## 1 Introduction and Background
### Approaches to the Problem, Actual Tests of Stability, and the Need for a New Test Facility Concept  
The key point to ensure the operators' safety as well as the operability of a machine is the full knowledge of the stability performance of agricultural machines. The critical parameter is the CoG position as a function of other constructive parameters, also in vehicle operating configurations that foresee the presence of payloads or mounted/trailed implements [23; 24; 25; 26], or of a battery pack as a consequence of the electric hybridization of a conventional vehicle [27]. As acknowledged in literature, the CoG position affects the operation of any active-safety device acting on several on-board technical systems [16; 28; 29; 30; 31]. Every passive- or active-safety controller (or, generally, every control strategy to correct or optimize the trajectory of a vehicle) is based on the knowledge of the CoG position to infer the vehicle dynamic behavior and perform trajectory optimization for given initial conditions [32; 33; 34]. In addition, the capability of leveraging the CoG position could be the starting point to redesign or modify a tractor by varying its wheelbase, track width, front-axle mounting point or other design parameters [3; 35]. Consequently, the study of the CoG position is a hot topic both for the scientific community and for the manufacturers of vehicles and, in particular, of agricultural machinery. Several studies on vehicle stability have approached the problem of characterizing the stability of machines primarily from two points of view:  
* Theoretical-numerical [4; 36; 37; 38; 39]: By modeling a vehicle in terms of masses, constraints and supports, and developing equations in more or less complex simulators, as done by [PERSON] and [PERSON] [25], suitable to calculate the position of the CoG of the machine possibly with some mounted implements and trailers [23; 24], thus predicting the static conditions and the security level for many inclinations of the supporting plane. For example, several scholars [1; 5; 36; 37] use an analytical-Newtonian approach combined with a kineto-static approach based on rigid bodies. In some cases, these simulators have allowed to simulate the dynamics of a vehicle also in terms of response to an external disturbance: therefore, they have been used to investigate the robustness and fine-tune the characteristics of the software controllers that could be installed on such vehicles [32; 33; 34]. * Practical-experimental [22; 40; 41]: Using a dedicated test-facility, by following, developing or refining the test methods/procedures described by the legislation in force, e.g., ISO 789-6 [42], ISO 16231-2 [43], SAE J2141 [44], and SAE J2926 [45]. Other than obtaining a characterization of the tested machines which is very useful for comparisons or homologous, the same data can be used to set the operation of several active-safety devices, which include sensors connected to actuators, or simply alarms for the driver [16; 28; 29] based on the real behavior of vehicles registered in many field-tests. Hence, this approach takes into account all the disturbing factors that normally occur during the everyday use of a vehicle. In particular, as for the experimental methods and the related equipment, it is possible to distinguish two types of tests:  
1. Tests aimed at the detection of the (relative) spatial position of the vehicle center of gravity (i.e., the three coordinates of the CoG, referred to a frame of reference fixed to the vehicle), e.g., by lifting the vehicle in two different points and measuring the weight supported by the wheels and the lifting system [43; 46], or at least aimed at determining the height of the CoG from the supporting surface (e.g., pendulum test) as proposed by [PERSON] and [PERSON] [47]. [PERSON] et al. [48] inquired also the influence of springs, fuels, hydraulic oil, lubrication oil and elastic cells on the CoG measurement accuracy by lifting a vehicle, specifically a mower. 2.