Patent Publication Number: US-2021179225-A1

Title: Leaning-vehicle-steering-actuator controller and leaning vehicle

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This is a continuation-in-part application of International Application PCT/JP2019/034103 filed on Aug. 30, 2019, which claims priority from a Japanese Patent Application No. 2018-161336, filed on Aug. 30, 2018. The contents of the applications are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present teaching relates to a leaning-vehicle-steering-actuator controller controlling a steering actuator configured to output a steering torque, and a leaning vehicle. 
     BACKGROUND ART 
     For example, a leaning vehicle as disclosed in Patent Literature 1 is known as a conventional leaning vehicle. The leaning vehicle includes a vehicle body frame, a steerable wheel, a steering torque transmission mechanism, a steering torque detector, and a motor. 
     When the leaning vehicle is turning left, the vehicle body frame leans in a leaning-vehicle-leftward direction, and when the leaning vehicle is turning right, the vehicle body frame leans in a leaning-vehicle-rightward direction. The steerable wheel is supported by the vehicle body frame. The steering torque transmission mechanism includes a steering shaft and a handlebar assembly. The steering shaft is supported by the vehicle body frame in a rotatable manner. The handlebar assembly is connected to the steering shaft directly or indirectly. When a rider manipulates the handlebar assembly, the steering torque transmission mechanism steers the steerable wheel via the steering shaft. The steering torque detector detects the steering torque inputted to the steering torque transmission mechanism. The motor generates a torque to assist the rider in his/her steering action, based on the steering torque detected by the steering torque detector. 
     CITATION LIST 
     Patent Literature 
     Patent Literature 1: International Patent Application Publication WO2016/175263 
     SUMMARY OF INVENTION 
     Technical Problem 
     New suggestions about a steering actuator controller as described above are demanded. 
     An object of the present teaching is to provide a leaning-vehicle-steering-actuator controller that controls a steering actuator in an unconventional manner, and a leaning vehicle. 
     Solution to Problem 
     In the leaning vehicle disclosed in Patent Literature 1, the steering torque detector detects the steering torque acting on the steering shaft, and the actuator (motor) generates a torque to assist the rider&#39;s manipulation, based on the steering torque. However, the present inventors conducted studies while considering the actuator as not a device for assisting the rider&#39;s manipulation but a device for controlling the posture of the vehicle body frame. Then, the present inventors conducted studies about what action the rider takes for a roll angle change of the vehicle body frame, which is an example of a posture change of the vehicle body frame. 
     In order to change the roll angle of the vehicle body frame, the rider applies a steering force to the handlebar. Then, the steering force is transmitted from the handlebar to the steering shaft, and a steering torque is applied to the steering shaft. In accordance with the steering torque, the steering shaft rotates, and the steerable wheel is steered. When the steerable wheel is steered, the roll angle of the vehicle body frame changes. In other words, the posture of the vehicle body frame changes. Thus, the rider controls the posture of the vehicle body frame by using the steering torque applied to the steering shaft as an input parameter. 
     The greater the absolute value of the steering force (i.e., steering torque) is, the greater the absolute value of the rate of change of the roll angle (i.e., roll rate) of the vehicle body frame is. Also, the smaller the absolute value of the steering force (i.e., steering torque) is, the smaller the absolute value of the roll rate of the vehicle body frame is. Accordingly, the present inventors obtained a view that there is a correlation between the steering torque and the roll rate. Then, the present inventors conceived of an idea that the roll rate, instead of the steering torque, can be used as an input parameter for posture control of the vehicle body frame. In other words, the present inventors conceived of detecting the roll rate and controlling the posture of the vehicle body frame based on the roll rate. 
     In order to solve the problem above, the present teaching employs the following configurations. 
     (1) A leaning-vehicle-steering-actuator controller for a leaning vehicle, the leaning vehicle including: 
     a vehicle body frame configured to lean in a leaning-vehicle-leftward direction when the leaning vehicle is turning left and to lean in a leaning-vehicle-rightward direction when the leaning vehicle is turning right; 
     at least one steerable wheel supported by the vehicle body frame; 
     a handlebar configured to be manipulated by a rider to steer the at least one steerable wheel, and supported by the vehicle body frame in a rotatable manner; 
     a steering actuator configured to apply a torque to the at least one steerable wheel to steer the at least one steerable wheel; and 
     a roll rate sensor configured to detect a roll rate that is an amount of change per unit time of a roll angle of the vehicle body frame around a roll axis extending along a leaning-vehicle-front-back direction, the roll angle changing as the vehicle body frame is rotating around the roll axis; 
     wherein the leaning-vehicle-steering-actuator controller controls the steering actuator by using the roll rate sensor without using a torque sensor configured to detect a torque generated around a rotation axis of the handlebar by a rider&#39;s manipulation and based on the roll rate obtained from the roll rate sensor, not the torque detected by the torque sensor as the torque generated around the rotation axis of the handlebar by the rider&#39;s manipulation. 
     The leaning-vehicle-steering-actuator controller of (1) can control the steering actuator in an unconventional manner. More specifically, in order to change the roll angle of the vehicle body frame, the rider manipulates the handlebar to generate a steering torque around the rotation axis of the handlebar. Then, the roll angle of the vehicle body frame changes, and the posture of the vehicle body frame changes. Thus, the rider can control the posture of the vehicle body frame by using the steering torque applied to the steering shaft as an input parameter. 
     The greater the absolute value of the steering torque is, the greater the absolute value of the roll rate, which is the rate of change of the roll angle of the vehicle body frame, is. The smaller the absolute value of the steering torque is, the smaller the absolute value of the roll rate of the vehicle frame is. Thus, there is a correlation between the steering torque and the roll rate. Therefore, instead of the steering torque, the roll rate can be used as an input parameter for posture control of the vehicle body frame. Accordingly, the leaning-vehicle-steering-actuator controller of (1) controls the steering actuator based on the roll rate. 
     For the following reason, the leaning-vehicle-steering-actuator controller of (1) controls the steering actuator without using the torque sensor configured to detect the steering torque and not based on the steering torque detected by the torque sensor. There is a correlation between the steering torque and the roll rate, and therefore, the steering torque does not need to be detected if the roll rate is detected. Accordingly, the leaning-vehicle-steering-actuator controller can control the steering actuator not based on the steering torque, which is conventionally used for control of the steering actuator. 
     For the reason above, the leaning-vehicle-steering-actuator controller of (1) can control the steering actuator by using the roll rate sensor without using the torque sensor configured to detect the steering torque, and based on the roll rate obtained from the roll rate sensor, not the steering torque detected by the torque sensor. Thus, the leaning-vehicle-steering-actuator controller of (1) can control the steering actuator in an unconventional manner. 
     The leaning-vehicle-steering-actuator controller of (1) does not use the steering torque for control of the steering actuator. Accordingly, a leaning vehicle including the leaning-vehicle-steering-actuator controller of (1) does not need to include a torque sensor configured to detect the steering torque. However, the leaning vehicle including the leaning-vehicle-steering-actuator controller of (1) may include a torque sensor configured to detect the steering torque. 
     (2) The leaning-vehicle-steering-actuator controller according to (1), wherein the leaning-vehicle-steering-actuator controller controls the steering actuator by using the roll rate sensor using neither the torque sensor configured to detect the torque generated around the rotation axis of the handlebar by the rider&#39;s manipulation nor a roll sensor configured to detect the roll angle, and based on the roll rate obtained from the roll rate sensor, neither the torque detected by the torque sensor nor the roll angle detected by the roll sensor. 
     The leaning-vehicle-steering-actuator controller of (2) can control the steering actuator in an unconventional manner. More specifically, the present inventors also conducted studies about the correlation between the steering torque and the roll angle. As a result, the inventors found that the correlation between the steering torque and the roll angle is not so high as the correlation between the steering torque and the roll rate in a transient state where a roll rate is generated. Then, the leaning-vehicle-steering-actuator controller controls the steering actuator by using the roll rate sensor with using neither the torque sensor configured to detect the steering torque nor the roll sensor configured to detect the roll angle, and based on the roll rate obtained from the roll rate sensor, neither the steering torque detected by the torque sensor nor the roll angle detected by the roll sensor. Thus, the leaning-vehicle-steering-actuator controller of (2) can control the steering actuator in an unconventional manner. 
     (3) The leaning-vehicle-steering-actuator controller according to (1) or (2), wherein: 
     the leaning vehicle further includes a speed sensor configured to detect a speed of the leaning vehicle; and 
     the leaning-vehicle-steering-actuator controller controls the steering actuator by using the roll rate sensor and the speed sensor without using the torque sensor configured to detect the torque generated around the rotation axis of the handlebar by the rider&#39;s manipulation and based on the roll rate obtained from the roll rate sensor and the speed of the leaning vehicle obtained from the speed sensor, not the torque detected by the torque sensor as the torque generated around the rotation axis of the handlebar by the rider&#39;s manipulation. 
     The leaning-vehicle-steering-actuator controller of (3) can control the steering actuator in an unconventional manner. As described below, there is a correlation between the posture change of the vehicle body frame and the speed of the leaning vehicle. As the absolute value of the speed of the leaning vehicle is increasing, the absolute value of the rotation speed of the steerable wheel becomes greater, and the absolute value of the angular momentum of the steerable wheel becomes greater. Then, an external force of a greater absolute value is needed to change the angular momentum of the steerable wheel, and it becomes harder to change the posture of the vehicle body frame. On the other hand, as the absolute value of the speed of the leaning vehicle is decreasing, the absolute value of the rotation speed of the steerable wheel becomes smaller, and the absolute value of the angular momentum of the steerable wheel becomes smaller. Then, an external force of a smaller absolute value is needed to change the angular momentum of the steerable wheel, and it becomes easier to change the posture of the vehicle body frame. Therefore, the leaning-vehicle-steering-actuator controller of (3) controls the steering actuator based on the speed of the leaning vehicle. Thus, the leaning-vehicle-steering-actuator controller of (3) can control the steering actuator in an unconventional manner. 
     (4) The leaning-vehicle-steering-actuator controller of any one of (1) to (3), wherein: 
     the leaning vehicle further includes a speed sensor configured to detect a speed of the leaning vehicle; and 
     the leaning-vehicle-steering-actuator controller estimates an estimated steering torque, which is an estimated value of the torque generated around the rotation axis of the handlebar by the rider&#39;s manipulation, by using the roll rate sensor and the speed sensor without using the torque sensor configured to detect the torque generated around the rotation axis of the handlebar by the rider&#39;s manipulation, and based on the roll rate obtained from the roll rate sensor and the speed of the leaning vehicle obtained from the speed sensor, not the torque detected by the torque sensor as the torque generated around the rotation axis of the handlebar by the rider&#39;s manipulation, and controls the steering actuator based on the estimated steering torque. 
     The leaning-vehicle-steering-actuator controller of (4) can control the steering actuator in an unconventional manner. As described below, there is a correlation between the posture change of the vehicle body frame and the speed of the leaning vehicle. As the absolute value of the speed of the leaning vehicle is increasing, the absolute value of the rotation speed of the steerable wheel becomes greater, and the absolute value of the angular momentum of the steerable wheel becomes greater. Then, an external force of a greater absolute value is needed to change the angular momentum of the steerable wheel, and it becomes harder to change the posture of the vehicle body frame. On the other hand, as the absolute value of the speed of the leaning vehicle is decreasing, the absolute value of the rotation speed of the steerable wheel becomes smaller, and the absolute value of the angular momentum of the steerable wheel becomes smaller. Then, an external force of a smaller absolute value is needed to change the angular momentum of the steerable wheel, and it becomes easier to change the posture of the vehicle body frame. Therefore, the leaning-vehicle-steering-actuator controller of (4) estimates an estimated steering torque, which is an estimated value of the steering torque by using the roll rate sensor and the speed sensor configured to detect the speed of the leaning vehicle without using the torque sensor configured to detect the steering torque, and based on the roll rate obtained from the roll rate sensor and the speed of the leaning vehicle obtained from the speed sensor, not the steering torque detected by the torque sensor, and the leaning-vehicle-steering-actuator controller of (4) controls the steering actuator based on the estimated steering torque. Thus, the leaning-vehicle-steering-actuator controller of (4) can control the steering actuator in an unconventional manner. 
     (5) A leaning vehicle comprising: 
     a vehicle body frame configured to lean in a leaning-vehicle-leftward direction when the leaning vehicle is turning left and to lean in a leaning-vehicle-rightward direction when the leaning vehicle is turning right; 
     at least one steerable wheel supported by the vehicle body frame; 
     a handlebar configured to be manipulated by a rider to steer the at least one steerable wheel, and supported by the vehicle body frame in a rotatable manner; 
     a steering actuator configured to apply a torque to the at least one steerable wheel to steer the at least one steerable wheel; and 
     a roll rate sensor configured to detect a roll rate that is an amount of change per unit time of a roll angle of the vehicle body frame around a roll axis extending along a leaning-vehicle-front-back direction, the roll angle changing as the vehicle body frame is rotating around the roll axis; and 
     the leaning-vehicle-steering-actuator controller according to any one of (1) to (4). 
     For the same reasons as described in connection with the leaning-vehicle-steering-actuator controllers of (1) to (4), the leaning vehicle of (5) can control the steering actuator in an unconventional manner. 
     (6) The leaning vehicle according to (5), wherein the roll rate sensor is supported by the vehicle body frame in such a manner as not to be displaceable relative to the vehicle body frame. 
     This arrangement in the leaning vehicle of (6) inhibits a great delay of a posture change of the roll rate sensor from a posture change of the vehicle body frame. 
     Some embodiments of the present teaching will hereinafter be described in detail with reference to the drawings, and the detailed description of the embodiments will provide a clearer picture of the above-mentioned object and other objects, the features, the aspects and the advantages of the present teaching. 
     The term “and/or” used herein includes one of the associated items in a list and all possible combinations of the associated items. 
     The terms “including”, “comprising”, or “having”, and variations thereof used herein specify the presence of stated features, steps, operations, elements, components, and/or equivalents thereof, and can include one or more of steps, operations, elements, components, and/or their groups. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skilled in the art to which the present teaching pertains. 
     It should be understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the present disclosure and relevant art and should not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     It should be understood that the description of the present teaching discloses a number of techniques and steps. Each of these has individual benefit, and each can also be used in conjunction with one or more, or in some cases all, of the other disclosed techniques. Accordingly, for the sake of clarity, this description will refrain from repeating every possible combination of the individual steps in an unnecessary fashion. Nevertheless, Description and Claims should be read with the understanding that such combinations are entirely within the scope of the present teaching and the claims. 
     In the description given below, for the purpose of explanation, numerous specific details are set forth in order to provide a complete understanding of the present teaching. It will be apparent, however, that those skilled in the art may practice the present teaching without these specific details. The present disclosure is to be considered as an exemplification of the present teaching, and is not intended to limit the present teaching to the specific embodiments illustrated by drawings or descriptions below. 
     Advantageous Effect of Invention 
     The present teaching makes it possible to control a steering actuator in an unconventional manner. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1A  is a looking-to-the-right (R) view of a leaning vehicle  1 . 
         FIG. 1B  is a looking-to-the-right (R) view of a leaning vehicle  1   a.    
         FIG. 2  is a schematic looking-to-the-back (B) view of the leaning vehicle  1   a.    
         FIG. 3  is a schematic looking-to-the-down (D) view of the leaning vehicle  1   a.    
         FIG. 4  is a schematic looking-to-the-back (B) view of the leaning vehicle  1   a.    
         FIG. 5  is a graph showing the relationship between correlation coefficient and speed of a first test vehicle. 
         FIG. 6  is a graph showing the relationship between correlation coefficient and speed of a second test vehicle. 
         FIG. 7  is a block diagram of a leaning-vehicle-steering-actuator controller  606 . 
         FIG. 8  is a flowchart showing operations carried out by the leaning-vehicle-steering-actuator controller  606 . 
         FIG. 9  is a looking-to-the-right view, with respect to a vehicle body frame  1021 , of a leaning vehicle  1   b  when the vehicle body frame  1021  is in an upright posture. 
         FIG. 10  is a looking-to-the-back view, with respect to the vehicle body frame  1021 , of a front part of a leaning vehicle  1   b  when the vehicle body frame  1021  is in an upright posture. 
         FIG. 11  is a looking-to-the-down (d) view of the front part of the leaning vehicle  1   b  when the vehicle body frame  1021  is in an upright posture. 
         FIG. 12  is a looking-to-the-down (d) view of the front part of the leaning vehicle  1   b  when the leaning vehicle  1   b  is steered leftward. 
