vehicle to the desired reference vehicle behavior [24]. Therefore, a four-wheel planar vehicle model is employed for the CA considering the 4 WS, tyre load transfer and nonlinear tyre characteristics; see Figure 4b and Section 5. This is intended to make optimal use of the available tyre-road friction potential. The output of the CA includes the RWS angle \(\delta_{r}\) and the wheel torques \(T_{w,i}\), \(i\in\{1,2,3,4\}\), in addition to the feed-through FWS angle \(\delta_{f}\).