# Steering Assist Control for Bicycles with Variable Trail Effect
## 2 Materials and Methods
### Steering Assist Control  
Bicycles are inherently unstable vehicles, and many studies have been conducted on their stability [1; 14; 15]. For such an unstable vehicle, the rider rides as intended when the bicycle mechanism and the rider's balance cooperate [13]. However, for riders such as the  
Figure 1: System configuration of experimental bicycle with power steering mechanism.  
Figure 3: DC motor in power steering mechanism to generate assist torque.  
Figure 2: IMU:AU7684N mounted on experimental bicycle.  
elderly and women who have difficulty in applying large steering torque, the load luggage in the front basket of the bicycle handlebar may have a significant impact on steering operation [2]. Therefore, this study examines what kind of handlebar assist control would make it easier for a person to operate a bicycle with a load in the front basket.  
So two types of steering assist control are implemented on the experimental bicycle equipped with the power steering mechanism shown in the previous section. The first of the steering assist control is \"proportional assist control\". It generates an assist torque proportional to the steering torque applied by the rider to the handlebars. The second one is \"variable trail control\". It comes from the mechanism of the caster angle and the offset of the front wheel of the bicycle. They make the trail effect, in which the front wheel is automatically steered in the tilting direction when the bicycle tilts the roll angle. In this study, we make the trail effect pseudo-variable by the control law.  
Strain gauges are attached to the handlebar shaft of this experimental bicycle to measure the rider's steering torque in real time. In the proportional assist control, the assist torque is calculated by multiplying the steering torque measured by the strain gauges by gains. The calculated assist torque is 1.5 times the steering torque input to the bicycle handlebar axle. Its block diagram is shown in Figure 4. The assist torque calculated by the proportional assist control is generated by the motor in the power steering mechanism. This torque is applied to the handlebar shaft via gears and is combined with the rider's steering torque.  
The IMU mounted on the bicycle can measure the roll angle and roll angular velocity in real time. The intersection point between the handlebar axis and the ground is offset from the ground contact point of the front wheel due to the caster angle and the offset of the bicycle. Due to this geometry of the front wheel, the front wheel of the bicycle is automatically steered by tilting the body, which is called the trail effect. As mentioned, the trail effect is determined by the geometry of the front wheel, but in the experimental machine with the power steering mechanism, the trail effect can be varied by using the motor to generate a torque around the handlebar axis in response to the roll angle and angular velocity of the vehicle body.  
Therefore, we propose to a steering assist control for the power steering mechanism by adjusting the trail effect to a desirable amount. The block diagram is shown in Figure 5. The variable trail control allows the desired steering angle to be calculated from the roll angle and roll angular velocity of the bicycle. The motor torque applied to the handlebar axis is determined by a PD feedback control of the difference between the desired steering angle and the current rider's steering angle. In the control system, the desired steering angle is set to three times, the roll angle of the vehicle body and 0.3 times the roll angular velocity. The proportional gain and differential gain of the PD feedback controller are set to 40 and 0.0002, respectively.  
Figure 4: Block diagram (proportional assist control).