         FIG. 13  is a looking-to-the-back (b) view of the front part of the leaning vehicle  1   b  when the vehicle body frame  1021  leans in a leftward direction L. 
         FIG. 14  is a block diagram of an actuator controller  1606 . 
         FIG. 15  is a flowchart showing operations carried out by the actuator controller  1606 . 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     (Outline) 
     The overall structure of a leaning vehicle  1  according to the gist of the present teaching will hereinafter be described with reference to the drawings. In the present embodiment, a two-wheeled leaning vehicle (which will hereinafter be referred to simply as a leaning vehicle) including a vehicle body frame capable of leaning, a front wheel and a rear wheel is described as an example of a leaning vehicle.  FIG. 1A  is a looking-to-the-right (R) view of the leaning vehicle  1 . 
     The leaning vehicle  1  includes at least one steerable wheel  3   o , a vehicle body frame  21 , a handlebar  60 , a steering actuator  600 , a roll rate sensor  602 , and a leaning-vehicle-steering-actuator controller  606 . 
     The vehicle body frame  21  leans in a leaning-vehicle-leftward direction when the leaning vehicle  1  is turning left and leans in a leaning-vehicle-rightward direction when the leaning vehicle  1  is turning right. The at least one steerable wheel  3   o  is supported by the vehicle body frame  21 . The at least one steerable wheel  3   o  may include two or more steerable wheels. 
     The handlebar  60  is to be manipulated by a rider to steer the at least one steerable wheel  3   o . The handlebar  60  is supported by the vehicle body frame  21  in a rotatable manner. The handlebar  60  is connected to a steering shaft extending along a vehicle-body-frame-up-down direction. The steering shaft is supported by the vehicle body frame  21 . Accordingly, the handlebar  60  is rotatable around a central axis of the steering shaft relative to the vehicle frame body  21 . The handlebar  60  is, for example, a handlebar extending along a vehicle-body-left-right direction. 
     The steering actuator  600  applies a torque to the at least one steerable wheel  3   o  to steer the at least one steerable wheel  3   o . Steering means causing the at least one steerable wheel  3   o  to rotate clockwise or counterclockwise in a vehicle-body-frame-downward view. 
     As the vehicle body frame  21  is rotating around a roll axis Ax extending along a leaning-vehicle-front-back direction, the roll angle changes, and the roll rate sensor  602  is configured to detect the roll rate that is the amount of change per unit time of the roll angle. 
     The leaning-vehicle-steering-actuator controller  606  is used for the leaning vehicle  1 , which includes at least one steerable wheel  3   o , a vehicle body frame  21 , a handlebar  60 , a steering actuator  600  and a roll rate sensor  602 . The leaning-vehicle-steering-actuator controller  606  does not use a torque sensor that detects the steering torque T that is generated by the rider&#39;s manipulation and acts around the rotation axis of the handlebar  60 , and uses the roll rate sensor  602 . Then, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  not based on the steering torque T that is detected by the torque sensor as the torque generated by the rider&#39;s manipulation and acting around the rotation axis of the handlebar  60  but based on the roll rate obtained from the roll rate sensor  602 . 
     The leaning-vehicle-steering-actuator controller  606  can control the steering actuator  600  in an unconventional manner. More specifically, in order to change the roll angle of the vehicle body frame  21 , the rider manipulates the handlebar  60  to generate a steering torque (i.e., the first steering torque) that acts around the rotation axis of the handlebar  60 . Then, the roll angle of the vehicle body frame  21  changes, and the posture of the vehicle body frame  21  changes. Thus, the rider can control the posture of the vehicle body frame  21  by using the steering torque applied to the steering shaft as an input parameter. 
     The greater the absolute value of the steering torque is, the greater the absolute value of the roll rate that represents the change of the roll angle of the vehicle body frame  21  is. The smaller the absolute value of the steering torque is, the smaller the absolute value of the roll rate of the vehicle body frame  21  is. Thus, there is a correlation between the steering torque and the roll rate. Therefore, for posture control of the vehicle body frame  21 , the roll rate can be used as an input parameter instead of the steering torque. Then, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  based on the roll rate. 
     For the following reason, the leaning-vehicle-steering-actuator controller  606  does not use a torque sensor that detects the steering torque, and controls the steering torque actuator  600  not based on the steering torque detected by the torque sensor. There is a correlation between the steering torque and the roll rate. Accordingly, as long as the roll rate is detected, it is not necessary to detect the steering torque. Therefore, the leaning-vehicle-steering-actuator controller  606  can control the steering actuator  600  not based on the steering torque, which is conventionally used for control of a steering actuator. 
     For the reason above, the leaning-vehicle-steering-actuator controller  606  can control the steering actuator  600  by using the roll rate sensor  602  without using a torque sensor configured to detect the steering torque, and based on the roll rate obtained from the roll rate sensor  602 , not the steering torque detected by the torque sensor. Thus, the leaning-vehicle-steering-actuator controller  606  can control the steering actuator  600  in an unconventional manner. 
     The leaning-vehicle-steering-actuator controller  606  does not use the steering torque for control of the steering torque actuator  600 . Accordingly, the leaning vehicle  1  including the leaning-vehicle-steering-actuator controller  606  does not need to include a torque sensor configured to detect the steering torque. However, the leaning vehicle  1  including the leaning-vehicle-steering-actuator controller  606  may include a torque sensor configured to detect the steering torque. 
     First Embodiment 
     [Overall Structure] 
     The overall structure of a leaning vehicle  1   a  according to a first embodiment will hereinafter be described with reference to the drawings. In the present embodiment, as an example of the leaning vehicle, a two-wheeled leaning vehicle including a vehicle body frame capable of leaning, a front wheel and a rear wheel (the two-wheeled leaning vehicle hereinafter being referred to simply as a leaning vehicle) is described.  FIG. 1B  is a looking-to-the-right (R) view of the leaning vehicle  1   a .  FIG. 2  is a schematic looking-to-the-back (B) view of the leaning vehicle  1   a . In  FIG. 2 , the leaning vehicle  1   a  is in an upright posture. Since  FIG. 2  is a schematic view, there are some inconsistencies in size, etc. between  FIG. 1B  and  FIG. 2 .  FIG. 2  shows only principal parts, and a vehicle body cover  22  is omitted in  FIG. 2 . 
     In the following paragraphs, a forward direction in a front-back direction of the leaning vehicle  1   a  is referred to as a forward direction F (leaning-vehicle-forward direction). A backward direction in the front-back direction of the leaning vehicle  1   a  is referred to as a backward direction B (leaning-vehicle-backward direction). A leftward direction in a left-right direction of the leaning vehicle  1   a  is referred to as a leftward direction L (leaning-vehicle-leftward direction). A rightward direction in the left-right direction of the leaning vehicle  1   a  is referred to as a rightward direction R (leaning-vehicle-rightward direction). An upward direction in an up-down direction of the leaning vehicle  1   a  is referred to as an upward direction U (leaning-vehicle-upward direction). A downward direction in the up-down direction of the leaning vehicle  1   a  is referred to as a downward direction D (leaning-vehicle-downward direction). The front-back direction of the leaning vehicle  1   a  is referred to as a front-back direction FB (leaning-vehicle-front-back direction). The left-right direction of the leaning vehicle  1   a  is referred to as a left-right direction LR (leaning-vehicle-left-right direction). The up-down direction of the leaning vehicle  1   a  is referred to as an up-down direction UD (leaning-vehicle-up-down direction). The forward direction in the front-back direction of the leaning vehicle  1   a  is a forward direction relative to a rider straddling the leaning vehicle  1   a . The backward direction in the front-back direction of the leaning vehicle  1   a  is a backward direction relative to a rider straddling the leaning vehicle  1   a . The leftward direction in the left-right direction of the leaning vehicle  1   a  is a leftward direction relative to a rider straddling the leaning vehicle  1   a . The rightward direction in the left-right direction of the leaning vehicle  1   a  is a rightward direction relative to a rider straddling the leaning vehicle  1   a . The upward direction in the up-down direction of the leaning vehicle  1   a  is an upward direction relative to a rider straddling the leaning vehicle  1   a . The downward direction in the up-down direction of the leaning vehicle  1   a  is a downward direction relative to a rider straddling the leaning vehicle  1   a.    
     The vehicle body frame  21  of the leaning vehicle  1   a  is capable of leaning in the leftward direction L and the rightward direction R. When the vehicle body frame  21  leans in the leftward direction L or the rightward direction R, the up-down direction and the left-right direction of the vehicle body frame  21  are not same with the up-down direction UD and the left-right direction LR of the leaning vehicle  1   a , respectively. On the other hand, when the vehicle body frame  21  is in an upright posture, the up-down direction and the left-right direction of the vehicle body frame  21  are same with the up-down direction UD and the left-right direction LR of the leaning vehicle  1   a , respectively. In the following paragraphs, a forward direction in the front-back direction of the vehicle body frame  21  is referred to as a forward direction f (vehicle-body-frame-forward direction). A backward direction in the front-back direction of the vehicle body frame  21  is referred to as a backward direction b (vehicle-body-frame-backward direction). A leftward direction in the left-right direction of the vehicle body frame  21  is referred to as a leftward direction l (vehicle-body-frame-leftward direction). A rightward direction in the left-right direction of the vehicle body frame  21  is referred to as a rightward direction r (vehicle-body-frame-rightward direction). An upward direction in the up-down direction of the vehicle body frame  21  is referred to as an upward direction u (vehicle-body-frame-upward direction). A downward direction in the up-down direction of the vehicle body frame  21  is referred to as a downward direction d (vehicle-body-frame-downward direction). The front-back direction of the vehicle body frame  21  is referred to as a front-back direction fb (vehicle-body-frame-front-back direction). The left-right direction of the vehicle body frame  21  is referred to as a left-right direction lr (vehicle-body-frame-left-right direction). The up-down direction of the vehicle body frame  21  is referred to as an up-down direction ud (vehicle-body-frame-up-down direction). 
     In the present specification, a shaft or a member that extends along the front-back direction does not necessarily mean a shaft or a member that extends in parallel to the front-back direction. A shaft or a member that extends along the front-back direction includes a shaft or a member that is inclined from the front-back direction at an angle within ±45 degrees. In a similar way, a shaft or a member that extends along the up-down direction includes a shaft or a member that is inclined from the up-down direction at an angle within ±45 degrees. A shaft or a member that extends along the left-right direction includes a shaft or a member that is inclined from the left-right direction at an angle within ±45 degrees. The upright posture of the vehicle body frame  21  means a state wherein nobody is riding the leaning vehicle  1   a , the leaning vehicle  1   a  is out of fuel, and the front wheel is neither steered nor caused to lean. 
     In the present specification, a statement that a first member is supported by a second member includes a case in which the first member is attached to the second member such that the first member is immovable (that is, fixed in a place) relative to the second member and a case in which the first member is attached to the second member such that the first member is movable relative to the second member. The statement that a first member is supported by a second member also includes both a case in which the first member is directly attached to the second member and a case in which the first member is attached to the second member via a third member. 
     In the present specification, a statement that a first member and a second member are arranged in the front-back direction means the following situation. When the first member and the second member are viewed in a direction perpendicular to the front-back direction, both the first member and the second member are on an arbitrary line indicating the front-back direction. In the present specification, a statement that a first member and a second member are arranged in the front-back direction in a view along the up-down direction means the following situation. When the first member and the second member are viewed in the up-down direction, both the first member and the second member are on an arbitrary line indicating the front-back direction. In this case, when the first member and the second member are viewed in the left-right direction, which is different from the up-down direction, either one of the first member and the second member may not be arranged on the arbitrary line indicating the front-back direction. Further, the first member and the second member may be in contact with each other. The first member and the second member may be out of contact with each other. A third member may be positioned between the first member and the second member. This definition applies to other directions as well as the front-back direction. 
     In the present specification, a statement that a first member is positioned farther in the forward direction than a second member means the following situation. The first member is positioned farther in the forward direction than a plane that passes a front edge of the second member and is perpendicular to the front-back direction. The first member and the second member may or may not be arranged in the front-back direction. This definition applies to other directions as well as the front-back direction. 
     In the present specification, a statement that a first member is positioned in front of a second member means the following situation. At least a part of the first member is positioned in a range that the second member passes during a translation thereof in the forward direction. Accordingly, the first member may be positioned within the range that the second member passes during a translation thereof in the forward direction, or may protrude from the range that the second member passes during a translation thereof in the forward direction. In this case, the first member and the second member are arranged in the front-back direction. This definition applies to other directions as well as the front-back direction. 
     In the present specification, a statement that a first member is positioned in front of a second member in a view along the left-right direction means the following situation. The first member and the second member are arranged in the front-back direction in a view along the left-right direction, and the part of the first member facing the second member is positioned farther in the forward direction than the second member in a view along the left-right direction. According to this definition, three-dimensionally, the first member and the second member are not necessarily arranged in the front-back direction. This definition applies to other directions as well as the front-back direction. 
     In the present specification, unless otherwise noted, parts of a first member are defined as follows. A front part of the first member means the front half of the first member. A rear part of the first member means the rear half of the first member. A left part of the first member means the left half of the first member. A right part of the first member means the right half of the first member. An upper part of the first member means the upper half of the first member. A lower part of the first member means the lower half of the first member. An upper edge of the first member means the edge of the first member in the upward direction. A lower edge of the first member means the edge of the first member in the downward direction. A front edge of the first member means the edge of the first member in the forward direction. A rear edge of the first member means the edge of the first member in the backward direction. A right edge of the first member means the edge of the first member in the rightward direction. A left edge of the first member means the edge of the first member in the leftward direction. An upper end part of the first member means the upper edge and its vicinity of the first member. A lower end part of the first member means the lower edge and its vicinity of the first member. A front end part of the first member means the front edge and its vicinity of the first member. A rear end part of the first member means the rear edge and its vicinity of the first member. A right end part of the first member means the right edge and its vicinity of the first member. A left end part of the first member means the left edge and its vicinity of the first member. The first member is a component of the leaning vehicle  1   a.    
     As shown in  FIG. 1B , the leaning vehicle  1   a  includes a vehicle body  2 , a front wheel  3 , a rear wheel  4 , and a steering mechanism  7 . The vehicle body  2  includes a vehicle body frame  21 , a vehicle body cover  22 , a seat  24 , a power unit  25 , and a swing arm  26 . 
     The vehicle body frame  21  leans in the leftward direction L when the leaning vehicle  1   a  is turning left. The vehicle body frame  21  leans in the rightward direction R when the leaning vehicle  1   a  is turning right. In  FIG. 1B , the vehicle body frame  21  is indicated by bold lines. However, the vehicle body frame  21  is covered by the vehicle body cover  22 , and therefore, under ordinary conditions, the vehicle body frame  21  cannot be seen in  FIG. 1B . 
     The vehicle body frame  21  includes a head pipe  211 , a main frame  212 , and a seat rail  213 . The head pipe  211  is positioned in the front part of the leaning vehicle  1   a . The front part of the leaning vehicle  1   a  is a part thereof that is positioned in front of the front edge of the seat  24  in the forward direction f. The rear part of the leaning vehicle  1   a  is a part thereof that is positioned behind the front edge of the seat  24  in the backward direction b. In a view in the leftward direction l or the rightward direction r, the head pipe  211  is inclined from the up-down direction ud such that the upper end part of the head pipe  211  is positioned behind the lower end part of the head pipe  211  in the backward direction b. 
     In a view in the rightward direction r, the main frame  212  is positioned farther in the backward direction b than the head pipe  211 . The seat rail  213  linearly extends from the main frame  212  to a backward and upward direction b, u. 
     In a view in the rightward direction r, the swing arm  26  extends from the lower and rear part of the main frame  212  to the backward direction b. The swing arm  26  is supported by the main frame  212  in such a manner as to be capable of rotating on the front end part of the swing arm  26 . Thereby, the rear end part of the swing arm  26  is movable up and down. 
     The vehicle body cover  22  covers the vehicle body frame  21 . The vehicle body cover  22  also covers some part of the power unit  25 . 
     The seat  24  is to be sat on by a rider. The seat  24  is supported by the seat rail  213 . The power unit  25  includes a power source, such as an engine, an electric motor or the like, and a power transmission system, such as a transmission device or the like. The power unit  25  is supported by the main frame  212 . 
