Steer-by-wire control device and steer-by-wire control method
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-06-01
- Publication Date
- 2026-08-11
AI Technical Summary
[0023]根据本发明,能够提供能够利用不易给车辆的驾驶员带来不安感、不适感的方法,高精度地推算方向盘的控制参数的线控转向控制装置和线控转向控制方法。
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Figure CN117545679B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a steer-by-wire control device mounted on an automobile as a steering control device. Background Technology
[0002] In steering control devices for automobiles (hereinafter referred to as "vehicles"), there is a known type of steering control device with a steering shaft that is mechanically separated from the steering mechanism, which is called steer-by-wire. As a steering control device with steer-by-wire, the steer-by-wire device detects the rotation angle and direction of the steering shaft, and controls the amount of actuation of the electric actuator for steering to drive the steering shaft based on these detection signals.
[0003] In steer-by-wire systems, the correspondence between the steering wheel input and the steering input of the electric actuator can be set without mechanical constraints. Therefore, steer-by-wire control devices offer the advantage of flexible response to changes in steering characteristics related to vehicle speed, turning radius, and acceleration / deceleration, thus increasing design freedom. Furthermore, steer-by-wire control devices have several advantages over conventional steering control devices, including ease of development into automatic steering systems such as lane-keeping control.
[0004] An electric actuator for applying a steering reaction torque (also called torque) to the steering wheel is installed on the steering shaft, which is separate from the steering control mechanism. By applying a moderate steering reaction torque to the steering wheel, the driver of the vehicle can perform steering operations with the feeling that the steering wheel and the steering control mechanism are mechanically connected.
[0005] In a vehicle equipped with such a steering control device, it is envisioned that the steering control device switches between an automatic steering control mode (hereinafter also referred to as "active steering mode" or "automatic driving mode") and a manual steering control mode (hereinafter also referred to as "manual steering mode" or "manual driving mode") while driving. Moreover, generally speaking, for example, the steering control device has a structure that executes the manual steering mode when the driver holds the steering wheel and executes the active steering mode when the driver does not hold the steering wheel.
[0006] When active steering mode is activated, the steering control unit calculates the steering angle of the steering wheel based on external steering command values from the automatic steering system, and controls the electric actuator to drive the steering wheel to achieve the calculated steering angle. In this case, the steering wheel rotates in accordance with the steering angle of the steering wheel due to the reaction force via the electric actuator, making the rotation angle of the steering wheel consistent with the steering angle of the steering wheel.
[0007] Furthermore, automatic steering control systems include lane keeping control, which ensures the vehicle stays within the white lines on the road, and automatic driving control, which allows the vehicle to follow its designated driving path. If the automatic steering control system determines that it is difficult to continue automatic steering control during its execution, it can transfer driving control to the driver. Additionally, when active steering mode is in operation, if the driver intentionally manipulates the steering wheel to cancel automatic steering control, the system must quickly detect this and transfer driving control back to the driver.
[0008] In these situations, the automatic steering system needs to transfer driving control to the driver when it detects that the driver is holding or manipulating the steering wheel. Therefore, detecting the driver's grip on the steering wheel (grip detection) and detecting the driver's manipulation of the steering wheel (manipulation detection) are important technical issues in steering control devices.
[0009] Regarding the grip and manipulation detection described above, a method is known to calculate the torque applied by the driver (hereinafter referred to as "driver torque") and detect the driver's grip and manipulation based on the calculated driver torque value. The calculation of driver torque uses the inertial torque of the steering wheel. The inertial torque of the steering wheel is a crucial parameter directly related to the accuracy of the driver torque calculation and is a control parameter affecting the steering wheel's movement. In addition to inertial torque, such steering wheel control parameters also include frictional torque and gravitational torque, etc.
[0010] The technical problem of calculating the inertial torque of a load mounted on an actuator is a common technical problem not limited to steer-by-wire control devices. Prior art for calculating the inertial torque of a load mounted on an actuator is described, for example, in Patent Document 1. In the technology described in Patent Document 1, in a power-assisted moving body that is moved by the force of a motor and the force of a person, the equivalent inertial torque of the moving body is calculated by using the acceleration of the moving body detected by an acceleration detection unit and the armature current of the motor detected by a current sensor, thereby calculating the inertial torque of the load (moving body such as a trolley) mounted on the motor.
[0011] Existing technical documents
[0012] Patent documents
[0013] Patent Document 1: Japanese Patent Application Publication No. 2005-153648 Summary of the Invention
[0014] The technical problem that the invention aims to solve
[0015] The technology described in Patent Document 1 does not take into account the situation where the driver is holding the steering wheel. If the technology described in Patent Document 1 is used in a steering control device, the inertial torque of the steering wheel may not be able to be calculated with high accuracy when the driver is holding the steering wheel.
[0016] Furthermore, when calculating the inertial torque of the steering wheel, the torque of the electric motor is needed to move the steering wheel. At this time, if the steering wheel moves significantly independently of the driver's intention, there is a concern that the driver may feel uneasy or uncomfortable.
[0017] Therefore, there is a need for a steer-by-wire control device and a steer-by-wire control method that can accurately calculate steering wheel control parameters such as inertial torque using a method that does not easily cause anxiety or discomfort to the driver of the vehicle (steer-by-wire control method).
[0018] The purpose of this invention is to provide a steer-by-wire control device and a steer-by-wire control method that can accurately calculate the control parameters of the steering wheel using a method that does not easily cause anxiety or discomfort to the driver of the vehicle.
[0019] Technical solutions for solving technical problems
[0020] The steer-by-wire control device of the present invention includes: a first motor for moving the steering wheel of a vehicle; a second motor for controlling the steering action (i.e., steering maneuvering action) of the vehicle's wheels; and a control device for controlling the first motor and the second motor. Before the vehicle transitions to an autonomous driving mode, the control device applies a predetermined input torque to the steering wheel via the first motor in both the forward and reverse directions of the first motor's rotation direction. The control device acquires information regarding the steering wheel's action (i.e., behavior) resulting from the applied input torque, namely, action information. Based on the action information, the control device determines whether to transition to a control parameter calculation mode that calculates control parameters for the steering wheel. The action information includes at least one of the value of the steering wheel's rotation angle and a value obtained by time differentiation of the rotation angle.
