# Design and Lateral Stability Analysis of an Attitude Adjustment Tractor for Moving on Side Slopes
## 1 Introduction  
Tractors, known for their multitasking capacity, are widely used in many different farm situations [1]. In particular, tractor overturn accidents account for more than half of all tractor-related deaths [2, 3]. It is no wonder that sideways overturning, or lateral rollover, accounts for the majority of overturning injuries [4, 5]. A considerable amount of research has been devoted to tractor lateral stability, which can be divided into passive safety prevention and active safety protection [6, 7]. The rollover protection structure (ROPS), as a kind of passive way, has been one of the most important advances in protecting the driver from tractor overturn accidents. In addition, ROPS do nothing to prevent accidents, they only reduce the likelihood of serious injury [8]. By contrast, mainstream research on active safety prevention seeks to establish static/quasistatic/dynamic models to reveal the behavior of tractors on different terrains [1, 3, 4, 5, 6, 7, 8, 9, 10, 11]. Based on these models, tractor stability indicators are able to evaluate the stability of the tractor. However, these results (tractor speed, slope angle, etc.) can only provide some warning to tractors [12, 13]. Thus, a locomotion system for tractors that is able to maintain stability in various situations (especially side slopes and uneven terrains) is still essential [14, 15]. Locomotion systems with attitude adjustment mechanisms can alter their structures and configurations to change the center of mass. These systems can better adapt to various,complicated and completely unstructured environments [16; 17]. Most of these systems are applied for mobile robots, for example, the Sample Return Rover, Scarab, Tri-Star IV, ATHLETE, Workpartner, MAMMOTH, Hylos, and Sherpa [18; 19; 20; 21; 22; 23; 24; 25; 26]. They are mostly a hybrid wheel-legged type with many degrees of freedom (DOFs), adding complexity to the control system [26]. In addition, most of such robots are driven by a motor with no transmission systems. For tractors, several mechanisms for locomotion systems with attitude adjustment functions have been designed and developed [27; 28; 29; 30; 31; 32]. As the degrees of active freedoms are independently actuated, they can actively adjust their postures and structures, thereby enhancing their stability and traction. A four-wheeled slope tractor has been described to change its attitude on side slopes. However, it needs additional active control to keep all four wheels in contact with the ground, adding complexity to the control system [27]. Another four-wheeled tractor has been developed to move on transverse slopes; a brachial mechanism to the rear wheels is used to change the height of the wheels, and a linkage system of the front wheels is provided as the passive part to keep wheels in contact with the ground. As it is a rear-wheel-drive vehicle, the driving performance would be affected when compared to the all-wheel-drive ones [28]. Additionally, a hillside tractor with a balance-rocker mechanism is designed to achieve variable ground clearance and variable wheel tread. But the mechanism systems are complicated [29]. The design and testing of a hillside track tractor with a differential pressure device are also investigated [30]. These studies primarily focused on the design, manufacturing, and testing of such locomotion systems. However, the effects of posture change on the stability of such reconfigurable systems were neither considered explicitly nor evaluated. The stability of the tractor may be significantly influenced by posture or configuration. In fact, it has long been established that sideways overturning, or lateral rollover, accounts for the majority of rollover injuries and fatalities [5]. Meanwhile, several studies have found that when the attitude of a locomotion system is controlled, the stability can be enhanced [25; 33; 34]. Thus, the model representing the relationship between the configuration/posture of a tractor and its lateral stability is highly required to be established.