     The steering mechanism  7  is arranged around the head pipe  211 . The steering mechanism  7  is configured to steer the front wheel  3  in accordance with the rider&#39;s manipulation. As shown in  FIG. 2 , the steering mechanism  7  includes a handlebar  60 , a steering shaft  62 , a front fork  64 , an upper bracket  66 , and an under bracket  68 . The handlebar  60  is to be manipulated by the rider for steering of the front wheel  3 . The handlebar  60  is supported by the vehicle body frame  21  in a rotatable manner. The steering shaft  62  is supported by the vehicle body frame  21  in a rotatable manner on its central axis in accordance with the rider&#39;s manipulation of the handlebar  60 . More specifically, the upper bracket  66  and the under bracket  68  are, as shown in  FIG. 2 , plate-like members extending along the left-right direction. The upper bracket  66  is positioned farther in the upward direction u than the head pipe  211 . The under bracket  68  is positioned farther in the downward direction d than the head pipe  211 . The steering shaft  62  is inserted in the head pipe  211  and thereby is supported by the head pipe  211  in a rotatable manner. Further, the steering shaft  62  is fixed to the upper bracket  66  and the under bracket  68 . The handlebar  60  is fixed to the upper bracket  66 . 
     The front fork  64  is fixed to the upper bracket  66  and the under bracket  68 . Specifically, as shown in  FIG. 2 , the front fork  64  includes a left shock absorber  64 L and a right shock absorber  64 R. The left shock absorber  64 L extends from the upper bracket  66  and the under bracket  68  to the downward direction d. The left shock absorber  64 L is positioned to the left (l) of the center of the vehicle body frame  21  in an upright posture with respect to the left-right direction lr. The right shock absorber  64 R extends from the upper bracket  66  and the under bracket  68  in the downward direction d. The right shock absorber  64 R is positioned to the right (r) of the center of the vehicle body frame  21  in an upright posture with respect to the left-right direction lr. Accordingly, when the rider turns the handlebar  60 , the steering shaft  62 , the front fork  64 , the upper bracket  66  and the under bracket  68  integrally rotated around the central axis of the steering shaft  62  in a body. 
     The left shock absorber  64 L and the right shock absorber  64 R are what are called telescopic shock absorbers. The left shock absorber  64 L and the right shock absorber  64 R each, for example, include a combination of a damper and a spring. The left shock absorber  64 L and the right shock absorber  64 R expand and contract along the up-down direction ud and thereby absorb displacements of the front wheel  3 , which will be described later, along the up-down direction ud. 
     The front wheel  3  is a steerable wheel of the leaning vehicle  1   a . The front wheel  3  is positioned in the front part of the leaning vehicle  1   a . The front wheel  3  is supported by the lower end part of the front fork  64  in a rotatable manner around an axle. Thus, the front wheel  3  is supported by the vehicle body frame  21  via the steering mechanism  7 . Accordingly, the rider can steer the front wheel  3  by manipulating the handlebar  60 . 
     The rear wheel  4  is a driving wheel of the leaning vehicle  1   a . The rear wheel  4  is rotated by a driving force generated by the power unit  25 . The rear wheel  4  is positioned in the rear part of the leaning vehicle  1   a . The rear wheel  4  is supported by the lower end part of the swing arm  26  in a rotatable manner around an axle. 
     [Steering Motion] 
     Next, steering motions of the leaning vehicle  1   a  are described with reference to the drawings.  FIG. 3  is a schematic looking-to-the-down (D) view of the leaning vehicle  1   a .  FIG. 3  shows a state wherein the front wheel  3  is steered in the leftward direction L, a state wherein the front wheel  3  is not steered, and a state wherein the front wheel  3  is steered in the rightward direction R. As indicated in  FIG. 3 , the direction in which the handlebar  60  is turned counterclockwise in a view in the downward direction d is defined as a positive direction. The direction in which the handlebar  60  is turned clockwise in a view in the downward direction d is defined as a negative direction. 
     As shown in  FIG. 3 , in a view in the downward direction D, the front wheel  3  is turned counterclockwise when the rider turns the handlebar  60  counterclockwise (in the positive direction). Then, the front wheel  3  is steered in the leftward direction L (steered leftward). 
     As shown in  FIG. 3 , in a view in the downward direction D, the front wheel  3  is turned clockwise when the rider turns the handlebar  60  clockwise (in the negative direction). Then, the front wheel  3  is steered in the rightward direction R (steered rightward). 
     [Leaning Motion] 
     Next, leaning motions of the leaning vehicle  1   a  are described with reference to the drawings.  FIG. 4  is a schematic looking-to-the-back (B) view of the leaning vehicle  1   a .  FIG. 4  shows a state wherein the vehicle body frame  21  leans in the leftward direction L and a state wherein the vehicle body frame  21  leans in the rightward direction R.  FIG. 4  shows that the front wheel  3  is steered leftward by self-steering when the vehicle body frame  21  leans in the leftward direction L.  FIG. 4  shows that the front wheel  3  is steered rightward by self-steering when the vehicle body frame  21  leans in the rightward direction R. 
     The vehicle body frame  21  leans in the leftward direction L or the rightward direction R by rotating around a roll axis Ax. The roll axis Ax is an axis extending along the front-back direction FB. More specifically, as shown in  FIG. 1B , the roll axis Ax is a straight line that passes the contact point between the rear wheel  4  and the ground and is perpendicular to the steering shaft  62  when the vehicle body frame  21  is in an upright posture. In a view in the backward direction d, the roll axis Ax is in the center of the vehicle body frame  21  in an upright posture with respect to the left-right direction lr. 
     As the vehicle body frame  21  is rotating around the roll axis Ax, the rotation angle of the vehicle body frame  21  around the roll axis Ax changes, and the rotation angle of the vehicle body frame  21  around the roll axis Ax is referred to as a roll angle θ. In the following paragraphs, as shown in  FIG. 2 , the straight line that passes the center of the vehicle body frame  21  in an upright posture with respect to the left-right direction lr and extends along the up-down direction ud is defined as a center line C. As shown in  FIG. 4 , when the vehicle body frame  21  leans in the leftward direction L or the rightward direction R, the center line C leans in the leftward direction L or the rightward direction R together with the vehicle body frame  21 . The roll angle θ is an angle formed between the vertical axis and the center line C. The vertical axis is an axis parallel to the up-down direction UD. The roll angle θ may be an angle formed between a line normal to the road surface and the center line C. The definition of the roll axis Ax is not limited to the above definition, and any other definition may be applicable. 
     Further, as shown in  FIG. 4 , when the vehicle body frame  21  leans in the leftward direction L, the direction of the lean is referred to as a positive direction of the roll angle θ. In other words, the clockwise direction around the roll axis Ax in a view in the backward direction B is defined as a positive direction of the roll angle θ. When the vehicle body frame  21  leans in the rightward direction R, the direction of the lean is referred to as a negative direction of the roll angle θ. In other words, the counterclockwise direction around the roll axis Ax in a view in the backward direction B is defined as a negative direction of the roll angle θ. The roll angle θ changes within a range of −90° to 90°. 
     As shown in  FIG. 4 , in a view in the backward direction B, the vehicle body frame  21  rotates clockwise around the roll axis Ax and leans in the leftward direction L. In this case, the roll angle θ is a positive value. Also, the front wheel  3  is steered leftward by self-steering. Then, the leaning vehicle  1   a  turns in the leftward direction L. 
     As shown in  FIG. 4 , in a view in the backward direction B, the vehicle body frame  21  rotates counterclockwise around the roll axis Ax and leans in the rightward direction R. Also, the front wheel  3  is steered rightward by self-steering. In this case, the roll angle θ is a negative value. The leaning vehicle  1   a  turns in the rightward direction R. 
     [Leaning-Vehicle-Steering-Actuator Controller] 
     Next, the leaning-vehicle-steering-actuator controller  606  of the leaning vehicle  1   a  is described with reference to the drawings.  FIG. 5  is a graph showing the relationship between correlation coefficient and speed of a first test vehicle.  FIG. 6  is a graph showing the relationship between correlation coefficient and speed of a second test vehicle. The vertical axis indicates the correlation coefficient. The horizontal axis indicates the speed of the vehicle.  FIG. 7  is a block diagram of the leaning-vehicle-steering-actuator controller  606 . 
     In order to find out the correlation between the roll rate ω and the steering torque T, the present inventors conducted the following experiment. The steering torque T is a torque that is generated by the rider&#39;s manipulation of the handlebar  60  and acts on the steering shaft  62 . More specifically, the steering torque T is a torque that is inputted to the steering shaft  62  by the rider&#39;s manipulation of the handlebar  60  when the roll angle θ of the vehicle body frame  21  of the leaning vehicle  1   a  running at a speed V is changing at a roll rate ω. The steering torque T is a moment that acts around the steering shaft  62 . When the steering torque T acts in the counterclockwise direction in a view in the downward direction d, the steering shaft  62  is rotated counterclockwise (in the positive direction) by the steering torque T. When the steering torque T acts in the clockwise direction in a view in the downward direction d, the steering shaft  62  is rotated clockwise (in the negative direction) by the steering torque T. 
     The present inventors prepared a first test vehicle and a second test vehicle. The first test vehicle was a sport-type three-wheeled motorcycle. The sport-type three-wheeled motorcycle included two front wheels and one rear wheel. The second test vehicle was a sport-type two-wheeled motorcycle. The present inventors operated the first test vehicle and the second test vehicle to run, and measured the roll rate ω and the steering torque T with the speed set to seven values and with the roll angle θ set to two values. More specifically, the present inventors changed the steering torque T while operating each of the first test vehicle and the second test vehicle to run at seven different speeds V. The present inventors changed the steering torque T by manipulating the handlebar while the vehicle is running. The present inventors measured the steering torque T in relation to time and measured the roll rate ω in relation to time. A torque sensor was used for the measurement of the steering torque T. A roll rate sensor was used for the measurement of the roll rate. Then, the correlation coefficient between the roll rate ω and the steering torque T was calculated. The seven values of the speed V were 20 km/h, 40 km/h, 60 km/h, 80 km/h, 100 km/h, 120 km/h, and 140 km/h. The two values of the roll angle θ were 8° and 20°. The correlation coefficient was the Pearson product-moment correlation coefficient. 
       FIGS. 5 and 6  show that there was a high correlation between the roll angle ω and the steering torque T. Also, the greater the speed V was, the higher the correlation coefficient between the roll angle ω and the steering torque T was. Especially when the speed was 40 km/h or higher, the correlation coefficient was 0.8 or more, and when the speed was 60 km/h or higher, the correlation coefficient was 0.9 or more. Thus, the present inventors confirmed by the experiment that there is a high correlation between the roll angle ω and the steering torque T. Therefore, the present inventors conceived of an idea that the steering torque T can be estimated based on the roll angle ω. The present inventors also conceived of an idea that the rider&#39;s manipulation of the handlebar  60  can be assisted based on the estimated steering torque T. Then, the leaning vehicle  1   a  includes the leaning-vehicle-steering-actuator controller  606  as described below. 
     As shown in  FIG. 1B , the leaning vehicle  1   a  further includes a steering actuator  600 , a roll rate sensor  602  and a speed sensor  604  as well as the leaning-vehicle-steering-actuator controller  606 . 
     The steering actuator  600  is supplied with electric power and outputs a supplementary steering torque Tc to cause the steering shaft  62  to rotate on its central axis. More specifically, as shown in  FIG. 2 , the steering actuator  600  is fixed to the upper end part of the head pipe  211 . The steering actuator  600  is a combination of an electric motor and a gear. The electric motor generates a torque. The torque generated by the electric motor is outputted to the steering shaft  62  as a supplementary steering torque Tc (i.e., the second steering torque) via the gear. 
     The roll rate sensor  602  detects the roll rate ω that is the amount of change per unit time of the roll angle θ. When the vehicle body frame  21  leans in the leftward direction L, the direction of the lean is referred to as a positive direction of the roll rate ω. In other words, the clockwise direction around the roll axis Ax in a view in the backward direction B is defined as a positive direction of the roll rate ω. When the vehicle body frame  21  leans in the rightward direction R, the direction of the lean is referred to as a negative direction of the roll rate ω. In other words, the counterclockwise direction around the roll axis Ax in a view in the backward direction B is defined as a negative direction of the roll rate ω. 
     The speed sensor  604  detects the speed V of the leaning vehicle  1   a . The speed V is a positive value when the leaning vehicle  1   a  is running forward. 
     The leaning-vehicle-steering-actuator controller  606  is, for example, an IC (integrated circuit) for control of the steering actuator  600 . However, the leaning-vehicle-steering-actuator controller  606  does not need to be achieved by a single IC, and the leaning-vehicle-steering-actuator controller  606  may be a combination of one or more ICs, one or more electronic components and/or one or more circuit boards. 
     The steering actuator  600 , the roll rate sensor  602  and the leaning-vehicle-steering-actuator controller  606  are combined in such a manner as not to be displaceable relative to one another. More specifically, for example, the roll rate sensor  602  and the leaning-vehicle-steering-actuator controller  606  are fixed in a case of the steering actuator  600 . The means for fixing the roll rate sensor  602  and the leaning-vehicle-steering-actuator controller  606  to the steering actuator  600  may be a combination of a bolt and a nut, a screw, a snap-fit, an adhesive, an adhesive tape, welding, brazing, etc. The steering actuator  600  is to output a supplementary steering torque Tc to the steering shaft  62 . Therefore, the steering actuator  600  is supported by the vehicle body frame  21  in such a manner as not to be displaceable relative to the vehicle body frame  21 . In this structure, the roll rate sensor  602  and the leaning-vehicle-steering-actuator controller  606  are not displaceable relative to the steering actuator  600 , and the steering actuator  600  is not displaceable relative to the vehicle body frame  21 . In the present specification, when it is stated that a first member is supported by a second member in such a manner as not to be displaceable relative to the second member, it also means that there is no elastic member for impact absorption, such as a rubber mount or the like, between the first member and the second member. The roll rate sensor  602  is positioned on the center line C in a view in the backward direction B. 
     The description is now returned to the leaning-vehicle-steering-actuator controller  606 . The leaning-vehicle-steering-actuator controller  606  obtains the roll rate ω from the roll rate sensor  602 . Specifically, an electric signal representing the roll rate ω (which will hereinafter be referred to simply as roll rate ω) detected by the roll rate sensor  602  is inputted to the leaning-vehicle-steering-actuator controller  606 . 
     The leaning-vehicle-steering-actuator controller  606  obtains the speed V from the speed sensor  604 . Specifically, an electric signal representing the speed V (which will hereinafter be referred to simply as speed V) detected by the speed sensor  604  is inputted to the leaning-vehicle-steering-actuator controller  606 . 
     The leaning-vehicle-steering-actuator controller  606  does not use a torque sensor that detects the steering torque T that is generated by the rider&#39;s manipulation and acts around the rotation axis of the handlebar  60  (central axis of the steering shaft  62 ), but uses the roll rate sensor  602 . Then, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  not based on the steering torque T detected by the torque sensor as the steering torque generated by the rider&#39;s manipulation and acting around the the steering shaft  62  of the handlebar  60  but based on the roll rate ω sent from the roll rate sensor  602 . In the present embodiment, the leaning-vehicle-steering-actuator controller  606  uses neither a torque sensor that detects the steering torque T nor a roll sensor that detects the roll angle θ. The leaning-vehicle-steering-actuator controller  606  uses the roll rate sensor  602  and the speed sensor  604 . Then, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  based on neither the steering torque T detected by a torque sensor nor the roll angle θ detected by a roll sensor. The leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  based on the roll rate ω sent from the roll rate sensor  602  and the speed V sent from the speed sensor  604 . The statement that the leaning-vehicle-steering-actuator controller  606  uses neither a torque sensor nor a roll sensor means, for example, that the leaning-vehicle-steering-actuator controller  606  uses neither a signal sent from a torque sensor nor a signal sent from a roll sensor for control. The statement that the leaning-vehicle-steering-actuator controller  606  uses the roll rate sensor  602  and the speed sensor  604  means, for example, that the leaning-vehicle-steering-actuator controller  606  uses a signal sent from the roll rate sensor  602  and a signal sent from the speed sensor  604  for control. 
     In the present embodiment, the leaning-vehicle-steering-actuator controller  606  does not use a torque sensor that detects the torque that is generated by the rider&#39;s manipulation and acts around the rotation axis of the handlebar  60 , but uses the roll rate sensor  602  and the speed sensor  604  that detects the speed of the leaning vehicle  1   a . The leaning-vehicle-steering-actuator controller  606  estimates an estimated steering torque T(m, n) that is an estimated value of the steering torque T that is generated by the rider&#39;s manipulation and acts around the rotation axis of the handlebar  60 , not based on the torque detected by the torque sensor as the steering torque T that is generated by the rider&#39;s manipulation and acts around the rotation axis of the handlebar  60  but based on the roll rate &amp; sent from the roll rate sensor  602  and the speed V sent from the speed sensor  604 . Then, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  based on the estimated steering torque T(m, n). 
     The leaning-vehicle-steering-actuator controller  606  includes a torque estimation section  614  and a current determination section  616 . The torque estimation section  614  determines an estimated steering torque T(m, n), which is an estimated value of the steering torque T, based on the speed V and the roll rate ω. The values m and n are integers. The estimated steering torque T(m, n) is a value of the steering torque T that is estimated to be inputted to the steering shaft  62  by the rider&#39;s manipulation of the handlebar  60  when the roll angle θ of the vehicle body frame  21  is changing at the roll rate ω while the leaning vehicle  1   a  is running at the speed V. The torque estimation section  614  stores an estimated steering torque determination table as shown by TABLE 1. 
     