[0021] The steer-by-wire control method of the present invention is executed by a control device, which controls a first motor that moves the steering wheel of a vehicle and a second motor that controls the steering action (steering maneuvering action) of the vehicle's wheels. The steer-by-wire control method includes: before the vehicle transitions to an autonomous driving mode, applying a predetermined input torque to the steering wheel via the first motor in both the forward and reverse directions of the first motor's rotation direction; acquiring information about the steering wheel's movement resulting from the applied input torque, i.e., movement information; and determining, based on the movement information, whether to transition to a control parameter calculation mode that calculates the control parameters of the steering wheel. The movement information includes at least one of the value of the steering wheel's rotation angle and the value obtained by time differentiation of the rotation angle.
[0022] The effects of the invention
[0023] According to the present invention, a steer-by-wire control device and a steer-by-wire control method are provided that can accurately calculate the control parameters of the steering wheel using a method that does not easily cause anxiety or discomfort to the driver of the vehicle. Attached Figure Description
[0024] Figure 1 This is a diagram showing the structure of the steer-by-wire control device according to Embodiment 1 of the present invention.
[0025] Figure 2 This is a diagram showing a cross-section of the steering mechanism along its axial direction.
[0026] Figure 3 This is a schematic diagram showing the structure of the control device that controls the reaction force motor and the steering motor.
[0027] Figure 4 This is a diagram showing the balance of torque around the steering wheel in Embodiment 1.
[0028] Figure 5 This is a flowchart illustrating the process by which the control device detects changes in the inertial torque of the steering wheel.
[0029] Figure 6A This is a diagram showing an example of the waveform of the reference torque (input torque).
[0030] Figure 6B It means to apply Figure 6A The diagram shows an example of the steering wheel rotation angle obtained from the reference torque.
[0031] Figure 6C It means to apply Figure 6A The diagram shows an example of the steering wheel angular velocity obtained from the reference torque.
[0032] Figure 7A This is a diagram showing an example of the waveform of the reference torque (input torque) in the control parameter calculation mode.
[0033] Figure 7B It means to apply Figure 7A The diagram shows an example of the angular acceleration of the steering wheel obtained from the reference torque.
[0034] Figure 8A This is a diagram showing the balance of torque around the steering wheel in Embodiment 2.
[0035] Figure 8B It is a diagram used to illustrate gravitational torque. Detailed Implementation
[0036] The steer-by-wire control device of the present invention is a steering control device mounted on a vehicle, having, for example, the structure described in the claims. The steer-by-wire control method of the present invention is executed by a steering control device mounted on a vehicle, having, for example, the structure described in the claims.
[0037] For example, before the vehicle enters the autonomous driving mode, the steer-by-wire control device of the present invention applies a predetermined input torque to the steering wheel in both the forward and reverse directions of the first motor (e.g., a reaction force electric motor) to move the steering wheel, thereby obtaining steering wheel movement information, and determining whether to calculate steering wheel control parameters (e.g., inertial torque) based on the movement information.
[0038] By making such a judgment based on steering wheel movement information, the inertial torque of the steering wheel can be calculated when the driver releases his hands from the steering wheel, i.e., when the driver's torque is zero. The inertial torque can be calculated with high accuracy.
[0039] Furthermore, compared to applying input torque to the steering wheel in only one direction, applying input torque to the steering wheel in both the forward and reverse directions of the first motor's rotation allows for the generation of the same degree of acceleration change with a smaller steering wheel rotation, reducing driver discomfort while simultaneously detecting changes in inertial torque with high precision. Moreover, by applying input torque in both the forward and reverse directions of the first motor's rotation, the steering wheel can return to its neutral point after a rotation, preventing driver anxiety caused by the steering wheel deviating from its neutral position.
[0040] The steer-by-wire control device and method of the present invention, through the above-described control, can accurately calculate the control parameters of the steering wheel using a method that does not easily cause unease or discomfort to the driver of the vehicle, and can accurately realize steering wheel grip detection and steering detection.
[0041] Hereinafter, the steer-by-wire control device and steer-by-wire control method of embodiments of the present invention will be described in detail with reference to the accompanying drawings.
[0042] In the following embodiments, the inertial torque is mainly described as a control parameter affecting the movement of the steering wheel. The control parameters for the steering wheel also include frictional torque and gravitational torque, but these will be described in Embodiment 2.
[0043] Furthermore, the present invention is not limited to the embodiments described below, and various modifications and applications of the technical concept of the present invention are also included within the scope of the present invention.
[0044] Example 1
[0045] Before describing specific embodiments of the present invention, using Figure 1 , 2 The general structure of the steer-by-wire control device will be described below. In the steer-by-wire control device described below, for a structure in which the steering shaft and the steering control shaft are separated, sensors (e.g., rotation angle sensor, current sensor, and rack position sensor) are used to detect the rotation angle of the steering shaft, the disturbance torque, and the steering control angle of the steering wheel, etc., and the actuation amount of the electric actuator for steering control and the electric actuator for reaction force are controlled based on the detection signals of the sensors.
[0046] Figure 1 This is a diagram showing the structure of the steer-by-wire control device according to Embodiment 1 of the present invention. The steer-by-wire control device of this embodiment includes a control device 19, a reaction force electric motor 18, and a steering control electric motor disposed in the steering control electric motor mechanism 21.
[0047] The steering wheel (steering control wheel) 10 is operated by a tie rod (steering tie rod) 11. The tie rod 11 is connected to the steering control shaft 17 (also called a rack) of the steering control mechanism 16. The steering control mechanism 16 includes the steering control shaft 17 and a steering control electric motor mechanism 21.
[0048] The steering wheel 12 is connected to the steering shaft 13. Sensors such as a steering angle sensor can be installed on the steering shaft 13 as needed.
[0049] The steering shaft 13 is not connected to the steering control shaft 17, and a reaction force electric motor 18 is located at the front end of the steering shaft 13. That is, the steering shaft 13 has a structure that is not mechanically connected to the steering control mechanism 16, resulting in the steering shaft 13 and the steering control mechanism 16 being separated from each other.
[0050] The reaction force electric motor 18 is controlled by the control device 19 and is a reaction force electric actuator that applies a steering operation reaction torque to the steering shaft 13 to move the steering wheel 12. The reaction force electric actuator can also be an electric actuator other than an electric motor. Hereinafter, the reaction force electric motor 18 will be referred to as the reaction force motor 18.
