# A Study of a Cornering Braking Control System for a Motorcycle
## 1 Introduction  
It is well known that motorcycles are still popular in more and more crowded cities due to their flexibility and practicability. A general motorcycle can travel at speeds of up to 80-100 km/h, but it occupies half the space of a car, allowing them to avoid traffic jams and parking difficulties. However, the dynamics of a motorcycle are similar to an inverted pendulum system, and they have static instability. When a motorcycle is cornering, the roll angle appears to offset the centrifugal effect. If a motorcycle is cornering and braking concurrently, the risk of overturn increases greatly. With the progress of intelligent control systems in recent years, active safety systems, such as the electronic stability program (ESC), vehicle stability control (VSC) have been widely used in cars, which also provide a good reference point for improving the safety of motorcycles. Overall, given the wide application and inherent instability of motorcycles, researching and developing active safety systems for motorcycles to improve their security has great significance [1]. Previous research mainly focused on the dynamics model and stability control of motorcycles. Regarding the dynamics model, [PERSON] and [PERSON] conducted a systematic and comprehensive study. [PERSON] et al. [2] primarily simplified a two-wheeler astwo rigid bodies that are connected by a revolute pair and derived the dynamic equations using the Lagrange method to determine characteristics such as wobble, weave, and cap-sizing. In [3, 4], [PERSON] et al. used a parametric modeling tool, Autosim, to create a nonlinear model of a motorcycle to determine its stability under braking and acceleration. [PERSON] [5, 6] proposed an 11-DOF nonlinear dynamic model using a Cartesian method and analyzed the kinematics, tires, steady turning, vibration, and handling characteristics of a motorcycle systematically. In [7], [PERSON] et al. linearized the dynamic model from [5] and then analyzed the eigenvalue and model characteristics. In [8], by combining suspension stiffness, [PERSON] et al. conducted time-domain simulation, nonlinear steady-state analysis, linear stability analysis, and frequency domain analysis. [PERSON] et al. [9] conducted a comparative analysis of the linear roll dynamics and nonlinear roll dynamics models of motorcycles under turning conditions. [PERSON] et al. [10] developed a multibody model of a Honda VFR that consisted of six bodies and eleven degrees of freedom. [PERSON] et al. [11] derived a mathematical model of a motorcycle using the Lagrange method, which was a non-linear second-order ordinary differential equation (ODE). [PERSON], [PERSON] et al. [12] presented longitudinal and lateral models focusing on the dynamics of powered two-wheelers. In terms of active safety, the roll angle and tires have critical effects, so [PERSON] et al. [13] proposed an active braking control system that determines the best slip using the roll angle as the input to control the braking behavior on a curve. [PERSON] et al. [14] proposed an electronic stability-control system that modulates braking and traction torque using a full-authority saturated controller with time-varying saturations. The robustness of the control systems with respect to different maneuvers was tested using BikeSim, which is a multibody motorcycle simulator. [PERSON] et al. [15] proposed a motorcycle stability control (MSC) system that combines ABS, an electronic braking system, traction control, and inertial sensors. This system uses an algorithm that considers the vehicle state and controls the braking and traction force to increase safety. [PERSON] et al. [16] used a model predictive control algorithm (MPCA) to distribute the braking force between the front and rear wheels to reduce unwanted brake steer torque during cornering. [PERSON] [17] presented a braking control algorithm that could identify the negative sign of the time derivative of the lateral force that acts on the wheels.