       
         
           
               
               
             
               
                   
                 TABLE 1 
               
             
            
               
                   
                   
               
               
                   
                 ω(n)(deg/s) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 . . . 
                 ω(−5) 
                 ω(−4) 
                 ω(−3) 
                 ω(−2) 
                 ω(−1) 
                 ω(0) = 0 
                 ω(1) 
                 ω(2) 
                 ω(3) 
                 ω(4) 
                 ω(5) 
                 . . . 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 V(m) 
                 V(1) 
                 . . . 
                 T(1, −5) 
                 T(1, −4) 
                 T(1, −3) 
                 T(1, −2) 
                 T(1, −1) 
                 T(1, 0) = 0 
                 T(1, 1) 
                 T(1, 2) 
                 T(1, 3) 
                 T(1, 4) 
                 T(1, 5) 
                 . . . 
               
               
                 (km/h) 
                 V(2) 
                 . . . 
                 T(2, −5) 
                 T(2, −4) 
                 T(2, −3) 
                 T(2, −2) 
                 T(2, −1) 
                 T(2, 0) = 0 
                 T(2, 1) 
                 T(2, 2) 
                 T(2, 3) 
                 T(2, 4) 
                 T(2, 5) 
                 . . . 
               
               
                   
                 V(3) 
                 . . . 
                 T(3, −5) 
                 T(3, −4) 
                 T(3, −3) 
                 T(3, −2) 
                 T(3, −1) 
                 T(3, 0) = 0 
                 T(3, 1) 
                 T(3, 2) 
                 T(3, 3) 
                 T(3, 4) 
                 T(3, 5) 
                 . . . 
               
               
                   
                 V(4) 
                 . . . 
                 T(4, −5) 
                 T(4, −4) 
                 T(4, −3) 
                 T(4, −2) 
                 T(4, −1) 
                 T(4, 0) = 0 
                 T(4, 1) 
                 T(4, 2) 
                 T(4, 3) 
                 T(4, 4) 
                 T(4, 5) 
                 . . . 
               
               
                   
                 V(5) 
                 . . . 
                 T(5, −5) 
                 T(5, −4) 
                 T(5, −3) 
                 T(5, −2) 
                 T(5, −1) 
                 T(5, 0) = 0 
                 T(5, 1) 
                 T(5, 2) 
                 T(5, 3) 
                 T(5, 4) 
                 T(5, 5) 
                 . . . 
               
               
                   
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
               
               
                   
               
            
           
         
       
     
     In the estimated steering torque determination table, estimated steering torque T(m, n) are stored in association with values of the speed V(m) and values of the roll rate ω(n). The values of the speed V(m) are greater than 0 km/h. The greater the value m is, the greater the speed V(m) is. Accordingly, V(m)&lt;V(m+1) holds. 
     When the value n is positive, the roll rate ω(n) is a positive value. In this case, the greater the value n is, the greater the roll rate ω(n) is. On the other hand, when the value n is negative, the roll rate ω(n) is a negative value. In this case, the smaller the value n is, the smaller the roll rate ω(n) is (the greater the absolute value of the roll rate ω(n) is). Accordingly, ω(n)&lt;ω(n+1) holds. 
     While the leaning vehicle  1   a  is running forward, when the rider turns the handlebar  60  clockwise (in the negative direction), the front wheel  3  is rotated at a roll rate ω(n) of a positive value. For example, while the vehicle body  21  is in an upright posture, when the rider turns the handlebar  60  clockwise (in the negative direction), the front wheel  3  is steered rightward. Then, the vehicle body frame  21  leans in the leftward direction L. On the other hand, while the leaning vehicle  1   a  is running forward, when the rider turns the handlebar counterclockwise (in the positive direction), the front wheel  3  is rotated at a roll rate ω(n) of a negative value. For example, while the vehicle body frame  21  is in an upright posture, when the rider turns the handlebar counterclockwise (in the positive direction), the front wheel  3  is steered leftward. Then, the vehicle body frame  21  leans in the rightward direction R. Thus, the rider performs counter-steering to generate a roll rate ω(n). Therefore, the estimated steering torque T(m, n) has the following relationship with the values m and n. 
     When the value n is positive (when the roll rate ω(n) is a positive value), the estimated steering torque T(m, n) is a negative value. In this case, the estimated steering torque T(m, n) indicates a steering torque to cause the steering shaft  62  to rotate clockwise (in the negative direction) in a view in the downward direction d. In this case, the greater the value n is (the greater the roll rate ω(n) is), the smaller the estimated steering torque T(m, n) is (the greater the absolute value of the estimated steering torque T(m, n) is). Also, the greater the value m is (the greater the speed V(m) is), the smaller the estimated steering torque T(m, n) is (the greater the absolute value of the estimated steering torque T(m, n) is). 
     On the other hand, when the value n is negative (when the roll rate ω(n) is a negative value), the estimated steering torque T(m, n) is a positive value. In this case, the estimated steering torque T(m, n) indicates a steering torque to cause the steering shaft  62  to rotate counterclockwise (in the positive direction) in a view in the downward direction d. In this case, the smaller the value n is (the smaller the roll rate ω(n) is), the greater the estimated steering torque T(m, n) is. Also, the greater the value m is (the greater the speed V(m) is), the greater the estimated steering torque T(m, n) is. 
     The torque estimation section  614  identifies a speed V(m) that is closest to the speed V that the leaning-vehicle-steering-actuator controller  606  has obtained. Also, the torque estimation section  614  identifies a roll rate ω(n) that is closest to the roll rate ω that the leaning-vehicle-steering-actuator controller  606  has obtained. Then, the torque estimation section  614  determines an estimated steering torque T(m, n) in association with the speed V(m) and the roll rate ω(n) with reference to TABLE 1. 
     The current determination section  616  controls the steering actuator  600  based on the estimated steering torque T(m, n) determined by the torque estimation section  614 . Specifically, the current determination section  616  determines a control current value I(m, n) to be outputted to the steering actuator  600 , based on the estimated steering torque T(m, n). For this purpose, the current determination section  616  stores a control current determination table as shown by TABLE 2. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
             
            
               
                 . . . 
                 T(1, −5) 
                 T(1, −4) 
                 T(1, −3) 
                 T(1, −2) 
                 T(1, −1) 
                 T(1, 0) = 0 
                 T(1, 1) 
                 T(1, 2) 
                 T(1, 3) 
                 T(1, 4) 
                 T(1, 5) 
                 . . . 
               
               
                   
                 I(1, −5) 
                 I(1, −4) 
                 I(1, −3) 
                 I(1, −2) 
                 I(1, −1) 
                 I(1, 0) = 0 
                 I(1, 1) 
                 I(1, 2) 
                 I(1, 3) 
                 I(1, 4) 
                 I(1, 5) 
               
               
                 . . . 
                 T(2, −5) 
                 T(2, −4) 
                 T(2, −3) 
                 T(2, −2) 
                 T(2, −1) 
                 T(2, 0) = 0 
                 T(2, 1) 
                 T(2, 2) 
                 T(2, 3) 
                 T(2, 4) 
                 I(2, 5) 
                 . . . 
               
               
                   
                 I(2, −5) 
                 I(2, −4) 
                 I(2, −3) 
                 I(2, −2) 
                 I(2, −1) 
                 I(2, 0) = 0 
                 I(2, 1) 
                 I(2, 2) 
                 I(2, 3) 
                 I(2, 4) 
                 I(2, 5) 
               
               
                 . . . 
                 T(3, −5) 
                 T(3, −4) 
                 T(3, −3) 
                 T(3, −2) 
                 T(3, −1) 
                 T(3, 0) = 0 
                 T(3, 1) 
                 T(3, 2) 
                 T(3, 3) 
                 T(3, 4) 
                 T(3, 5) 
                 . . . 
               