[0051] The reaction force motor 18 includes a rotation angle sensor 14 as a steering operation amount sensor for detecting the rotation of the steering shaft 13. The rotation angle sensor 14 detects the rotation angle of the reaction force motor 18, i.e., the rotation angle of the steering wheel 12. This steering operation amount sensor may not be a rotation angle sensor 14, but may be any sensor capable of detecting the rotation of the steering shaft 13; for example, it could be a steering operation angle sensor that detects the steering operation angle of the steering shaft 13.
[0052] Additionally, the reaction force motor 18 includes a current sensor 15, which serves as a steering operation amount sensor. The current sensor 15 detects the current flowing in the coil of the reaction force motor 18. This current can be used, for example, to calculate interference torque (e.g., the torque applied to the steering wheel 12 during vehicle operation) and to determine whether the driver of the vehicle is holding the steering wheel 12.
[0053] A steering control electric motor mechanism 21 is provided in the steering control mechanism 16, which includes the steering control shaft 17. The steering control electric motor mechanism 21 controls the steering operation of the steering control shaft 17. In this embodiment, the steering control mechanism 16 includes the steering control electric motor mechanism 21 so that an electric motor (the steering control electric motor 35 described later) can be used as the steering control electric actuator, but the steering control electric actuator may also be an electric actuator of a form other than an electric motor.
[0054] The control device 19 controls the electric motor mechanism 21 for steering control of the reaction force motor 18 and the steering control mechanism 16. The control device 19 inputs signals regarding the rotation angle of the steering wheel 12 detected by the rotation angle sensor 14 and signals regarding the current flowing in the coil of the reaction force motor 18 detected by the current sensor 15. In addition to these detection signals, the control device 19 also inputs various detection signals from external sensors 20.
[0055] The control device 19 calculates the control quantity of the steering electric motor mechanism 21 based on the input rotation angle and current information, and controls the steering electric motor mechanism 21. The control quantity of the steering electric motor mechanism 21 can also be obtained based on parameters other than rotation angle and current.
[0056] The electric motor mechanism 21 for steering control rotates the output pulley of the steering control mechanism 16 via the input pulley and the transmission belt, and then rotates the steering control shaft 17 to move axially via the steering control nut to operate the steering wheel 10. Details will be explained later.
[0057] The control device 19 calculates the control quantity for the reaction force motor 18 based on the input rotation angle and current information, as well as the rack position information detected by the rack position sensor 22, and controls the reaction force motor 18. The rack position sensor 22 detects the amount of movement of the steering shaft 17 from the reference position (neutral position). The amount of movement of the steering shaft 17 is equivalent to the steering angle (steering amount) of the steering wheel 10, which can also be called the steering control angle (steering control amount). Furthermore, the control quantity for the reaction force motor 18 can also be obtained based on parameters other than the rotation angle and / or current information, and the rack position information.
[0058] Control device 19 in Figure 1 The diagram is represented by a functional block, which includes a reaction force actuator control device and a steering control actuator control device. The reaction force actuator control device and the steering control actuator control device are interconnected via a communication line. The reaction force actuator control device is located in the reaction force motor 18 and controls the electric actuator for reaction force (reaction force motor 18). The steering control actuator control device is located in the steering electric motor mechanism 21 and controls the electric actuator for steering (steering electric motor 35 described later). Alternatively, the reaction force actuator control device and the steering control actuator control device can be configured using a single control device 19, which controls both the electric actuator for reaction force and the electric actuator for steering.
[0059] The steering mechanism 16 includes a rack position sensor 22 as a steering amount sensor to detect the amount of steering of the steering wheel 10 (i.e., the amount of steering maneuver). The rack position sensor 22 detects the axial travel of the steering shaft 17 and detects and outputs the actual amount of steering of the steering wheel 10 (steering angle). The steering amount sensor may not be such a rack position sensor 22, but can be any sensor capable of detecting the position (steering amount) of the steering shaft 17, for example, it may be a rotation angle sensor installed in the steering electric motor mechanism 21 that applies steering force to the steering shaft 17.
[0060] In addition, the steering control mechanism 16 includes a steering control shaft 17, a steering control electric motor mechanism 21, and a reduction mechanism, but the mechanism that transmits steering force from the steering control electric motor mechanism 21 to the steering wheel 10 is not limited to this.
[0061] Figure 2This is a diagram showing a cross-section of the steering mechanism 16 along the axial direction. (Using...) Figure 2 The structure of the steering control mechanism 16 will be described.
[0062] All components of the steering mechanism 16, except for the steering motor mechanism 21, are housed within the housing 32. The housing 32 comprises a steering shaft housing 30 and a reducer housing 31. The steering shaft housing 30 houses the steering shaft 17 in a manner that allows axial movement of the steering shaft 17. The reducer housing 31 is located at the axial center of the steering shaft housing 30 and is formed to surround the steering shaft 17. A reduction mechanism 33 is housed within the reducer housing 31.
[0063] The electric motor mechanism 21 for steering includes: an electric motor for steering 35, a steering actuator control device 44 for controlling the electric motor for steering 35, and a threaded mechanism 36 for transmitting the output of the electric motor for steering 35 to the steering shaft 17. The electric motor for steering 35 is controlled by the control device 19 to control the steering action of the vehicle's steering wheels 10. The steering actuator control device 44 controls the rotation amount and rotation speed of the electric motor for steering 35 according to the amount of steering operation applied by the driver to the steering wheel 12. Hereinafter, the electric motor for steering 35 will be referred to as the steering motor 35.
[0064] The threaded mechanism 36 includes a steering control nut 37 and an output pulley 38. The output pulley 38 is a cylindrical component fixed to the steering control nut 37 and rotates integrally with it. A cylindrical input pulley 39 is fixed to the drive shaft of the steering motor 35. The input pulley 39 rotates integrally with the drive shaft of the steering motor 35. A drive belt 40 is wound between the output pulley 38 and the input pulley 39. The reduction mechanism 33 consists of the input pulley 39, the output pulley 38, and the drive belt 40.
[0065] The steering nut 37 is annular and surrounds the steering shaft 17, and is configured to rotate relative to the steering shaft 17. The steering nut 37 has a helical groove on its inner circumference, which forms a nut-side ball screw groove. The steering shaft 17 has a helical groove on its outer circumference, which forms steering shaft-side ball screw grooves 17a and 17b.
