# Steering Assist Control for Bicycles with Variable Trail Effect
## 1 Introduction  
Bicycles are a familiar and affordable means of transportation, and are widely used all over the world. Users, young and old, men and women alike, ride bicycles for a variety of purposes, including short-distance transportation such as commuting to work or school, hobbies such as road racing and travel, and daily activities such as shopping and taking children to and from school. Bicycles have been appropriately improved according to their uses, especially in terms of ensuring their safety [1]. Electrically assisted bicycles are one of the fruits of these efforts. In Japan, the number of electrical power-assisted bicycles sold in 2022 exceeded that of ordinary bicycles, reaching 795,000 units. In addition, special bicycles to accommodate two infants in child seats attached to the handlebar and rear carrier of the bicycle have been developed and are becoming popular [2]. Research has also reported that electrical power-assisted bicycles are safer than conventional bicycles [3, 4]. Furthermore, shared bicycle rides are getting increasingly popular, allowing people to use bicycles when and where they need them even if they do not own a bicycle [5, 6, 7, 8]. In addition, forward-thinking attempts have sought to further improve the efficiency of bicycles, such as automated bicycle operation [9, 10, 11] and energy regeneration from the vibration generated during bicycle riding [12]. While the use of bicycles is increasing, the need to reduce bicycle accidents has been highlighted. Although bicycles are inherently unstable vehicles, they can be ridden as intended when the bicycle mechanism and the rider's balance work cooperatively [13]. Therefore, the dynamics of bicycles have been analyzed by many researchers [1; 2; 14; 15; 16; 17; 18; 19]. One of the factors leading to bicycle accidents such as falls is considered to be an increase in the moment of inertia around the handlebar and a change in the center of gravity position around the handlebar axis when baggage is placed in the front basket, or when an infant is carried in a child seat which is attached to the bicycle handlebar. It has been pointed out by [20; 21; 22; 23] that an increase in the moment of inertia and a change in the center of gravity position require a larger steering torque than when nothing is placed in the front basket, which may result in reduced steering maneuverability. However, for riders such as the elderly or women who have difficulty in applying large steering torque, the load in the front basket may have a large impact on the steering operation. That is, it leads to the inability to make quick steering maneuvers, which causes fall accidents. Our research group has paid attention to such a problem and has proposed a power steering system for bicycles that assists the rider in steering the bicycle in order to reduce the number of bicycle crashes [24]. Assistance in conventional electric bicycles has been supplying the additional biking torque generated by a motor [25; 26; 27; 28]. However, in this study, we focus on the assist mechanism designed to assist the steering of the handlebar. As a previous study in this direction, [PERSON] et al. [24] developed an experimental power steering mechanism. In the power steering mechanism, the output shaft of the motor is linked to the handlebar shaft via gears, and the output torque of the motor is added to the steering torque by the rider. A disturbance observer designed for the mechanism, which is derived based on the equation of motion around the handlebar of the developed bicycle, estimates the rider's steering torque. By supplying an assist torque proportional to the estimated steering torque, the system successfully reduces bicycle wobble even when a load is placed in the front basket. In another previous study, [PERSON] et al. [29] achieved stable biking by designing a control system that cancels out the effect of baggage loaded on the front basket of the handlebar. The control system was designed based on the derived linearized model around the handlebar axis.