               
                   
                 I(3, −5) 
                 I(3, −4) 
                 I(3, −3) 
                 I(3, −2) 
                 I(3, −1) 
                 I(3, 0) = 0 
                 I(3, 1) 
                 I(3, 2) 
                 I(3, 3) 
                 I(3, 4) 
                 I(3, 5) 
               
               
                 . . . 
                 T(4, −5) 
                 T(4, −4) 
                 T(4, −3) 
                 T(4, −2) 
                 T(4, −1) 
                 T(4, 0) = 0 
                 T(4, 1) 
                 T(4, 2) 
                 T(4, 3) 
                 T(4, 4) 
                 T(4, 5) 
                 . . . 
               
               
                   
                 I(4, −5) 
                 I(4, −4) 
                 I(4, −3) 
                 I(4, −2) 
                 I(4, −1) 
                 I(4, 0) = 0 
                 I(4, 1) 
                 I(4, 2) 
                 I(4, 3) 
                 I(4, 4) 
                 I(4, 5) 
               
               
                 . . . 
                 T(5, −5) 
                 T(5, −4) 
                 T(5, −3) 
                 T(5, −2) 
                 T(5, −1) 
                 T(5, 0) = 0 
                 T(5, 1) 
                 T(5, 2) 
                 T(5, 3) 
                 T(5, 4) 
                 T(5, 5) 
                 . . . 
               
               
                   
                 I(5, −5) 
                 I(5, −4) 
                 I(5, −3) 
                 I(5, −2) 
                 I(5, −1) 
                 I(5, 0) = 0 
                 I(5, 1) 
                 I(5, 2) 
                 I(5, 3) 
                 I(5, 4) 
                 I(5, 5) 
               
               
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
               
               
                   
               
            
           
         
       
     
