## 1 Introduction and Background
### Approaches to the Problem, Actual Tests of Stability, and the Need for a New Test Facility Concept
Tests designed to characterize the vehicle with reference to its tilt angle (usually referred to as side inclination), regardless of the exact knowledge of the CoG position but, rather, directly observing the effects of its spatial placement in terms of stability/overturning of the whole vehicle. These tests are very simple albeit effective: the vehicle to be tested, equipped with its own tires (i.e., in a condition as close as possible to real world applications), is placed on a 'tiltable' flat platform and the angle of the platform necessary to have a side overturning of the vehicle is identified. In the last few years, some variations/improvements of the classic flat-platform test were proposed. For example, [PERSON] et al. [3] developed a test bench able to measure the reactions on the wheels of a vehicle under static load with a gradual increase of the vehicle roll angle, thereby investigating the effect of the rear-track width and of an additional weight on the wheels on the stability. Similar variable-tilting testing devices have been used in the field of off-road robotics. [PERSON] and [PERSON] [49] used a 16-foot square 'tiltable' table, the Variable Terrain Tilt Platform (VTTP), to test the ability of a model of the Mars Exploration Rover. The vehicle was driven on the VTTP at 0-20 degree slope angles, at different orientations to the slope, while simultaneously traversing over obstacles up to 25 cm in height. This allowed to quantify the translation down the slope and the vehicle slip as a percentage of total drive over two different surfaces. The same results were also used to validate the vehicle-terrain interaction model in the physics-based \"ROAMS\" rover simulator [50]. [PERSON] et al. [51] used a tiltable sandbox, 2-m-length and 1-m-width, capable of being inclined up to 20 degrees, to test the slippage experimented by a reconfigurable planetary rover on a slope-traversing path. Finally, in the study by [PERSON] et al. [52], a pre-fabricated steel spiral roll-over ramp was used to provoke the vehicle lateral roll-over. This ramp had an initial side-slope of 18\({}^{\circ}\) and a final slope of 55\({}^{\circ}\), with the side angle increasing progressively along the ramp length. The tests of the second type, using a tiltable flat platform, are surely more common for farm tractors: the equipment for performing such tests is often available even at the tractor production facilities. Nevertheless, such tests have some limitations. Firstly, they are referred to a specific static overturning condition (typically a side-overturning), and the vehicle steering components (wheels, central joint) are positioned as for a straight-path trajectory. However, the most dangerous situations happen during turning maneuvers, so a further investigation is worthwhile since the supporting polygon could be modified [1; 5; 6; 23] when the steering wheels or the two halves of the vehicle (respectively, for traditional/articulated vehicles) are angled, and the speed contributes with a destabilizing effect during turns due to the centrifugal force. For these reasons, articulated tractors are tested also according to the norms foreseen for other types of vehicles with an articulated chassis and central steering joint, i.e., telehandlers, pallet stackers, double stackers, and order-picking trucks [53; 54]. As explained in [55], the additional information that can be obtained by performing this type of test does not yet provide a complete knowledge basis of the behavior of articulated tractors because the test configuration relates to a single steering angle. Furthermore, such angle is dependent on the dimensions of the vehicle support polygon, thereby preventing test data of different vehicles from being fully comparable with each other. Another critical situation takes place when a tractor exits an inter-row (i.e., a retracing) of a field placed on a hillside: there could be a sharp change in the slope and one of the wheels might not be able to touch the ground (Figure 1).