# A Review of Recent Advances in Roll Stability Control in On-Road and Off-Road Vehicles
## 3 Theoretical Foundations of Roll Stability Control
### Basic Principles of Roll Stability Control  
The core objective of vehicle roll stability control is to suppress the roll angle and reduce the load transfer ratio, thereby preventing rollover accidents under extreme conditions, while ensuring dynamic controllability. This objective typically involves a trade-off between maneuverability and stability, ensuring that the vehicle maintains reliable roll stability during sharp turns, emergency maneuvers, high-speed driving, and in complex terrain, while preserving reasonable handling performance.  
In a roll stability control system, key control variables include the roll angle, roll rate, yaw rate, lateral acceleration, and load transfer ratio (LTR). Among these, the roll angle and LTR directly reflect the vehicle rollover risk, while the yaw rate and lateral acceleration are closely related to the overall stability of the vehicle. In the context of active control, the actuated variables primarily involve active suspension stiffness and damping, wheel braking force distribution (differential braking), and active front steering (AFS), which are used to actively adjust the roll dynamics. Active suspension reduces body roll and improves ride comfort by adjusting suspension stiffness and damping forces, but it comes with higher costs and implementation complexity. Active steering enhances maneuverability and stability by adjusting the front/rear wheel angles, making it suitable for integration with Advanced Driver Assistance Systems (ADASs), but it increases system complexity. Differential braking quickly responds to roll risk by distributing braking force without adding extra actuators, but it may reduce vehicle efficiency and accelerate brake wear. Each actuating mechanism has its advantages, and a comprehensive selection or combined control strategy should be employed, depending on the application scenario, to optimize vehicle roll stability.  
Model-based control methods are the mainstream strategy for roll stability control, with the core idea being the use of a vehicle dynamic model to construct a control law that adjusts control inputs in real time based on the measurement or estimation of key state variables. Typical roll stability control strategies include the following: Linear Quadratic Regulator (LQR), sliding mode control (SMC), model predictive control, and Fuzzy Logic Control (FLC).  
In recent years, researchers have increasingly focused on multi-system collaborative control strategies, which aim to achieve better roll stability by coordinating the control of  
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multiple actuators. The desired outcome of roll stability control is to minimize the rollover risk and enhance vehicle safety without significantly compromising maneuverability. This optimization process requires balancing lateral stability and handling flexibility to ensure good dynamic responses across various operating conditions. For example, during high-speed obstacle avoidance, the control system should maintain reasonable yaw dynamics while ensuring stability, allowing the driver or autonomous driving system to complete the maneuver successfully. Additionally, in special applications such as off-road terrains or mining transport, roll stability control needs to incorporate terrain adaptability to enhance vehicle safety on slopes and complex surfaces. Therefore, roll stability control involves various physical variables and control strategies, with the goal of achieving synergistic optimization of maneuverability and rollover prevention through active adjustments of the vehicle's dynamic behavior.