     In the control current determination table, values of the estimated steering torque T(m, n) and values of the control current I(m, n) are stored in association with each other. The control current I(m, n) is a current that the steering actuator  600  requires to output a supplementary steering torque Tc corresponding to the assist rate (for example, 20%) of the estimated steering torque T(m, n) to the steering shaft  62 . The steering actuator  600  outputs a supplementary steering torque Tc corresponding to 20% of the estimated steering torque T(m, n) to the steering shaft  62 . Accordingly, the rider only needs to manipulate the handlebar  60  to apply 80% of the estimated steering torque T(m, n) to the steering shaft  62 . In this way, the steering actuator  600  assists the rider&#39;s manipulation of the handlebar  60 . The assist rate is an arbitrary value and may be a value other than 20%. In order to allow the rider to manipulate the handlebar  60  with less power, the assist rate should be more than 20%. In order to allow the rider to manipulate the handlebar  60  with more power, the assist rate should be less than 20%. The assist rate may be a negative value. In this case, the steering actuator  600  outputs a supplementary steering torque Tc to resist the rider&#39;s manipulation of the handlebar  60 . Then, the steering actuator  600  functions as a steering damper. 
     When the value n is positive, the control current I(m, n) is a negative value. The greater the value n is, the smaller the control current I(m, n) is (the greater the absolute value of the control current I(m, n) is). Also, the greater the value m is, the smaller the control current I(m, n) is (the greater the absolute value of the control current I(m, n) is). 
     On the other hand, when the value n is negative, the control current I(m, n) is a positive value. The smaller the value n is, the greater the control current I(m, n) is. Also, the greater the value m is, the greater the control current I(m, n) is. 
     The steering actuator  600  outputs a supplementary steering torque Tc to the steering shaft  62  by the control current I(m, n) outputted from the current determination section  616 . However, the current determination section  616  does not need to output the control current I(m, n) to the steering actuator  600  directly. The control current I(m, n) may be supplied to the steering actuator  600  from a power source that is provided separately from the leaning-vehicle-steering-actuator controller  606 . 
     When receiving a negative control current value I(m, n), the steering actuator  600  outputs a supplementary steering torque Tc to rotate the steering shaft  62  clockwise (in the negative direction). In this case, the greater the absolute value of the control current I(m, n) is, the greater the absolute value of the supplementary steering torque Tc is. Then, in a view in the backward direction B, the vehicle body frame  21  rotates clockwise (in the positive direction) around the roll axis Ax at the roll rate ω. 
     On the other hand, when receiving a positive control current value I(m, n), the steering actuator  600  outputs a supplementary steering torque Tc to rotate the steering shaft  62  counterclockwise (in the positive direction). In this case, the greater the absolute value of the control current I(m, n) is, the greater the absolute value of the supplementary steering torque Tc is. Then, in a view in the backward direction B, the vehicle body frame  21  rotates counterclockwise (in the negative direction) around the roll axis Ax at the roll rate ω. 
     As described above, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  to output a supplementary steering torque Tc, based on the speed V and the roll rate ω. Then, the steering shaft  62  rotates, and the vehicle body frame  21  rotates clockwise or counterclockwise around the roll axis Ax in a view in the backward direction B. Accordingly, the posture of the vehicle body frame  21  changes. In this way, the leaning-vehicle-steering-actuator controller  606  controls the posture of the vehicle body frame  21  based on the speed V and the roll rate ω. 
     Next, operations of the leaning-vehicle-steering-actuator controller  606  will be described with reference to the drawings.  FIG. 8  is a flowchart showing operations performed by the leaning-vehicle-steering-actuator controller  606 . The leaning-vehicle-steering-actuator controller  606  performs a process that will be described below by running a software program stored in a storage device (not shown). 
     The process is started when an ignition source of the leaning vehicle  1   a  is turned on. As long as the ignition source is on, the roll rate sensor  602  keeps outputting the roll rate ω to the leaning-vehicle-steering-actuator controller  606 . Also, the speed sensor  604  keeps outputting the speed V to the leaning-vehicle-steering-actuator controller  606 . 
     The torque estimation section  614  obtains the roll rate ω from the roll rate sensor  602  (step S 1 ). Further, the torque estimation section  614  obtains the speed V from the speed sensor  604  (step S 2 ). 
     Next, the torque estimation section  614  identifies one of the roll rate value listed in the estimation steering torque table as shown by TABLE 1 as a roll rate ω(n) closest to the roll rate ω. Further, the torque estimation section  614  identifies one of the speed values listed in the estimation steering torque table as shown by TABLE 1 as a speed V(m) closest to the speed V. Then, the torque estimation section  614  determines an estimated steering torque T(m, n) in association with the roll rate ω(n) and the speed V(m) with reference to the the estimated steering torque determination table as shown by TABLE 1 (step S 3 ). 
     Next, the current determination section  616  determines a control current value I(m, n) corresponding to the estimated steering torque T(m, n) determined by the torque estimation section  614  by using the control current determination table as shown by TABLE 2 (step S 4 ). The current determination section  616  outputs the control current value I(m, n) to the steering actuator  600 . The steering actuator  600  outputs a supplementary steering torque Tc corresponding to the control current value I(m, n) to the steering shaft  62 . Thereafter, the process returns to step S 1 . The process from step S 1  to S 4  is repeated until the ignition source is switched from on to off. 
     [Effects] 
     The leaning-vehicle-steering-actuator controller  606  can control the steering actuator  600  in an unconventional manner. More specifically, in order to change the roll angle θ of the vehicle body frame  21 , the rider manipulates the handlebar  60  to generate a steering torque T acting around the rotation axis of the handlebar  60 . Thereby, the roll angle θ of the vehicle body frame  21  is changed, and the posture of the vehicle body frame  21  is changed. In this way, the rider can control the posture of the vehicle body frame  21  by using the steering torque T acting on the steering shaft  62  as an input parameter. 
     The greater the absolute value of the steering torque T is, the greater the absolute value of the roll rate ω that represents the change of the roll angle θ of the vehicle body frame  21  is. The smaller the absolute value of the steering torque T is, the smaller the absolute value of the roll rate ω of the vehicle body frame  21  is. Thus, there is a correlation between the steering torque T and the roll rate ω. Therefore, instead of the steering torque T, the roll rate ω can be used as an input parameter for posture control of the vehicle body frame  21 . Then, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  based on the roll rate ω. 
     For the following reason, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  without using a torque sensor that detects the steering torque T, and not based on the steering torque T detected by the torque sensor. Since there is a correlation between the steering torque T and the roll rate ω, the steering torque T does not need to be detected if the roll rate ω is detected. Thus, the leaning-vehicle-steering-actuator controller  606  can control the steering actuator  600  not based on the steering torque T, which is conventionally used for control of the steering actuator  600 . 
     For the reason above, the leaning-vehicle-steering-actuator controller  606  uses not a torque sensor that detects the steering torque T but the roll rate sensor  602 , and controls the steering actuator  600  not based on the steering torque T detected by the torque sensor but based on the roll rate ω sent from the roll rate sensor  602 . As a result, the leaning-vehicle-steering-actuator controller  606  can control the steering actuator  600  in an unconventional manner. 
     The leaning-vehicle-steering-actuator controller  606  does not use the steering torque T for control of the steering actuator  600 . Therefore, the leaning vehicle  1  having the leaning-vehicle-steering-actuator controller  606  does not need to include a torque sensor that detects the steering torque T. However, the leaning vehicle  1  having the leaning-vehicle-steering-actuator controller  606  may include a torque sensor that detects the steering torque T. 
     The leaning-vehicle-steering-actuator controller  606  can control the steering actuator  600  in an unconventional manner also for another reason as described below. More specifically, the present inventors conducted studies about the correlation between the steering torque T and the roll angle θ. Then, the present inventors found that in a transient state where a roll rate ω is generated, the correlation between the steering torque T and the roll angle θ is not so high as the correlation between the steering torque T and the roll rate ω. Therefore, the leaning-vehicle-steering-actuator controller  606  uses the roll rate sensor  602  with using neither a torque sensor that detects the steering torque T nor a roll sensor that detects the roll angle θ, and the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  based on the roll rate ω sent from the roll rate sensor  602 , neither the steering torque T detected by the torque sensor nor the roll angle θ detected by the roll sensor. Thus, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  in an unconventional manner. 
     The leaning-vehicle-steering-actuator controller  606  can control the steering actuator  600  in an unconventional manner also for still another reason as described below. There is a correlation as described below between the posture change of the vehicle body frame  21  and the speed V of the leaning vehicle  1   a . As the absolute value of the speed V of the leaning vehicle  1   a  is increasing, the absolute value of the rotation speed of the front wheel  3  becomes greater, and the absolute value of the angular momentum of the front wheel  3  becomes greater. Then, an external force of a greater absolute value is needed to change the angular momentum of the front wheel  3 , and it becomes harder to change the posture of the vehicle body frame  21 . On the other hand, as the absolute value of the speed V of the leaning vehicle  1   a  is decreasing, the absolute value of the rotation speed of the front wheel  3  becomes smaller, and the absolute value of the angular momentum of the front wheel  3  becomes smaller. Then, an external force of a smaller absolute value is needed to change the angular momentum of the front wheel  3 , and it becomes easier to change the posture of the vehicle body frame  21 . Therefore, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  based on the speed V of the leaning vehicle  1   a . Thus, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  in an unconventional manner. 
     The leaning-vehicle-steering-actuator controller  606  can control the steering actuator  600  in an unconventional manner also for still another reason as described below. There is a correlation as described below between the posture change of the vehicle body frame  21  and the speed V of the leaning vehicle  1   a . As the absolute value of the speed V of the leaning vehicle  1   a  is increasing, the absolute value of the rotation speed of the front wheel  3  becomes greater, and the absolute value of the angular momentum of the front wheel  3  becomes greater. Then, an external force of a greater absolute value is needed to change the angular momentum of the front wheel  3 , and it becomes harder to change the posture of the vehicle body frame  21 . On the other hand, as the absolute value of the speed V of the leaning vehicle  1   a  is decreasing, the absolute value of the rotation speed of the front vehicle  3  becomes smaller, and the absolute value of the angular momentum of the front wheel  3  becomes smaller. Then, an external force of a smaller absolute value is needed to change the angular momentum of the front wheel  3 , and it becomes easier to change the posture of the vehicle body frame  21 . Therefore, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  by using the roll rate sensor  602  and the speed sensor  604  that detects the speed V of the leaning vehicle  1   a  without using a torque sensor that detects the steering torque. The leaning-vehicle-steering-actuator controller  606  determines an estimated steering torque T(m, n), which is an estimated value of the steering torque T, not based on the steering torque T detected by the torque sensor but based on the roll rate ω sent from the roll rate sensor  602  and the speed V sent from the speed sensor  604 , and the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  based on the estimated steering torque T(m, n). Thus, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  in an unconventional manner. 
     Also, the leaning-vehicle-steering-actuator controller  606  does not require a torque sensor of high rigidity. More specifically, the steering torque T is a great torque, and for detection of the steering torque T, a torque sensor of high rigidity is required. However, the leaning-vehicle-steering-actuator controller  606  does not use the steering torque T for control of the steering actuator  600 . Therefore, the leaning vehicle  1   a  does not need to include a torque sensor of high rigidity. However, this does not exclude providing a torque sensor for the leaning vehicle  1   a.    
     The roll rate sensor  602  of the leaning vehicle  1   a  is supported by the vehicle body frame  21  in such a manner as not to be displaceable relative to the vehicle body frame  21 . This inhibits a great delay of a posture change of the roll rate sensor  602  from a posture change of the vehicle body frame  21 . Therefore, the detection accuracy of the roll rate ω by the roll rate sensor  602  can be improved. 
     Also, the roll rate sensor  602  is positioned on the center line C in a view in the backward direction B, and therefore, the detection accuracy of the roll rate ω by the roll rate sensor  602  can be improved. 
     Second Embodiment 
     [Overall Structure] 
     The overall structure of a leaning vehicle  1   b  according to a second embodiment will hereinafter be described with reference to the drawings. In the present embodiment, a three-wheeled leaning vehicle including a vehicle body frame capable of leaning, two front wheels, and a rear wheel is described as an example of the leaning vehicle  1   b .  FIG. 9  is a looking-to-the right (r) view, with respect to the vehicle body frame  21 , of the leaning vehicle  1   b  when the vehicle body frame  21  is in an upright posture.  FIG. 10  is a looking-to-the-back view, with respect to the vehicle body frame  21 , of the front part of the leaning vehicle  1   b  when the vehicle body frame  21  is in an upright posture. In  FIG. 10 , the vehicle body cover  22  is shown as being transparent. 
     As shown in  FIG. 9 , the leaning vehicle  1   b  includes a vehicle body  1002 , a left front wheel  1031 , a right front wheel  1032  (see  FIG. 10 ), a rear wheel  1004 , a link mechanism  1005 , and a steering mechanism  1007 . The vehicle body  1002  includes a vehicle body frame  1021 , a vehicle body cover  1022 , a seat  1024 , and a power unit  1025 . 
     The vehicle body frame  1021  leans in the leftward direction L when the leaning vehicle  1   b  is turning left. The vehicle body frame  1021  leans in the rightward direction R when the leaning vehicle  1   b  is turning right. The vehicle body frame  1021  includes a head pipe  1211 , a down frame  1212 , an underframe  1214 , and a rear frame  1215 . In  FIG. 9 , the part of the vehicle body frame  1021  covered by the vehicle body cover  1022  is indicated by a chain line. The vehicle body frame  1021  supports the seat  1024 , the power unit  1025 , etc. 
     The head pipe  1211  is positioned in the front part of the leaning vehicle  1   b . The front part of the leaning vehicle  1   b  is a part thereof that is in front of the front edge of the seat  1024  in the forward direction f. The rear part of the leaning vehicle  1   b  is a part thereof that is behind the front edge of the seat  1024  in the backward direction b. The head pipe  1211  is inclined from the up-down direction ud such that the upper end part of the head pipe  1211  is positioned behind the lower end part of the head pipe  1211  in the backward direction b in a view in the leftward direction l or the rightward direction r. 
     The down frame  1212  is positioned behind the head pipe  1211  in the backward direction b. The down frame  1212  is a cylindrical member extending along the up-down direction ud. The upper end part of the down frame  1212  is positioned farther in the backward direction b than the head pipe  1211  in a view in the leftward direction l. The down frame  1212  extends from its upper end part to the downward direction d. The upper end part of the down frame  1212  is fixed to the lower end part of the head pipe  1211  via a connecting part (not shown). 
     The underframe  1214  extends from the lower end part of the down frame  1212  to the backward direction b. The rear frame  1215  linearly extends from the rear edge of the underframe  1214  to a backward and upward direction b, u. 
     The vehicle body frame  1021  is covered by the vehicle body cover  1022 . The vehicle body cover  1022  includes a front cover  1221 , a pair of right and left front fenders  1223 , and a leg shield  1225 . The front cover  1221  is positioned farther in the forward direction f than the seat  1024 . The front cover  1221  covers at least some part of the steering mechanism  1007  and the link mechanism  1005 . 
     The power unit  1025  includes a power source, such as an engine, an electric motor or the like, and a power transmission system, such as a transmission device or the like. 
     The seat  1024  is to be sat on by a rider. The seat  1024  is supported by the rear frame  1215 . 
     The left front wheel  1031  is a left steerable wheel of the leaning vehicle  1   b . The left front wheel  1031  is positioned in the front part of the leaning vehicle  1   b . As shown in  FIG. 10 , the left front wheel  1031  is positioned to the left (l) of the center of the vehicle body frame  1021  with respect to the left-right direction lr. The left front wheel  1031  is rotatable around a left front axle  1314  (an example of an axle of a left steerable wheel). 
     The right front wheel  1032  is a right steerable wheel of the leaning vehicle  1   b . The right front wheel  1032  is positioned in the front part of the leaning vehicle  1   b . As shown in  FIG. 10 , the right front wheel  1032  is positioned to the right (r) of the center of the vehicle body frame  1021  with respect to the left-right direction lr. The right front wheel  1032  is rotatable around a right front axle  1324  (an example of an axle of a right steerable wheel). The left front wheel  1031  and the right front wheel  1032  are arranged lateral-symmetrically with respect to the center. 
     As shown in  FIG. 10 , the pair of front fenders  1223  includes a left front fender  1227  and a right front fender  1228 . The left front fender  1227  is positioned farther in the upward direction u than the left front wheel  1031 . The right front fender  1228  is positioned farther in the upward direction u than the right front wheel  1032 . 
     The rear wheel  1004  is a driving wheel of the leaning vehicle  1   b . The rear wheel  1004  is rotated by a driving force generated by the power unit  1025 . The rear wheel  1004  is positioned in the rear part of the leaning vehicle  1   b . The rear wheel  1004  is rotatable around an axle. 
     [Steering Mechanism] 
     The steering mechanism  1007  will hereinafter be described with reference to the drawings.  FIG. 11  is a looking-to-the-down (d) view of the front part of the leaning vehicle  1   b  when the vehicle body frame  1021  is in an upright posture. In  FIG. 11 , the vehicle body cover  1022  is shown as being transparent. 
     The steering mechanism  1007  is configured to steer the left front wheel  1031  and the right front wheel  1032  in accordance with the rider&#39;s manipulation. As shown in  FIGS. 10 and 11 , the steering mechanism  1007  includes a left shock absorber  1033 , a right shock absorber  1034 , a handlebar  1060 , a steering shaft  1062 , a tie rod  1067 , a left bracket  1317 , a right bracket  1327 , and a center bracket  1337 . 
     The left shock absorber  1033  supports the left front wheel  1031  such that the left front wheel  1031  is movable along the up-down direction ud relative to the vehicle body frame  1021 . The left shock absorber  1033  includes a left lower portion  1033   a , a left upper portion  1033   b , and a left support portion  1033   c . The left lower portion  1033   a  extends along the up-down direction ud. The left support portion  1033   c  is positioned in the lower end part of the left lower portion  1033   a . The left support portion  1033   c  supports the left front wheel  1031  such that the left front wheel  1031  is rotatable. The left front wheel  1031  is rotatable around the left front axle  1314 . The left front axle  1314  extends from the left support portion  1033   c  to the leftward direction l. The left upper portion  1033   b  extends along the up-down direction ud. The left upper portion  1033   b  is positioned father in the upward direction u than the left lower portion  1033   a  with the lower end part thereof inserted in the left lower portion  1033   a . The upper end part of the left upper portion  1033   b  is fixed to the left bracket  1317 , which will be described later. Accordingly, the left upper portion  1033   b  is supported by a left side member  1053 , which will be described later. 
     The left shock absorber  1033  is what is called a telescopic shock absorber. The left shock absorber  1033 , for example, includes a combination of a damper and a spring. The left upper portion  1033   b  moves relative to the left lower portion  1033   a  in the extending direction of the left lower portion  1033   a , and accordingly, the left shock absorber  1033  is expandable and contractable in the direction. In this way, the left shock absorber  1033  absorbs displacements of the left front wheel  1031  in the up-down direction ud relative to the left upper portion  1033   b.    
     The right shock absorber  1034  supports the right front wheel  1032  such that the right front wheel  1032  is movable along the up-down direction ud relative to the vehicle body frame  1021 . The right shock absorber  1034  includes a right lower portion  1034   a , a right upper portion  1034   b , and a right support portion  1034   c . The right lower portion  1034   a  extends along the up-down direction ud. The right support portion  1034   c  is positioned in the lower end part of the right lower portion  1034   a . The right support portion  1034   c  supports the right front wheel  1032  such that the right front wheel  1032  is rotatable. The right front wheel  1032  is rotatable around the right front axle  1324 . The right front axle  1324  extends from the right support portion  1034   c  to the rightward direction r. The right upper portion  1034   b  extends along the up-down direction ud. The right upper portion  1034   b  is positioned father in the upward direction u than the right lower portion  1034   a  with the lower end part thereof inserted in the right lower portion  1034   a . The upper end part of the right upper portion  1034   b  is fixed to the right bracket  1327 , which will be described later. Accordingly, the right upper portion  1034   b  is supported by a right side member  1054 , which will be described later. 
     The right shock absorber  1034  is what is called a telescopic shock absorber. The right shock absorber  1034 , for example, includes a combination of a damper and a spring. The right upper portion  1034   b  moves relative to the right lower portion  1034   a  in the extending direction of the right lower portion  1034   a , and accordingly, the right shock absorber  1034  is expandable and contractable in the direction. In this way, the right shock absorber  1034  absorbs displacements of the right front wheel  1032  in the up-down direction ud relative to the right upper portion  1034   b.    
     The handlebar  1060  is to be manipulated by the rider. The steering shaft  1062  is supported by the vehicle body frame  1021  in a rotatable manner on its central axis in accordance with the rider&#39;s manipulation of the handlebar  1060 . More specifically, the steering shaft  1062  is inserted in the head pipe  1211  and thereby is supported by the head pipe  1211  in a rotatable manner. The handlebar  1060  is fixed to the upper end part of the steering shaft  1062 . Then, when the rider manipulates the handlebar  1060 , the steering shaft  1062  rotates on its central axis. 
     The center bracket  1337  is fixed to the lower end part of the steering shaft  1062 . Accordingly, the center bracket  1337  is rotatable around the central axis of the steering shaft  1062  together with the steering shaft  1062 . 
