# Vehicle Motion Control for Overactuated Vehicles to Enhance Controllability and Path Tracking
## 1 Introduction  
With the electrification of powertrains, the number of drive motors in vehicles is increasing. Vehicle configurations are evolving from dual-motors for all-wheel drive to tri-motor systems with rear-axle torque vectoring (TV) and potentially to four motors [1]. Additionally, active front- and rear-wheel steering systems are being integrated to support automated driving functions. This raises the question of the advantages provided by multiple actuators for autonomous driving. Specifically, how do four-wheel steering (4 WS) and wheel-independent four-wheel drive (4 WD) influence vehicle handling, path tracking, and the stable domain of vehicle motion? A diversified set of actuators, as highlighted by [2] in Figure 1, allows integrated control or global chassis control to make optimal use of the available tyre-road friction potential [3, 4]. These integrated control strategies are part of the vehicle motion controller (VMC) in Figure 2, which facilitates the matched use of the available chassis actuators [5, 6]. By decoupling individual wheels with electric motors, TV can effectively be used to shape the vehicle response and influence its stability [7, 8, 9]. Improved vehicle performance benefits both manual and automated driving. Early path tracking controllers, such as pure pursuit controllers [10], operate without inherent vehicle stability considerations and heavily rely on electronic stability control (ESC). Advances in control theory, particularly model predictive control (MPC), integrate stability considerations through nonlinear vehicle models [11], stability constraints with a stability envelope (SE) based on phase plane analysis [12; 13; 14; 15], or positive invariant sets to constrain MPC within a robust tube [16]. In [17], the stable handling envelope is further extended by effectively using 4 WS and TV. Despite relying on a linear type model and unconstrained control allocation (CA), the method demonstrates a significantly enhanced vehicle response with combined control. Recent advancements, as shown in [18], incorporate nonlinear vehicle models and detailed tyre information. These studies illustrate a TV stability controller based on MPC, which optimizes brake intervention. Meanwhile, Ref. [19] utilizes an optimization-based approach to study the theoretical limits of TV and 4 WS for vehicle stability control, highlighting the significant potential for increased vehicle controllability. Ref. [9] demonstrates how TV can be used to adjust the linear understeer characteristics and extend the maximum attainable lateral acceleration by allocating wheel torques through minimum slip-based optimization. For automated driving, [PERSON]. [20] investigates vehicle stability and minimal lateral displacement during evasive maneuvers by using a basic driver model approach as a controller, combined with a linear CA to optimize tyre force utilization through 4 WS and TV. Similarly, [PERSON]. [21] applies offline optimized TV maps with a proportional-integral-derivative (PID)  
Figure 1: Impact of integrated control on friction circle; adapted from [2]. Figure 2: Vehicle motion controller as part of a multilayered upstream control architecture [3]. controller to improve the vehicle stability for an autonomous racing vehicle at the limits. However, in both cases, the feedback controllers may exceed the physical limits as the tyre saturations are not considered online. To incorporate detailed tyre information into the feedback controller, [PERSON]. [22] uses a semi-empirical tyre model combined with linear time-varying model predictive control (LTV-MPC) to utilize brakes for TV, improving path tracking.