[0066] With the steering control shaft 17 inserted into the steering control nut 37, a ball circulation groove is formed by the ball screw groove on the nut side and the ball screw grooves 17a and 17b on the steering control shaft side. The ball circulation groove is filled with multiple metal balls. When the steering control nut 37 rotates, the balls move within the ball circulation groove, thereby causing the steering control shaft 17 to move axially (lengthwise) relative to the steering control nut 37, thus performing a stroke action.
[0067] The steering control mechanism 16 has the structure described above. The steering motor 35 is controlled by the steering control actuator control device 44 to rotate, rotate in the direction of rotation and rotate at the speed of rotation, so as to move the steering control shaft 17 in accordance with the steering operation of the steering wheel 12, thereby controlling the vehicle.
[0068] also, Figure 2 The steering mechanism 16 is indicated as being mounted on the front wheels of the vehicle, but it can also be mounted on the rear wheels. Therefore, not only can the front wheels of the vehicle be steered using the steering motor 35, but the rear wheels can also be steered using the steering motor 35.
[0069] Figure 3 It means Figure 1 The diagram shows a schematic representation of the structure of the control device 19 controlling the reaction force motor 18 and the steering motor 35. As already described, the control device 19 includes a reaction force actuator control device and a steering actuator control device 44 disposed on the reaction force motor 18. Figure 3 The control device 19 shown represents both the reaction force actuator control device and the steering control actuator control device 44.
[0070] A rotation angle sensor 14 and a current sensor 15 are provided on the reaction force motor 18 connected to the steering shaft 13. The reaction force motor 18 is mechanically connected to the steering wheel 12. The rotation angle sensor 14 is a sensor that detects the rotation angle of the reaction force motor 18, in other words, the rotation angle of the steering wheel 12. The current sensor 15 is a sensor that detects the current flowing in the coil of the reaction force motor 18.
[0071] The control device 19 can identify whether the driver is holding the steering wheel 12 or not holding it based on the information of the rotation angle of the steering wheel 12 obtained by the rotation angle sensor 14 and the torque information of the reaction force motor 18.
[0072] Furthermore, in order to distinguish between the state in which the driver is holding the steering wheel 12 and the state in which the driver is not holding the steering wheel 12, the control device 19 can also use information from the current sensor 15. For example, the control device 19 can detect the vibration component of the current and determine whether the driver is holding the steering wheel 12 based on the change in the peak of the vibration component. In this way, a sensor suitable for the system can be used to distinguish between the state in which the driver is holding the steering wheel 12 and the state in which the driver is not holding the steering wheel 12.
[0073] The reaction force motor 18 is an electric motor that imparts a steering reaction torque to the steering shaft 13, and is controlled by the control device 19 via the motor driver 23. The steering motor 35 is an electric motor that actuates the steering shaft 17, and is controlled by the control device 19 via the motor driver 24.
[0074] The control device 19 receives information from the rack position sensor 22 and the rotation angle sensor 14, and controls the reaction force motor 18 based on the received information to apply a steering control reaction torque to the steering shaft 13, thereby rotating the steering wheel 12. Additionally, the control device 19 controls the steering motor 35 based on information received from the rotation angle sensor 14 and the current sensor 15, as well as information from the external steering command value, thereby driving the steering control shaft 17, which is mechanically connected to the steering motor 35.
[0075] The control unit 19 receives information about the rotation angle of the reaction force motor 18 from the rotation angle sensor 14, and information about the current flowing in the coil of the reaction force motor 18 from the current sensor 15. Furthermore, the control unit 19 receives information about the vehicle's driving state affecting steering (i.e., steering control) from driving state sensors such as the vehicle speed sensor 25 and the yaw rate sensor 26. Additionally, the control unit 19 receives information about the movement position of the steering control shaft 17 from the rack position sensor 22. The control unit 19 can derive the steering amount (steering angle) of the steering wheel 10 based on the movement position of the steering control shaft 17.
[0076] The rack position sensor 22 is mounted in the middle section of the housing 32 covering the steering control shaft 17 (see reference). Figure 1 , 2 The control device 19 can detect the position of the steering control shaft 17, which is directly connected to the tie rod 11. Therefore, the control device 19 can detect the steering angle of the steering wheel 10 based on the position information of the rack position sensor 22. In this way, the rack position sensor 22 functions as a detector for detecting the steering angle of the steering wheel 10.
[0077] Additionally, the control unit 19 receives external steering command values from the automatic steering system 27 (e.g., an advanced driver assistance system, ADAS), which serves as the external steering control unit. The external steering command values are command values calculated and derived by the automatic steering system 27, and are external steering command information. For example, the external steering command values are commands used to steer the steering wheels via the steering mechanism 16 in situations such as when the vehicle has deviated from the white lines on the road due to lane keeping control, or when avoiding obstacles.
[0078] The steer-by-wire control device of this embodiment has the above structure. The control device 19 calculates the driver torque by detecting the driver's grip on the steering wheel 12. To calculate the driver torque, it is necessary to obtain the inertial torque of the steering wheel 12. To obtain this inertial torque, it is necessary to obtain the inertial moment of the steering wheel 12. An example of how the steer-by-wire control device of this embodiment calculates and obtains the inertial moment of the steering wheel 12 will be described below. As described above, the inertial moment is a control parameter that affects the movement of the steering wheel.
[0079] Figure 4 It is a diagram showing the balance of torque around the steering wheel 12. Figure 4 This represents the driver torque Ts, motor torque Tm, and inertial torque Tj. Driver torque Ts is the torque applied by the driver. Motor torque Tm is the torque applied by the reaction force motor 18. Inertial torque Tj is the torque generated by the inertial torque of the steering wheel 12 (i.e., the inertial torque of the steering wheel 12 and the parts rotating in conjunction with it). When calculating the driver torque Ts, the following is considered... Figure 4 The torque balance is shown.
[0080] Below, as an example, regarding... Figure 4 As shown, the case in which the driver torque Ts is applied clockwise when viewed from above the paper, and the motor torque Tm is applied counterclockwise when viewed from above the paper in a manner that opposes the driver torque Ts, will be explained.
[0081] like Figure 4 As shown, the balance of driver torque Ts, motor torque Tm and inertial torque Tj is represented by equation (1).