     The tie rod  1067  transmits the rotation of the steering shaft  1062  caused by the rider&#39;s manipulation of the handlebar  1060  to the left shock absorber  1033  and the right shock absorber  1034 . The tie rod  1067  extends along the left-right direction LR. The center of the tie rod  1067  with respect to the left-right direction LR is supported by the center bracket  1337 . The left end part of the tie rod  1067  is supported by the left bracket  1317 . The right end part of the tie rod  1067  is supported by the right bracket  1327 . 
     [Link Mechanism] 
     The link mechanism  1005  will hereinafter be described with reference to  FIGS. 10 and 11 . The link mechanism  1005  is a parallelogram link mechanism. The link mechanism  1005  is positioned below the handlebar  1060  in the downward direction d. The link mechanism  1005  is supported by the head pipe  1211  of the vehicle body frame  1021 . 
     The link mechanism  1005  includes an upper cross member  1051 , a lower cross member  1052 , a left side member  1053  and a right side member  1054 . The upper cross member  1051 , the lower cross member  1052 , the left side member  1053  and the right side member  1054  are link members that are displaceable relative to the vehicle body frame  1021 . In the present specification, a displacement includes a displacement by translation, a displacement by rotation, and a displacement by combination of translation and rotation. 
     The upper cross member  1051  extends along the left-right direction LR. The upper cross member  1051  is positioned father in the forward direction f than the head pipe  1211  and above the left front wheel  1031  and the right front wheel  1032  in the upward direction u. The upper cross member  1051  is supported by the head pipe  1211  via a support C. The support C is positioned in a middle part of the upper cross member  1051  and in the upper part of the head pipe  1211 . When the upper cross member  1051  is divided into three equal parts along the left-right direction LR, the part positioned farthest in the leftward direction L of the three parts is a left part of the upper cross member  1051 . When the upper cross member  1051  is divided into three equal parts along the left-right direction LR, the part positioned farthest in the rightward direction R of the three parts is a right part of the upper cross member  1051 . When the upper cross member  1051  is divided into three equal parts along the left-right direction LR, t the part positioned in the middle of the three parts is a middle part of the upper cross member  1051 . The support C is a shaft extending along the front-back direction fb. The support C extends from the head pipe  1211  to the forward direction f, slightly inclined to the upward direction u. The upper cross member  1051  is rotatable around the support C and accordingly rotatable relative to the head pipe  1211 . 
     The lower cross member  1052  includes a front lower cross member  1052 A and a rear lower cross member  1052 B. The front lower cross member  1052 A extends along the left-right direction LR. The front lower cross member  1052 A is positioned farther in the forward direction f than the head pipe  1211 , below the upper cross member  1051  in the downward direction d, and above the left front wheel  1031  and the right front wheel  1032  in the upward direction u. The front lower cross member  1052 A is supported by the head pipe  1211  via a support F. The support F is positioned in a middle part of the front lower cross member  1052 A and in the lower part of the head pipe  1211 . When the front lower cross member  1052 A is divided into three equal parts along the left-right direction LR, the part positioned farthest in the leftward direction L of the three parts is a left part of the front lower cross member  1052 A. When the front lower cross member  1052 A is divided into three equal parts along the left-right direction LR, the part positioned farthest in the rightward direction R of the three parts is a right part of the front lower cross member  1052 A. When the front lower cross member  1052 A is divided into three equal parts along the left-right direction LR, the part positioned in the middle of the three parts is a middle part of the front lower cross member  1052 A. The support F is a shaft extending along the front-back direction fb. The support F extends from the head pipe  1211  to the forward direction f, slightly inclined to the upward direction u. The front lower cross member  1052 A is rotatable around the support F and accordingly rotatable relative to the head pipe  1211 . 
     The rear lower cross member  1052 B extends along the left-right direction LR. The rear lower cross member  1052 B is positioned farther in the backward direction b than the head pipe  1211 , below the upper cross member  1051  in the downward direction d, and above the left front wheel  1031  and the right front wheel  1032  in the upward direction u. The rear lower cross member  1052 B is supported by the head pipe  1211  via the support F. The support F is positioned in a middle part of the rear lower cross member  1052 B and in the lower part of the head pipe  1211 . When the rear lower cross member  1052 B is divided into three equal parts along the left-right direction LR, the part positioned farthest in the leftward direction L of the three parts is a left part of the rear lower cross member  1052 B. When the rear lower cross member  1052 B is divided into three equal parts along the left-right direction LR, the part positioned farthest in the rightward direction R of the three parts is a right part of the rear lower cross member  1052 B. When the rear lower cross member  1052 B is divided into three equal parts along the left-right direction LR, the part positioned in the middle of the three parts is a middle part of the rear lower cross member  1052 B. As mentioned above, the support F is a shaft extending along the front-back direction fb. The support F extends from the head pipe  1211  also to the backward direction b, slightly inclined to the downward direction d. The rear lower cross member  1052 B is rotatable around the support F and accordingly rotatable relative to the head pipe  1211 . 
     The left side member  1053  extends along the up-down direction ud. Accordingly, the extending direction of the left side member  1053  is parallel to the extending direction of the head pipe  1211 . The left side member  1053  is positioned farther in the leftward direction l than the head pipe  1211 . The left side member  1053  is positioned farther in the upward direction u than the left front wheel  1031  and farther in a left-upward direction lu than the left shock absorber  1033 . The left side member  1053  is supported by the upper cross member  1051  via a support D. The support D is positioned in the upper part of the left side member  1053  and in the left part of the upper cross member  1051 . The support D is a shaft extending along the front-back direction fb. The left side member  1053  is rotatable around the support D and accordingly rotatable relative to the upper cross member  1051 . 
     Also, the left side member  1053  is supported by the front lower cross member  1052 A and the rear lower cross member  1052 B via a support G. The support G is positioned in the lower part of the left side member  1053 , in the left part of the front lower cross member  1052 A and in the left part of the rear lower cross member  1052 B. The support G is a shaft extending along the front-back direction fb. The left side member  1053  is rotatable around the support G and accordingly rotatable relative to the front lower cross member  1052 A and the rear lower cross member  1052 B. 
     The left bracket  1317  is supported by the lower end part of the left side member  1053 . The left bracket  1317  is rotatable around a left central axis Y 1  and rotatable relative to the left side member  1053 . The left central axis Y 1  is a central axis of the left side member  1053 . The left central axis Y 1  extends along the up-down direction ud. 
     The right side member  1054  extends along the up-down direction ud. Accordingly, the extending direction of the right side member  1054  is parallel to the extending direction of the head pipe  1211 . The right side member  1054  is positioned farther in the rightward direction r than the head pipe  1211 . The right side member  1054  is positioned farther in the upward direction u than the right front wheel  1032  and farther in a right-upward direction ru than the right shock absorber  1034 . The right side member  1054  is supported by the upper cross member  1051  via a support E. The support E is positioned in the upper part of the right side member  1054  and in the right part of the upper cross member  1051 . The support E is a shaft extending along the front-back direction fb. The right side member  1054  is rotatable around the support E and accordingly rotatable relative to the upper cross member  1051 . 
     Also, the right side member  1054  is supported by the front lower cross member  1052 A and the rear lower cross member  1052 B via a support H. The support H is positioned in the lower part of the right side member  1054 , in the right part of the front lower cross member  1052 A and in the right part of the rear lower cross member  1052 B. The support H is a shaft extending along the front-back direction fb. The right side member  1054  is rotatable around the support H and accordingly rotatable relative to the front lower cross member  1052 A and the rear lower cross member  1052 B. 
     The right bracket  1327  is supported by the lower end part of the right side member  1054 . The right bracket  1327  is rotatable around a right central axis Y 2  and rotatable relative to the right side member  1054 . The right central axis Y 2  is a central axis of the right side member  1054 . The right central axis Y 2  extends along the up-down direction ud. 
     As described above, the upper cross member  1051 , the lower cross member  1052 , the left side member  1053  and the right side member  1054  are connected to one another such that the upper cross member  1051  and the lower cross member  1052  are kept parallel to each other and such that the left side member  1053  and the right side member are kept parallel to each other. 
     The left shock absorber  1033  is positioned farther in a right-downward direction rd than the left side member  1053 . The left shock absorber  1033  is supported by the left bracket  1317 . Specifically, the upper end part of the left shock absorber  1033  is fixed to the left bracket  1317 . Further, the left shock absorber  1033  supports the left front wheel  1031 . Accordingly, the left side member  1053  supports the left front wheel  1031  via the left bracket  1317  and the left shock absorber  1033 . In this way, the link mechanism  1005  supports the left front wheel  1031 . The left shock absorber  1033  leans in the left-right direction LR together with the left side member  1053 . 
     The right shock absorber  1034  is positioned farther in a left-downward direction ld than the right side member  1054 . The right shock absorber  1034  is supported by the right bracket  1327 . Specifically, the upper end part of the right shock absorber  1034  is fixed to the right bracket  1327 . Further, the right shock absorber  1034  supports the right front wheel  1032 . Accordingly, the right side member  1054  supports the right front wheel  1032  via the right bracket  1327  and the right shock absorber  1034 . In this way, the link mechanism  1005  supports the right front wheel  1032 . The right shock absorber  1034  leans in the left-right direction LR together with the right side member  1054 . 
     [Steering Motion] 
     Next, steering motions of the leaning vehicle  1   b  will be described with reference to  FIG. 12 .  FIG. 12  is a looking-to-the-down (d) view of the front part of the leaning vehicle  1   b  when the leaning vehicle  1   b  is steered leftward. 
     As shown in  FIG. 12 , when the rider steers the handlebar  1060  leftward, the steering shaft  1062  rotates counterclockwise in a view in the downward direction d. Since the center bracket  1337  is fixed to the lower end part of the steering shaft  1062 , the center bracket  1337  rotates counterclockwise in a view in the downward direction d together with the steering shaft  1062 . 
     The tie rod  1067  makes a parallel translation in a backward and leftward direction l, b with the rotation of the center bracket  1337 . The left end part of the tie rod  1067  is supported by the front end part of the left bracket  1317 . The left bracket  1317  is rotatable around the left central axis Y 1  (see  FIG. 10 ). Accordingly, with the parallel translation of the tie rod  1067 , the left bracket  1317  rotates counterclockwise in a view in the downward direction d. Also, the right end part of the tie rod  1067  is supported by the front end part of the right bracket  1327 . The right bracket  1327  is rotatable around the right central axis Y 2  (see  FIG. 10 ). Accordingly, with the parallel translation of the tie rod  1067 , the right bracket  1327  rotates counterclockwise in a view in the downward direction d. 
     The left front wheel  1031  is connected to the left bracket  1317  via the left shock absorber  1033 . Therefore, with the rotation of the left bracket  1317 , the left front wheel  1031  rotates counterclockwise around the left central axis Y 1  (see  FIG. 10 ) in a view in the downward direction d. Also, the right front wheel  1032  is connected to the right bracket  1327  via the right shock absorber  1034 . Therefore, with the rotation of the right bracket  1327 , the right front wheel  1032  rotates counterclockwise around the right central axis Y 2  (see  FIG. 10 ) in a view in the downward direction d. 
     When the rider steers the handlebar  1060  rightward, each of the elements described above rotates in a direction opposite to the direction of rotation when the rider steers the handlebar  1060  leftward (that is, rotates clockwise). Thus, the motion of each of the elements is laterally reversed, and no more description will be provided. 
     [Leaning Motion] 
     Next, leaning motions of the leaning vehicle  1   b  will be described with reference to the drawings.  FIG. 13  is a looking-to-the-back (b) view of the front part of the leaning vehicle  1   b  when the vehicle body frame  1021  leans in the leftward direction L. 
     The vehicle body frame  1021  rotates around the roll axis Ax and thereby leans in the leftward direction L or the rightward direction R. The roll axis Ax is an axis extending along the front-back direction FB. More specifically, as shown in  FIG. 9 , the roll axis Ax is a straight line that passes the contact point between the rear wheel  1004  and the ground and is perpendicular to the steering shaft  1062  when the vehicle body frame  1021  is in an upright posture. 
     As the vehicle body frame  1021  is rotating around the roll axis Ax, the rotation angle of the vehicle body frame  1021  around the roll axis Ax changes, and the rotation angle of the vehicle body frame  1021  around the roll axis Ax is referred to as a roll angle θ. The roll angle θ of the leaning vehicle  1   b  is the same as the roll angle θ of the leaning vehicle  1   a , and the description is omitted. 
     As shown in  FIG. 13 , when the leaning vehicle  1   b  is turning left, the upper cross member  1051 , the lower cross member  1052 , the left side member  1053  and the right side member  1054  of the link mechanism  1005  displace relative to the vehicle body frame  1021  such that the left front axle  1314  is positioned above the right front axle  1324  in the upward direction u, and thereby, the vehicle body frame  1021  is caused to lean in the leftward direction L. In this case, the roll angle θ is a positive value. Also, when the leaning vehicle  1   b  is turning right, the upper cross member  1051 , the lower cross member  1052 , the left side member  1053  and the right side member  1054  of the link mechanism  1005  displace relative to the vehicle body frame  1021  such that the right front axle  1324  is positioned above the left front axle  1314  in the upward direction u, and thereby, the vehicle body frame  1021  is caused to lean in the rightward direction R. In this case, the roll angle θ is a negative value. A case in which the vehicle body frame  1021  leans in the leftward direction L will be described below as an example. 
     As shown in  FIG. 13 , with a shape change of the link mechanism  1005 , the vehicle body frame  1021  leans from the upright posture to the leftward direction L. Specifically, as shown in  FIG. 10 , when the vehicle body frame  1021  is in an upright posture, the upper cross member  1051 , the lower cross member  1052 , the left side member  1053  and the right side member  1054  form a rectangle in the leaning vehicle  1   b . On the other hand, as shown in  FIG. 13 , when the vehicle body frame  1021  leans in the leftward direction L, the upper cross member  1051 , the lower cross member  1052 , the left side member  1053  and the right side member  1054  form a parallelogram in the leaning vehicle  1   b.    
     When the rider causes the vehicle body frame  1021  to lean in the leftward direction L, the head pipe  1211  leans in the leftward direction L. When the head pipe  1211  leans in the leftward direction L, the upper cross member  1051  rotates around the support C in such a manner as to rotate counterclockwise relative to the head pipe  1211  in a view in the backward direction b. In the same way, the lower cross member  1052  rotates around the support F in such a manner as to rotate counterclockwise relative to the head pipe  1211  in a view in the backward direction b. Then, in a view in the backward direction b, the upper cross member  1051  moves in the leftward direction L relative to the lower cross member  1052 . 
     With the movement of the upper cross member  1051 , the left side member  1053  rotates around the support D in such a manner as to rotate clockwise relative to the upper cross member  1051  in a view in the backward direction b. The right side member  1054  rotates around the support E in such a manner as to rotate clockwise relative to the upper cross member  1051  in a view in the backward direction b. With the movement of the upper cross member  1051 , also, the left side member  1053  rotates around the support G in such a manner as to rotate clockwise relative to the lower cross member  1052  in a view in the backward direction b. The right side member  1054  rotates around the support H in such a manner as to rotate clockwise relative to the lower cross member  1052  in a view in the backward direction b. In this way, the left side member  1053  and the right side member  1054  lean in the leftward direction L while being kept parallel to the head pipe  1211 . 
     The left bracket  1317  is supported by the lower end part of the left side member  1053 . Therefore, when the left side member  1053  leans in the leftward direction L, the left bracket  1317  leans in the leftward direction L. The left shock absorber  1033  is supported by the left bracket  1317 , and therefore, when the left bracket  1317  leans in the leftward direction L, the left shock absorber  1033  leans in the leftward direction L. The left front wheel  1031  is supported by the lower end part of the left shock absorber  1033 , and therefore, when the left shock absorber  1033  leans in the leftward direction L, the left front wheel  1031  leans in the leftward direction L. 
     The right bracket  1327  is supported by the lower end part of the right side member  1054 . Therefore, when the right side member  1054  leans in the leftward direction L, the right bracket  1327  leans in the leftward direction L. The right shock absorber  1034  is supported by the right bracket  1327 , and therefore, when the right bracket  1327  leans in the leftward direction L, the right shock absorber  1034  leans in the leftward direction L. The right front wheel  1032  is supported by the lower end part of the right shock absorber  1034 , and therefore, when the right shock absorber  1034  leans in the leftward direction L, the right front wheel  1032  leans in the leftward direction L. 
     The rear wheel  1004  (not shown in  FIG. 13 ) is supported by the vehicle body frame  1021 . Therefore, the rear wheel  1004  leans in the leftward direction L together with the vehicle body frame  1021 . 
     When the vehicle body frame  1021  leans in the rightward direction R, each of the elements described above moves in a direction opposite to the direction of motion when the vehicle body frame  1021  is leaning in the leftward direction L. Thus, the motion of each of the elements is laterally reversed, and no more description will be provided. 
     [Actuator Controller] 
     Next, the actuator controller  1606  of the leaning vehicle  1   b  will be described with reference to the drawings.  FIG. 14  is a block diagram of the actuator controller  1606 . 
     As shown in  FIG. 14 , the leaning vehicle  1   b  further includes a lean actuator  1600 , a roll rate sensor  1602 , a speed sensor  1604 , and an actuator controller  1606 . 
     The lean actuator  1600  outputs a posture control torque Td to displace the upper cross member  1051 , the lower cross member  1052 , the left side member  1053  and the right side member  1054  relative to the vehicle body frame  1021 . The posture control torque Td is a torque to control the posture of the vehicle body frame  1021 . In order to cause the vehicle body  1021  to lean, it is necessary to apply a torque to the lower cross member  1052 . A lean torque Tl is applied to the lower cross member  1052 , and the lean torque Tl has a strength required to cause the vehicle body frame  1021  of the leaning vehicle  1   b  running at a speed V to roll at a roll rate ω. The lean torque Tl is a moment acting around the support F. When the lean torque Tl acts counterclockwise in a view in the backward direction b, the lower cross member  1052  is rotated counterclockwise (in a positive direction) by the lean torque Tl. When the lean torque Tl acts clockwise in a view in the backward direction b, the lower cross member  1052  is rotated clockwise (in a negative direction) by the lean torque Tl. The lean actuator  1600  outputs a posture control torque Td to assist the rider in applying the lean torque Tl to the lower cross member  1052 . 
     The lean actuator  1600  is fixed to the support F of the vehicle body frame  1021 . The lean actuator  1600  includes a combination of an electric motor and a gear. The electric motor generates a torque. The torque generated by the electric motor is outputted to the lower cross member  1052  as a posture control torque Td via the gear. In this way, the lean actuator  1600  causes the lower cross member  1052  to rotate around the support F relative to the head pipe  1211 . 
     The roll rate sensor  1602  detects the roll rate ω that is the amount of change per unit time of the roll angle θ. The roll rate ω of the leaning vehicle  1   b  is the same as the roll rate ω of the leaning vehicle  1   a , and the description is omitted. The roll rate sensor  1602  is, for example, supported by the vehicle body frame  1021  in such a manner as not to be displaceable relative to the vehicle body frame  1021 . In the leaning vehicle  1   b , the roll rate sensor  1602  is fixed to the lean actuator  1600 . 
     The speed sensor  1604  detects the speed V of the leaning vehicle  1   b . The speed V is a positive value when the leaning vehicle  1   b  is running forward. 
     The actuator controller  1606  is, for example, an IC (integrated circuit) for control of the lean actuator  1600 . However, the actuator controller  1606  does not need to be achieved by a single IC, and the actuator controller  1606  may be a combination of one or more ICs, one or more electronic components and/or one or more circuit boards. 
     The actuator controller  1606  obtains the roll rate ω from the roll rate sensor  1602 . Specifically, an electric signal representing the roll rate ω (which will hereinafter be referred to simply as roll rate ω) detected by the roll rate sensor  1602  is inputted to the actuator controller  1606 . 
     The actuator controller  1606  obtains the speed V from the speed sensor  1604 . Specifically, an electric signal representing the speed V (which will hereinafter be referred to simply as speed V) detected by the speed sensor  1604  is inputted to the actuator controller  1606 . 
     Even in a case where there is an input from the outside of the actuator controller  1606  to the actuator controller  1606  about the steering torque T applied around the steering shaft  1062  by the rider&#39;s manipulation of the handlebar  1060 , the actuator controller  1606  controls the lean actuator  1600  not based on the steering torque T. Even in a case where there is an input from the outside of the actuator controller  1606  to the actuator controller  1606  about the roll angle θ, the actuator controller  1606  controls the lean actuator  1600  not based on the roll angle θ. The actuator controller  1606  controls the lean actuator  1600  based on the speed V detected by the speed sensor  1604  and the roll rate ω detected by the roll rate sensor  1602 . Thus, the actuator controller  1606  uses neither the steering torque T detected by a torque sensor or the like nor the roll angle θ detected by a roll sensor or the like. 
     As shown in  FIG. 14 , the actuator controller  1606  includes a torque estimation section  1614  and a current determination section  1616 . The torque estimation section  1614  determines an estimated lean torque Tl(m, n), which is an estimated value of the lean torque Tl, based on the speed V and the roll rate ω. The values m and n are integers. The torque estimation section  1614  stores an estimated lean torque determination table as shown by TABLE 3. 
     
