Keywords

1 Introduction

As the demand for personal mobility increases in urban areas, traffic problems such as congestion, fuel consumption, air pollution, and limited parking space are expected to worsen. To address these issues, one- and two-seater personal mobility vehicles, known as Narrow Tilting Vehicles (NTVs), have been developed. NTVs are expected to help alleviate traffic congestion during commuting hours. However, compared to conventional vehicles, NTVs are prone to impairing postural stability, making it essential to address this issue. As a solution, NTVs equipped with lean actuators that can control the vehicle's posture in the roll direction have been proposed [1,2,3].

In NTVs with lean actuators, the method of directly controlling the roll angle via the lean actuator is referred to as Direct Tilt Control (DTC), while the method of tilting the vehicle body via centrifugal force generated by counter-steering, as seen in motorbikes and bicycles, is known as Steering Tilt Control (STC). DTC is superior in roll angle stability at low speeds, but requires a large roll torque to change the roll angle and generates large lateral acceleration to the occupants along with the roll angular acceleration [4,5,6,7,8]. In contrast, STC does not require a lean actuator because to tilt the vehicle body by counter-steering, and the lateral acceleration to the occupant is relatively small. However, the roll angle becomes unstable at low speeds and the roll angle cannot be controlled when the vehicle is stationary [9, 10].

Based on the aforementioned considerations, two primary control challenges for NTVs are identified: (i) reducing the lateral acceleration experienced by occupants, thereby enhancing postural stability, and (ii) maintaining stable roll angle control across all vehicle speeds. To address these challenges, a control strategy has been proposed that either switches between DTC and STC based on vehicle speed, or employs a combined control approach integrating both DTC and STC, referred to as SDTC [11, 12]. One of the factors complicating the control of NTVs is the necessity for counter-steering in steering control. Front-wheel steering NTVs require counter-steering similar to that used in motorcycles and bicycles to reduce lateral acceleration caused by roll angle acceleration, thereby complicating steering angle control during turns. For example, a counter-steering control method utilizing a transfer function with unstable zeros has been proposed [13].

The authors proposed a method to control leaning and steering based on a single roll direction equation of motion, focuses on the yaw angular acceleration and roll inertia of the vehicle body. This approach aimed to avoid the complex combination control of STC and DTC in front-wheel steering vehicles while ensuring that occupants do not experience significant lateral acceleration. The effectiveness of this method was verified through driving simulations using a multi-degree-of-freedom dynamic model [14].

In this study, we conducted real vehicle evaluations using the proposed method and confirmed its effectiveness. Figure 1 and Table 1 show the appearance and main specifications of an NTV used in this research.

Fig. 1.
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A view of narrow tilting vehicle

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Table 1. Specifications of Narrow Tilting Vehicle.
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2 Vehicle and Control Specification

2.1 Vehicle Specification

Figure 2 shows the vehicle configuration of the NTV used in this study. This vehicle is a four-wheeled model with two front wheels and two rear wheels. It is equipped with lean actuators on both the front and rear wheels, which determine the target roll angle based on the driver's steering input. The lean actuators rotate the parallel links to raise and lower the left and right wheels, thereby tilting the vehicle body. Additionally, the front wheels are fitted with a steering actuator that controls the steering torque according to the proposed control method. Each rear wheel is equipped with an in-wheel motor that drives the wheels based on the driver's throttle input. Furthermore, the vehicle has a very narrow tread width of 550 mm, aiming to achieve stable driving with a width comparable to that of a motorcycle.

Fig. 2.
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Mechanical structure.

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2.2 Control Specification

Figure 3 shows a block diagram of the proposed control system. The “in-wheel motor” is the in-wheel motor for the left and right rear wheels, “Steer act.” is the steering actuator, “Lean act.” is the lean actuator, and “Controller” is a control system that adds a steering torque based on roll speed to the control method proposed in a previous paper [14]. The term \({\tau }_{wh}\) denotes the torque command to the in-wheel motor, determined by the driver's accelerator opening, V is the translational speed, and \(\theta \), \(\dot{\psi }\), and \(\ddot{\psi }\) denote the roll angle, yaw rate, and yaw angle acceleration of the vehicle's upper body, estimated by the inertial sensor, respectively. The term \({\theta }_{d}\) denotes the roll command angle, derived from the steering wheel angle and vehicle speed, \(Lean Trq\) and \(Steer Trq\) are the torque command derived from \({\theta }_{d}\) to the lean actuator and to the steering actuator.

Fig. 3.
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Control block diagram of Narrow Tilting Vehicle.

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3 Validation

To verify the effectiveness of the proposed method, a 180° turning maneuver was conducted using the experimental vehicle. Figure 4 shows the results for DTC, while Fig. 5 shows the results for the proposed method. The lean angle was varied from 0° to 18° and back to 0°, and the vehicle speed was maintained at 20 km/h. Graph [a] represents the roll angle, graph [b] represents the yaw rate, and graph [c] represents the lateral acceleration near the sprung mass center of gravity. In the DTC, significant lateral acceleration occurred during transitions from straight to turning and from turning to straight, with a maximum value of 0.19G, causing uncomfortable G-force variations for the occupants. In contrast, the maximum lateral acceleration with the proposed method was 0.03G, and the occupants barely felt any G-force variations. This indicates that the proposed method can reduce the lateral acceleration experienced by occupants during turning maneuvers by 84%, thereby enhancing passenger comfort. Additionally, concerns about degraded line tracing due to counter-steering were largely unfounded.

In the future, we will verify the effectiveness of the proposed method during 180° turning maneuvers at different speeds and during slalom maneuvers, ensuring that significant reductions in lateral acceleration are achieved, consistent with the simulation results.

Fig. 4.
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Results of the DTC.

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Fig. 5.
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Results of the Proposal.

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4 Conclusion

The following conclusions can be drawn from this study:

  1. (1)

    Using the method proposed in our previous paper, which focuses on the yaw angular acceleration and roll inertia of the vehicle body to determine the torque distribution between the lean actuator and the steering actuator, we conducted an evaluation with a developed experimental vehicle. This evaluation confirmed that the lateral acceleration experienced by occupants can be reduced by 84%.

  2. (2)

    By employing the proposed method, the maximum lateral acceleration during turning maneuvers was reduced to 0.03G, ensuring that occupants barely perceive any variations in lateral acceleration.

  3. (3)

    The deterioration in line tracing performance due to counter-steering, which was a concern with the proposed method, was barely perceptible.

In the future, we will verify the effectiveness of the proposed method during 180° turning maneuvers at different speeds and during slalom maneuvers, ensuring that significant reductions in lateral acceleration are achieved, consistent with the simulation results.