[0082] Ts=Tm-Tj……(1)
[0083] The motor torque Tm can be obtained from the current information of the current sensor 15. The inertial torque Tj can be obtained from the rotation angle information of the rotation angle sensor 14. Specifically, the motor torque Tm can be obtained by multiplying the current value detected by the current sensor 15 by the torque constant of the reaction force motor 18. The inertial torque Tj can be obtained by taking the rotation angle detected by the rotation angle sensor 14 twice to obtain the rotation angle acceleration, and then multiplying the rotation angle acceleration by the inertial torque of the steering wheel 12. The driver torque Ts can be calculated by substituting the motor torque Tm and the inertial torque Tj obtained in this way into equation (1).
[0084] When calculating the driver torque Ts, the following points should be noted. For example, if accessories such as a cover are installed on the steering wheel 12, or if the steering wheel 12 has been replaced, the actual value of the inertial torque of the steering wheel 12 will differ from the value based on the design value. Therefore, the value of the inertial torque Tj calculated based on the design value may sometimes differ from the actual value of the inertial torque Tj. In such cases, the calculation error of the driver torque Ts may increase. Therefore, in order to calculate the driver torque Ts with high accuracy, it is necessary to calculate the actual inertial torque of the steering wheel 12 with high accuracy.
[0085] In the steer-by-wire control device of this embodiment, the control device 19 applies a reference torque to the steering wheel 12 via the reaction force motor 18, and detects changes in the inertial torque based on the movement of the steering wheel 12 in response to this reference torque. The reference torque is a predetermined input torque that varies according to a pre-determined waveform. The reference torque can be arbitrarily determined, but preferably has a magnitude capable of detecting changes in the inertial torque of the steering wheel 12.
[0086] In order to detect the change in inertial torque based on the movement of the steering wheel 12 obtained by applying a reference torque, it is necessary to create a state in which the motor torque Tm and the inertial torque Tj are balanced as shown in Equation (2).
[0087] Tm=Tj……(2)
[0088] The state shown in Equation (2) is the state in Equation (1) where the driver torque Ts is zero, i.e., the state in which the driver is not touching the steering wheel 12. If the reference torque is applied in the state shown in Equation (2) and the change in inertial torque is detected, it is possible to prevent the inertial torque from changing due to the driver's influence. Therefore, the reference torque needs to be applied when the driver torque Ts is zero.
[0089] Furthermore, the inertial torque of the steering wheel 12 must be calculated before the vehicle transitions to the autonomous driving mode. If the driver torque Ts is calculated based on the design torque value even though the actual inertial torque value differs from the design value, the calculated driver torque Ts will contain an error, differing from the actual value. Moreover, due to this error, the vehicle may enter a dangerous state if the automatic steering system 27 incorrectly identifies whether the driver is holding the steering wheel 12.
[0090] To prevent this from happening, in the steer-by-wire control device of this embodiment, the control device 19 performs an operation to check whether the inertial torque of the steering wheel 12 has changed before the vehicle switches to autonomous driving mode. Figure 5 The process is shown in the flowchart.
[0091] Figure 5 This is a flowchart illustrating the process by which the control device 19 detects changes in the inertial torque of the steering wheel 12. Figure 5 The following is a flowchart illustrating the process by which control device 19 detects changes in inertial torque when triggered by the vehicle's ignition switch (hereinafter referred to as "IGN"). Furthermore, as long as control device 19 performs the process of detecting changes in inertial torque before transitioning to autonomous driving mode, it can also be triggered by conditions other than IGN being on. For example, it could be triggered by the unlocking of the vehicle or by sensing the driver's approach to the vehicle.
[0092] In S10, the control device 19 determines whether a signal indicating that IGN is turned on has been input. If IGN is turned on, the process in S11 is executed.
[0093] In S11, the control device 19 applies a reference torque (input torque) to the steering wheel 12 via the reaction force motor 18. As will be described later, the control device 19 determines which mode to switch to based on information about the movement of the steering wheel 12 obtained by applying the reference torque (S19 to S21).
[0094] In S12, the control device 19 acquires information (action information) regarding the movement of the steering wheel 12 obtained by applying a reference torque. This action information includes, for example, at least one of the following: the value of the rotation angle of the steering wheel 12, and the value of the angular velocity, the value of the angular acceleration, and the value of the angular jerk of the steering wheel 12 obtained by differentiating the rotation angle over time.
[0095] In S13, the control device 19 stores the action information acquired in S12. Furthermore, the control device 19 stores design values or post-manufacturing measurement values as initial values for the action information.
[0096] In S14, the control device 19 calculates and obtains the change in the action information. The control device 19 compares the action information obtained in S12 (the current action information) with the action information stored in S13 when IGN was last turned on (the previous action information), and calculates the change in the current action information from the previous action information.
[0097] The control device 19 preferably processes the change in action information using absolute values to account for both increases and decreases in the value of the action information. This is because the change in the current action information since the last action information includes both positive values (in the case of an increase in the value of the action information) and negative values (in the case of a decrease in the value of the action information). That is, when the control device 19 compares the change in action information with a threshold using the absolute value of the change in action information as the change in action information and through the processing described below, it preferably compares the magnitude of the absolute value of the change in action information with the magnitude of the threshold.
[0098] In S15, the control device 19 compares the change in the motion information obtained in S14 with a predetermined threshold A. Threshold A is a value used to determine whether the moment of inertia has changed. If the change is below threshold A, the control device 19 determines that the moment of inertia has not changed because the change is within a specified range, and executes the process in S17. If the change is greater than threshold A, the control device 19 executes the process in S16.
[0099] In S17, the control device 19 determines whether there is a request from the driver to activate the automatic driving mode (a request to switch to the automatic driving mode, i.e., the automatic steering mode). If there is a request from the driver to activate the automatic driving mode, the control device 19 executes the processing in S19.
[0100] In S19, control device 19 switches to automatic driving mode, causing the vehicle to enter automatic driving mode. In this case, control device 19 uses the value of the inertial torque used last time to calculate the driver torque Ts.
[0101] S16 is the processing procedure when the change in action information exceeds a threshold A. In S16, the control device 19 compares the change in action information obtained in S14 with a predetermined threshold B. The threshold B is a value greater than the threshold A and is used to determine whether the driver is in contact with the steering wheel 12 (i.e., whether equation (2) is satisfied). If the change is less than the threshold B, the control device 19 determines that the inertial torque needs to be calculated because the driver is not in contact with the steering wheel 12 (i.e., equation (2) is satisfied and the driver torque Ts is zero), but the change in inertial torque exceeds the specified range, and executes the processing procedure S20. If the change is greater than the threshold B, the control device 19 executes the processing procedure S18.
