## 1 Introduction  
The configuration (i.e., the absolute position and orientation) of a vehicle in the space (if assimilated to a rigid body) is uniquely defined by six independent variables called \"degrees of freedom\" (DoFs): three translational DoFs (the coordinates of its center of gravity (\(CoG\))) and 3 rotational DoFs (roll, pitch and yaw angles) [1; 2]. The first three DoFs characterize the absolute position of the vehicle (and, therefore, its trajectory, by observing how the coordinates of its \(CoG\) vary over time), the second three DoFs (referred also to as \"Euler angles\") characterize its orientation in the space and, therefore, its attitude [2]. In particular, the three rotational DoFs are directly involved in the balance of a terrestrial system/vehicle in relation to its support base. As demonstrated in other previous works principally focussed on agricultural machines stability [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17], a vehicle (or, more generally, a body) placed on a (rigid) plane with friction has a stable position on that plane if both the following conditions are verified:  
1. the resultant of external forces acting on the \(CoG\) intercepts the support plane inside the support polygon, defined by taking the footprints of the vehicle supports (e.g., the centers of the tyre footprints) as vertices [3; 4; 9; 10; 11];
2. the friction developed at the interface with the support ground is higher than the parallel component of the resultant of the external forces applied to that body [18; 19]. If the first condition is verified, the vehicle has a null moment of the external forces and, hence, does not experience any rotation, i.e., does not overturn [11; 20; 21; 22; 23; 24; 25]; if the second condition is verified, the vehicle has a null resultant of the external forces and, in particular, does not slide along the support surface [26; 27]. The stability of a vehicle is normally referred to as the overturning. Excluding the sliding/translation of the vehicle (hence, of the \(CoG\)) along the plane, which are not of interest in this study, because they had not been foreseen by any international test standards dealing with the stability of a vehicle [28; 29; 30; 31], all current stability tests aim at imposing known values of the three rotational DoFs from outside the vehicle under test, for example by acting on the orientation of the support system (in this case: a support platform). Traditional test equipment, mainly used in certification laboratories (e.g., OECD test stations), is composed basically by a tilting rigid platform with only one degree of freedom (i.e., the tilting angle of the platform). Such an equipment causes the vehicle to tilt when it has one of its main axles aligned with the tilt axis and it has the steering wheels in a straight-ahead traveling configuration or in a single specific steering configuration (as forecasted for telehandlers, pallet stacks, double stackers and order-picking trucks having an articulated frame with a central steering joint [28; 29]). Other less conventional equipment was developed principally for research purposes; for example [PERSON] [32] proposed a pre-fabricated steel spiral roll-over ramp with an increasing slope (from \(18^{\circ}\) to \(35^{\circ}\)), [PERSON] et al. [33] developed instead a four-post weighting test bench. By imposing respectively a roll or a pitch angle [30; 32; 34; 35], the experimenters test only the lateral or the longitudinal rollover, as prescribed also by international standards [28; 29; 30; 36]. To be sure that slippage does not occur during lateral overturning tests on conventional inclinable platforms, the cited standards even allow the use of removable prominences of 5 cm in height or with a height equal to 10% of the nominal wheel diameter to be placed in contact with the downstream tyres at the beginning of each lateral overturning test.