[0102] In S20, the control device 19 determines that the inertial torque has changed and the driver torque Ts is zero because the change in the action information is greater than threshold A but less than threshold B. It then switches to the control parameter calculation mode to calculate the steering wheel's control parameters. In the control parameter calculation mode, the control device 19 calculates the inertial torque of the steering wheel 12 using the method described later.
[0103] When or after switching to the control parameter calculation mode, the control device 19 can notify the driver that the switch has been completed, or instruct the driver to release their hands from the steering wheel 12 until the inertial torque is calculated. The control device 19 can make such notifications or instructions by outputting at least one of images, characters, and sounds.
[0104] S18 is the processing procedure when the change in the action information exceeds thresholds A and B. In this case, the control unit 19 determines that the driver is touching the steering wheel 12 (i.e., the driver torque Ts is not zero) or that the action information has changed due to interference. In S18, the control unit 19 determines whether there is a request from the driver to activate the automatic driving mode (a request to switch to the automatic driving mode). If there is a request from the driver to activate the automatic driving mode, the control unit 19 executes the processing procedure of S21.
[0105] In S21, control device 19 switches to automatic driving cancellation mode, canceling the automatic driving start request from the driver. In this case, since the driver is driving manually in manual driving mode, control device 19 does not need to calculate the inertial torque.
[0106] When or after switching to the autopilot cancellation mode, the control device 19 can notify the driver that autopilot cannot be performed, or instruct the driver to release their hands from the steering wheel 12. The control device 19 can make such notifications or instructions by outputting at least one of images, characters, and sounds.
[0107] In addition, the control device 19 can also re-execute the process that started from S11 after executing the process of S21.
[0108] Control device 19 executes Figure 5The process shown in the flowchart involves calculating the inertial torque using a method described later when the change in the steering wheel 12's inertial torque exceeds a specified range, the value of the inertial torque differs from the design value, and the driver's torque Ts is zero. Therefore, the driver's torque Ts can be calculated with high accuracy. Furthermore, if the control device 19 cannot correctly detect changes in inertial torque, such as when the driver is in contact with the steering wheel 12, it cancels the automatic driving activation request from the driver, preventing the vehicle from entering a dangerous state due to misidentification of the driver holding the steering wheel 12. Therefore, in the steer-by-wire control device of this embodiment, a safe transition to automatic driving is possible.
[0109] Figures 6A to 6C This is a diagram illustrating the method for calculating the change in information (action information) regarding the movement of the steering wheel 12 obtained with the applied reference torque. Using... Figures 6A to 6C ,right Figure 5 The method for calculating the change in action information in S14 will be explained in detail.
[0110] Figure 6A An example of a waveform representing the reference torque (input torque). In Figure 6A The example shown is a reference torque with a pulse-like waveform. Figure 6B Indicates applying Figure 6A The example shown is the rotation angle of the steering wheel 12 obtained from the reference torque. Figure 6C Indicates applying Figure 6A The example shown is the angular velocity of steering wheel 12 obtained from the reference torque. Figure 6B In the diagram, solid lines represent the previous action information (rotation angle), and dashed lines represent the current action information (rotation angle). The change in action information is represented by the difference between the peak values (arrival angle) of the previous and current rotation angles, i.e., the change in arrival angle. Figure 6C In the diagram, solid lines represent the previous action information (angular velocity), and dashed lines represent the current action information (angular velocity). As the change in action information, the difference between the peak values (arrival angular velocity) of the previous and current angular velocities is the change in arrival angular velocity.
[0111] For example, it can be assumed that if the steering wheel 12 is replaced with a steering wheel 12 with a smaller inertial torque compared to the one when the action information was last obtained, such as Figure 6B and Figure 6C As shown, the arrival angle and arrival angular velocity increased in this action information. Therefore, the control device 19... Figure 5 In step S14, when calculating the change in motion information, the change in arrival angle and the change in arrival angular velocity are calculated. Then, the control device 19 compares the calculated changes with threshold A in step S15 and with threshold B in step S16.
[0112] Control device 19 applies a pulsed reference torque (input torque) to the reaction force motor 18 in both the forward and reverse rotation directions. The pulsed torque, such as… Figure 6A As shown, the torque is represented by a rectangular waveform with positive and negative values. If the reference torque is pulsed, it has the following advantages: the position of the rotated steering wheel 12 can be returned to the neutral point using positive torque (forward rotation of the reaction force motor 18) and negative torque (reverse rotation of the reaction force motor 18), and the torque with rapidly changing rectangular waveform can be applied.
[0113] If the control device 19 applies a rapidly changing torque as a reference torque in both the forward and reverse directions of the rotation direction of the reaction force motor 18, it can produce the same degree of acceleration change with a smaller rotational movement of the steering wheel 12 compared to applying torque in only one direction. Therefore, the control device 19 can reduce driver discomfort while accurately detecting changes in inertial torque. Furthermore, by applying the reference torque in both the forward and reverse directions of the rotation direction of the reaction force motor 18, the control device 19 can return the steering wheel 12 to the neutral point after rotation. Therefore, the control device 19 can prevent the driver from feeling uneasy due to the steering wheel 12 deviating from the neutral point.
[0114] exist Figure 6B and Figure 6C In the example of motion information used to detect changes in inertial torque, rotation angle and angular velocity are represented. Angular acceleration obtained by differentiating angular velocity over time, and angular jerk obtained by differentiating angular acceleration over time, can also be used in the motion information.
[0115] Figure 7A and Figure 7B This diagram illustrates the method for calculating the moment of inertia of steering wheel 12. (Using...) Figure 7A and Figure 7B , for Figure 5 The method for calculating the inertial torque of the steering wheel 12 under the control parameter calculation mode of S20 is explained in detail.
[0116] In control parameter calculation mode, control device 19, and in Figure 5 The processes shown in S11 to S14 similarly apply a reference torque (input torque) to the steering wheel 12 via the reaction force motor 18, calculate and obtain the change in the steering wheel 12's movement information, and thus estimate the inertial torque of the steering wheel 12. The control device 19 stores the estimated inertial torque.
[0117] Figure 7AThis is an example of a waveform representing the reference torque (input torque) in the control parameter estimation mode. Figure 7A The example shown is a reference torque with a sinusoidal waveform. Figure 7B Indicates applying Figure 7A An example of the angular acceleration of the steering wheel 12 obtained from the reference torque shown. Figure 7B In the diagram, solid lines represent the previous motion information (angular acceleration), and dashed lines represent the current motion information (angular acceleration). The change in motion information is represented by the amplitude change, which is the difference between the peak values of the previous and current angular accelerations.
[0118] First, the control device 19 applies a reference torque to the steering wheel 12 via the reaction force motor 18. In control parameter calculation mode, the control device 19 applies a reference torque as an example. Figure 7A The waveform shown is a sinusoidal reference torque. If the waveform of the reference torque is sinusoidal, the steering wheel 12 can rotate smoothly without causing discomfort to the driver.
[0119] The control device 19 preferably applies a reference torque to the steering wheel 12 via the reaction force motor 18 in the control parameter calculation mode. This reference torque is obtained by processing that detects changes in the inertial torque of the steering wheel 12. Figure 5 The value of the steering wheel 12 movement information obtained by applying the reference torque in S11 is a reference torque that is larger than the value of the movement information. If the control device 19 can obtain a larger value of the movement information (e.g., a larger change in angular acceleration), it can calculate the inertial torque with higher accuracy.
[0120] Therefore, when the control device 19 applies the reference torque in the control parameter calculation mode, it notifies the driver of the steering wheel 12's movement and then causes the steering wheel 12 to move relative to the reference torque. Figure 5 The action is larger when a reference torque (in this embodiment, a reference torque with a pulsed waveform) is applied in S11. For example, the control device 19 preferably applies a maximum value greater than [the reference torque value is missing in the original text] in the control parameter calculation mode. Figure 5 The reference torque applied in S11 is a large reference torque.
[0121] Next, the control device 19 acquires the steering wheel 12's movement information (angular acceleration in this embodiment) obtained by applying a reference torque. Then, the control device 19 calculates the rate of change of the amplitude of the current movement information (angular acceleration) from the amplitude of the previous movement information (angular acceleration). The control device 19 can calculate the current inertial torque by multiplying the reciprocal of the calculated rate of change of the amplitude of the movement information by the previous inertial torque. The control device 19 stores the previous movement information and the previous inertial torque. In addition, the control device 19 stores the design value or the measured value after manufacturing as the initial value of the inertial torque.
[0122] For example, if the steering wheel 12 is replaced with a steering wheel 12 with a smaller inertial torque compared to the one with the previously calculated inertial torque, then... Figure 7B As shown, the amplitude of angular acceleration increases in this action information. The result of multiplying angular acceleration by the inertial torque is the inertial torque Tj. When the driver torque Ts is zero, the inertial torque Tj remains balanced with the reference torque (motor torque Tm). Therefore, the control device 19 knows that the inertial torque reduces the amount by which the amplitude of angular acceleration increases. The control device 19 can calculate the inertial torque of the steering wheel 12 after replacement (the current inertial torque) by multiplying the reciprocal of the rate of change of amplitude (the rate of increase in the above description) by the inertial torque of the steering wheel 12 before replacement (the previous inertial torque).
[0123] Furthermore, in the method for calculating the inertial torque of the steering wheel 12 using a control parameter calculation mode, the execution is related to... Figure 5 The processing steps S11 to S14 in the process of detecting changes in the inertial torque of the steering wheel 12 shown are performed using the same method (applying a reference torque, calculating and obtaining the change in motion information). Therefore, the control device 19 can also perform this process simultaneously. Figure 5 The processing shown includes S11 to S14, and the processing of calculating the inertial torque of the steering wheel 12 in the control parameter calculation mode. When the control device 19 performs these processes simultaneously, it is less likely to cause anxiety or discomfort to the driver of the vehicle, and it can quickly calculate the inertial torque.
[0124] However, in order to calculate the moment of inertia with higher accuracy, it is preferable to perform separate calculations. Figure 5 The processes S11 to S14 shown in the process, and the process of calculating the inertial torque of the steering wheel 12 in the control parameter calculation mode, apply a reference torque suitable for each process (for example, a pulsed reference torque and a sine wave reference torque are applied respectively).
[0125] In the steer-by-wire control device of this embodiment, the control device 19 can accurately calculate the inertial torque of the steering wheel 12 using a method that does not easily cause anxiety or discomfort to the driver of the vehicle, as described above. Therefore, the steer-by-wire control device of this embodiment can accurately calculate the driver's torque and can accurately detect whether the driver is holding the steering wheel 12 or whether the driver has performed steering operations on the steering wheel 12.
[0126] Example 2
[0127] The steer-by-wire control device of Embodiment 2 of the present invention will be described. In the steer-by-wire control device of this embodiment, the control device 19 is able to detect changes in the rotational friction of the steering shaft 13 and changes in the mounting angle of the steering wheel 12 based on the method for detecting changes in inertial torque described in Embodiment 1. By detecting these changes, for example, the influence of rotational friction on the long-term deterioration of the steering shaft 13 and the influence of adjusting the mounting angle of the steering wheel 12 can be determined.
[0128] Figure 8A This diagram illustrates the balance of torques around the steering wheel 12, taking into account the integration of driver torque Ts, motor torque Tm, and inertial torque Tj, as well as frictional torque Tf and gravitational torque Tg. Driver torque Ts, motor torque Tm, and inertial torque Tj were explained in Embodiment 1. Frictional torque Tf is the torque generated at the bearing portion of the steering shaft 13, etc. Gravitational torque Tg is the torque generated due to changes in the center of gravity position of the steering wheel 12. Frictional torque Tf and gravitational torque Tg are included in the control parameters of the steering wheel.
[0129] Figure 8B This diagram illustrates the gravitational torque Tg. As the steering wheel 12 rotates, the position of its center of gravity Gs changes, generating a gravitational torque Tg. It is assumed that the gravitational torque Tg is caused by the force of gravity acting on the center of gravity Gs of the steering wheel 12, and primarily changes as the installation angle of the steering wheel 12 in the tilt direction changes.
[0130] In this embodiment, when calculating the driver's torque Ts, the control device 19 considers Figure 8A The torque balance shown. The torque balance around the steering wheel 12 is represented by equation (3).
[0131] Ts=Tm-Tj-Tf-Tg……(3)
[0132] In this embodiment, the control device 19 can calculate the driver torque Ts with higher accuracy by taking into account the friction torque Tf and the gravitational torque Tg.
[0133] When the driver is not touching the steering wheel 12, since the driver torque Ts is zero, equation (3) is expressed as equation (4).
[0134] Tm=Tj+Tf+Tg……(4)
[0135] That is, when the driver torque Ts is zero, the motor torque Tm is balanced with the sum of the inertial torque Tj, friction torque Tf, and gravitational torque Tg (Tj+Tf+Tg). Therefore, considering the situation described in Embodiment 1, the control device 19 can detect not only changes in the inertial torque, but also changes in the friction torque Tf and gravitational torque Tg, by applying a reference torque (input torque) to the steering wheel 12 and by detecting the movement of the steering wheel 12 based on the reference torque.
[0136] Furthermore, when the control device 19 applies a reference torque that causes the steering wheel 12 to rotate at a certain speed, since the angular acceleration of the steering wheel 12 is zero, the inertial torque Tj is zero, as shown in equation (5), and the motor torque Tm is balanced with the sum of the friction torque Tf and the gravitational torque Tg (Tf+Tg).
[0137] Tm=Tf+Tg……(5)
[0138] Therefore, based on the movement of the steering wheel 12 obtained from the reference torque that causes the steering wheel 12 to rotate at a certain speed, the control device 19 can detect changes in frictional torque Tf and gravitational torque Tg, and can calculate changes in rotational friction of the steering shaft 13 and changes in the mounting angle of the steering wheel 12.
[0139] In the steer-by-wire control device of this embodiment, the control device 19 can detect changes in the rotational friction of the steering shaft 13 and changes in the mounting angle of the steering wheel 12 with high precision in a manner that does not easily cause unease or discomfort to the driver of the vehicle. Therefore, the steer-by-wire control device of this embodiment can accurately calculate the driver's torque and can accurately detect whether the driver is holding the steering wheel 12 or whether the driver has performed steering operations on the steering wheel 12.
[0140] Furthermore, the present invention is not limited to the above embodiments and various modifications are possible. For example, the above embodiments are detailed descriptions provided to facilitate understanding of the present invention, and the present invention is not necessarily limited to having all the described structures. Additionally, a portion of the structure of one embodiment can be replaced with the structure of another embodiment. Furthermore, structures of other embodiments can be added to the structure of one embodiment. Additionally, a portion of the structure of each embodiment can be deleted, added to, or replaced with other structures.
[0141] Explanation of reference numerals in the attached figures
[0142] 10 Steering wheel; 11 Tie rod; 12 Steering wheel; 13 Steering shaft; 14 Rotation angle sensor; 15 Current sensor; 16 Steering control mechanism; 17 Steering control shaft; 17a, 17b Ball screw grooves on the steering control shaft side; 18 Electric motor for reaction force; 19 Control device; 20 External sensor; 21 Electric motor mechanism for steering control; 22 Rack position sensor; 23 Motor driver; 24 Motor driver; 25 Vehicle speed sensor; 26 Yaw rate sensor; 27 Automatic steering control system; 30 Steering control shaft housing; 31 Reducer housing; 32 Housing; 33 Reduction mechanism; 35 Electric motor for steering control; 36 Threaded mechanism; 37 Steering control nut; 38 Output pulley; 39 Input pulley; 40 Drive belt; 44 Steering control actuator control device.
Claims
1. A steer-by-wire control device, characterized in that, include: The first motor that moves the vehicle's steering wheel; A second motor that controls the steering of the vehicle's wheels; A control device for controlling the first motor and the second motor. Before the vehicle switches to autonomous driving mode, the control device applies a predetermined input torque to the steering wheel via the first motor in both the forward and reverse directions of the first motor's rotation direction. The control device acquires information about the steering wheel's movement resulting from the application of the input torque, i.e., movement information. Based on the action information, the control device determines whether to switch to a control parameter calculation mode that calculates the control parameters of the steering wheel, including inertial torque, friction torque, and gravitational torque. The action information includes at least one of the value of the steering wheel rotation angle and the value obtained by differentiating the rotation angle over time.
2. The steer-by-wire control device according to claim 1, characterized in that: When the control device determines that it needs to switch to the control parameter calculation mode, it calculates the inertial torque of the steering wheel based on the action information.
3. The steer-by-wire control device according to claim 1, characterized in that: The input torque is a pulse-shaped torque.
4. The steer-by-wire control device according to claim 1, characterized in that: The input torque is a torque with a sinusoidal waveform.
5. The steer-by-wire control device according to claim 1, characterized in that: The control device compares the current action information obtained as action information obtained by applying the input torque with the previous action information obtained as action information obtained by applying the input torque last time, calculates the change in the current action information from the previous action information, and determines whether to switch to the control parameter calculation mode based on the change.
6. The steer-by-wire control device according to claim 5, characterized in that: The control device determines whether to switch to the control parameter calculation mode based on the absolute value of the change.
7. The steer-by-wire control device according to claim 5, characterized in that: When the change exceeds a predetermined first threshold, the control device switches to the control parameter calculation mode.
8. The steer-by-wire control device according to claim 7, characterized in that: When the change amount is below a predetermined second threshold, the control device switches to the control parameter calculation mode.
9. The steer-by-wire control device according to claim 8, characterized in that: When the change amount is below the first threshold, the control device causes the vehicle to switch to the autonomous driving mode; when the change amount is greater than the second threshold, it cancels the autonomous driving request from the driver of the vehicle.
10. The steer-by-wire control device according to claim 5, characterized in that: When the control device determines that it needs to switch to the control parameter calculation mode, it calculates the inertial torque of the steering wheel based on the change.
11. A steer-by-wire control method, characterized in that: The steer-by-wire control method is executed by a control device, which controls a first motor that moves the vehicle's steering wheel and a second motor that controls the steering of the vehicle's wheels. The steer-by-wire control method includes: Before the vehicle transitions to autonomous driving mode, a predetermined input torque is applied to the steering wheel by the first motor in both the forward and reverse directions of the first motor's rotation direction. The step of obtaining information about the steering wheel's movement as a result of applying the input torque, i.e., the movement information; and Based on the aforementioned action information, the step of determining whether to transition to a control parameter calculation mode for calculating the steering wheel's control parameters, wherein the steering wheel's control parameters include inertial torque, frictional torque, and gravitational torque, is described. The action information includes at least one of the value of the steering wheel rotation angle and the value obtained by differentiating the rotation angle over time.
Citation Information
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