       
         
           
               
               
             
               
                   
                 TABLE 3 
               
             
            
               
                   
                   
               
               
                   
                 ω(n)(deg/s) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 . . . 
                 ω(−5) 
                 ω(−4) 
                 ω(−3) 
                 ω(−2) 
                 ω(−1) 
                 ω(0) = 0 
                 ω(1) 
                 ω(2) 
                 ω(3) 
                 ω(4) 
                 ω(5) 
                 . . . 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 V(m) 
                 V(1) 
                 . . . 
                 Tl(1, −5) 
                 Tl(1, −4) 
                 Tl(1, −3) 
                 Tl(1, −2) 
                 Tl(1, −1) 
                 Tl(1, 0) = 0 
                 Tl(1, 1) 
                 Tl(1, 2) 
                 Tl(1, 3) 
                 Tl(1, 4) 
                 Tl(1, 5) 
                 . . . 
               
               
                 (km/h) 
                 V(2) 
                 . . . 
                 Tl(2, −5) 
                 Tl(2, −4) 
                 Tl(2, −3) 
                 Tl(2, −2) 
                 Tl(2, −1) 
                 Tl(2, 0) = 0 
                 Tl(2, 1) 
                 Tl(2, 2) 
                 Tl(2, 3) 
                 Tl(2, 4) 
                 Tl(2, 5) 
                 . . . 
               
               
                   
                 V(3) 
                 . . . 
                 Tl(3, −5) 
                 Tl(3, −4) 
                 Tl(3, −3) 
                 Tl(3, −2) 
                 Tl(3, −1) 
                 Tl(3, 0) = 0 
                 Tl(3, 1) 
                 Tl(3, 2) 
                 Tl(3, 3) 
                 Tl(3, 4) 
                 Tl(3, 5) 
                 . . . 
               
               
                   
                 V(4) 
                 . . . 
                 Tl(4, −5) 
                 Tl(4, −4) 
                 Tl(4, −3) 
                 Tl(4, −2) 
                 Tl(4, −1) 
                 Tl(4, 0) = 0 
                 Tl(4, 1) 
                 Tl(4, 2) 
                 Tl(4, 3) 
                 Tl(4, 4) 
                 Tl(4, 5) 
                 . . . 
               
               
                   
                 V(5) 
                 . . . 
                 Tl(5, −5) 
                 Tl(5, −4) 
                 Tl(5, −3) 
                 Tl(5, −2) 
                 Tl(5, −1) 
                 Tl(5, 0) = 0 
                 Tl(5, 1) 
                 Tl(5, 2) 
                 Tl(5, 3) 
                 Tl(5, 4) 
                 Tl(5, 5) 
                 . . . 
               
               
                   
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
               
               
                   
               
            
           
         
       
     
     In the estimated lean torque determination table, estimated lean torque Tl(m, n) are stored in association with values of the speed V(m) and values of the roll rate ω (n). The speed V(m) and the roll rate ω(n) of the leaning vehicle  1   b  are the same as the speed V(m) and the roll rate ω(n) of the leaning vehicle  1  and the description thereof is omitted. 
     When the value n is positive (when the roll rate ω(n) is a positive value), the estimated lean torque Tl(m, n) is a positive value. In this case, the estimated lean torque Tl(m, n) indicates a lean torque to cause the lower cross member  1052  to rotate counterclockwise (in the positive direction) in a view in the backward direction b. In this case, the greater the value n is (the greater the roll rate ω(n) is), the greater the estimated lean torque Tl(m, n) is. Also, the greater the value m is (the greater the speed V(m) is), the greater the estimated lean torque Tl(m, n) is. 
     On the other hand, when the value n is negative (when the roll rate ω(n) is a negative value), the estimated lean torque Tl(m, n) is a negative value. In this case, the estimated lean torque Tl(m, n) indicates a lean torque to cause the lower cross member  1052  to rotate clockwise (in the negative direction) in a view in the backward direction b. In this case, the smaller the value n is (the smaller the roll rate ω(n) is), the smaller the estimated lean torque Tl(m, n) is (the greater the absolute value of the estimated lean torque Tl(m, n) is). Also, the greater the value m is (the greater the speed V(m) is), the smaller the estimated lean torque Tl(m, n) is (the greater the absolute value of the estimated lean torque Tl(m, n) is). 
     The torque estimation section  1614  identifies a speed V(m) that is closest to the speed V that the actuator controller  1606  has obtained. Also, the torque estimation section  1614  identifies a roll rate ω(n) that is closest to the roll rate ω that the actuator controller  1606  has obtained. Then, the torque estimation section  1614  determines an estimated lean torque Tl(m, n) in association with the speed V(m) and the roll rate ω(n) with reference to TABLE 3. 
     The current determination section  1616  controls the lean actuator  1600  based on the estimated lean torque Tl(m, n) determined by the torque estimation section  1614 . Specifically, the current determination section  1616  determines a control current value I(m, n) to be outputted to the lean actuator  1600 , based on the estimated lean torque Tl(m, n). Therefore, the current determination section  1616  stores a control current determination table as shown by TABLE 4. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
             
            
               
                 . . . 
                 Tl(1, −5) 
                 Tl(1, −4) 
                 Tl(1, −3) 
                 Tl(1, −2) 
                 Tl(1, −1) 
                 Tl(1, 0) = 0 
                 Tl(1, 1) 
                 Tl(1, 2) 
                 Tl(1, 3) 
                 Tl(1, 4) 
                 Tl(1, 5) 
                 . . . 
               
               
                   
                 I(1, −5) 
                 I(1, −4) 
                 I(1, −3) 
                 I(1, −2) 
                 I(1, −1) 
                 I(1, 0) = 0 
                 I(1, 1) 
                 I(1, 2) 
                 I(1, 3) 
                 I(1, 4) 
                 I(1, 5) 
               
               
                 . . . 
                 Tl(2, −5) 
                 Tl(2, −4) 
                 Tl(2, −3) 
                 Tl(2, −2) 
                 Tl(2, −1) 
                 Tl(2, 0) = 0 
                 Tl(2, 1) 
                 Tl(2, 2) 
                 Tl(2, 3) 
                 Tl(2, 4) 
                 Tl(2, 5) 
                 . . . 
               
               
                   
                 I(2, −5) 
                 I(2, −4) 
                 I(2, −3) 
                 I(2, −2) 
                 I(2, −1) 
                 I(2, 0) = 0 
                 I(2, 1) 
                 I(2, 2) 
                 I(2, 3) 
                 I(2, 4) 
                 I(2, 5) 
               
               
                 . . . 
                 Tl(3, −5) 
                 Tl(3, −4) 
                 Tl(3, −3) 
                 Tl(3, −2) 
                 Tl(3, −1) 
                 Tl(3, 0) = 0 
                 Tl(3, 1) 
                 Tl(3, 2) 
                 Tl(3, 3) 
                 Tl(3, 4) 
                 Tl(3, 5) 
                 . . . 
               
               
                   
                 I(3, −5) 
                 I(3, −4) 
                 I(3, −3) 
                 I(3, −2) 
                 I(3, −1) 
                 I(3, 0) = 0 
                 I(3, 1) 
                 I(3, 2) 
                 I(3, 3) 
                 I(3, 4) 
                 I(3, 5) 
               
               
                 . . . 
                 Tl(4, −5) 
                 Tl(4, −4) 
                 Tl(4, −3) 
                 Tl(4, −2) 
                 Tl(4, −1) 
                 Tl(4, 0) = 0 
                 Tl(4, 1) 
                 Tl(4, 2) 
                 Tl(4, 3) 
                 Tl(4, 4) 
                 Tl(4, 5) 
                 . . . 
               
               
                   
                 I(4, −5) 
                 I(4, −4) 
                 I(4, −3) 
                 I(4, −2) 
                 I(4, −1) 
                 I(4, 0) = 0 
                 I(4, 1) 
                 I(4, 2) 
                 I(4, 3) 
                 I(4, 4) 
                 I(4, 5) 
               
               
                 . . . 
                 Tl(5, −5) 
                 Tl(5, −4) 
                 Tl(5, −3) 
                 Tl(5, −2) 
                 Tl(5, −1) 
                 Tl(5, 0) = 0 
                 Tl(5, 1) 
                 Tl(5, 2) 
                 Tl(5, 3) 
                 Tl(5, 4) 
                 Tl(5, 5) 
                 . . . 
               
               
                   
                 I(5, −5) 
                 I(5, −4) 
                 I(5, −3) 
                 I(5, −2) 
                 I(5, −1) 
                 I(5, 0) = 0 
                 I(5, 1) 
                 I(5, 2) 
                 I(5, 3) 
                 I(5, 4) 
                 I(5, 5) 
               
               
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
               
               
                   
               
            
           
         
       
     
     In the control current determination table, estimated lean torque Tl(m, n) and control current values I(m, n) are stored in association with each other. The control current I(m, n) is a current that the lean actuator  1600  requires to output a posture control torque Td corresponding to the assist rate (for example, 20%) of the estimated lean torque Tl(m, n) to the lower cross member  1052 . The lean actuator  1600  outputs a posture control torque Td corresponding to 20% of the estimated lean torque Tl(m, n) to the lower cross member  1052 . Accordingly, the rider only needs to tilt the vehicle body frame  1021  to apply 80% of the estimated lean torque Tl(m, n) to the lower cross member  1052 . In this way, the lean actuator  1600  assists the rider&#39;s manipulation to tilt the vehicle body frame  1021 . The assist rate is an arbitrary value and may be a value other than 20%. In order to allow the rider to tilt the vehicle body frame  1021  with less power, the assist rate should be more than 20%. In order to allow the rider to tilt the vehicle body frame  1021  with more power, the assist rate should be less than 20%. The assist rate may be a negative value. In this case, the lean actuator  1600  outputs a posture control torque Td to resist the rider&#39;s manipulation to tilt the vehicle body frame  1021 . 
     When the value n is positive, the control current I(m, n) is a positive value. In this case, the greater the value n is, the greater the control current I(m, n) is. Also, the greater the value m is, the greater the control current I(m, n) is. On the other hand, when the value n is negative, the control current I(m, n) is a negative value. In this case, the smaller the value n is, the smaller the control current I(m, n) is (the greater the absolute value of the control current I(m, n) is). Also, the greater the value m is, the smaller the control current value I(m, n) is (the greater the absolute value of the control current value I(m, n) is). 
     The lean actuator  1600  outputs a posture control torque Td to the lower cross member  1052  based on the control current value I(m, n) outputted from the actuator controller  1606 . When receiving a positive control current value I(m, n), the lean actuator  1600  outputs a posture control torque Td to cause a counterclockwise rotation of the lower cross member  1052 . In this case, the greater the absolute value of the control current value I(m, n) is, the greater the absolute value of the posture control torque Td is. Then, in a view in the backward direction B, the vehicle body frame  1021  rotates clockwise (in the positive direction) around the roll axis Ax at the roll rate ω. When receiving a negative control current value I(m, n), the lean actuator  1600  outputs a posture control torque Td to cause a clockwise rotation of the lower cross member  1052 . In this case, the greater the absolute value of the control current value I(m, n) is, the greater the absolute value of the posture control torque Td is. Then, in a view in the backward direction B, the vehicle body frame  1021  rotates counterclockwise (in the negative direction) around the roll axis Ax at the roll rate ω. 
     Next, operations of the actuator controller  1606  will be described with reference to the drawings.  FIG. 15  is a flowchart showing operations performed by the actuator controller  1606 . The actuator controller  1606  performs a process that will be described below along a software program stored in a storage device (not shown). 
     The process is started when an ignition source of the leaning vehicle  1   b  is turned on. As long as the ignition source is on, the roll rate sensor  1602  keeps outputting the roll rate ω to the actuator controller  1606 . Also, the speed sensor  1604  keeps outputting the speed V to the actuator controller  1606 . 
     The torque estimation section  1614  obtains the roll rate ω from the roll rate sensor  1602  (step S 11 ). Further, the torque estimation section  1614  obtains the speed V from the speed sensor  1604  (step S 12 ). 
     Next, the torque estimation section  1614  identifies a roll rate ω(n) closest to the roll rate ω. Further, the torque estimation section  1614  identifies a speed V(m) closest to the speed V. Then, the torque estimation section  1614  determines an estimated lean torque Tl(m, n) corresponding to the roll rate ω(n) and the speed V(m) with reference to the estimation lean torque table as shown by TABLE 3 (step S 13 ). 
     Next, the actuator controller  1606  determines a control current value I(m, n) corresponding to the estimated lean torque Tl(m, n) determined at step S 13  (step S 14 ). The current determination section  1616  outputs the control current value I(m, n) to the lean actuator  1600 . The lean actuator  1600  outputs a posture control torque Td corresponding to the control current value I(m, n) to the lower cross member  1052 . Thereafter, the process returns to step S 11 . The process from step S 11  to S 14  is repeated until the ignition source is switched from on to off. 
     [Effects] 
     The actuator controller  1606  can control the lean actuator  1600  in an unconventional manner. More specifically, in order to change the roll angle θ of the vehicle body frame  1021 , the rider leans his/her body to the leftward direction L or the right ward direction R. Thereby, a lean torque Tl is applied to the lower cross member  1052 , and the lower cross member  1052  rotates relative to the head pipe  1211 . Then, the roll angle θ of the vehicle body frame  1021  is changed, and the posture of the vehicle body frame  1021  is changed. In this way, the rider can control the posture of the vehicle body frame  1021  by using the lean torque Tl that causes a rotation of the lower cross member  1052  as an input parameter. 
     When the rider greatly leans his/her body to the leftward direction L or the rightward direction R, the absolute value of the lean torque Tl to cause a rotation of the lower cross member  1052  becomes large, and the absolute value of the roll rate ω of the vehicle body frame  1021  becomes large. On the other hand, when the rider slightly leans his/her body to the leftward direction L or the rightward direction R, the absolute value of the lean torque Tl to cause a rotation of the lower cross member  1052  becomes small, and the absolute value of the roll rate ω of the vehicle body frame  1021  becomes small. Thus, there is a correlation between the lean torque Tl to cause a rotation of the lower cross member  1052  and the roll rate ω. Therefore, the roll rate ω can be used as an input parameter for posture control of the vehicle body frame  1021 . Then, the actuator controller  1606  controls the lean actuator  1600  based on the roll rate ω. 
     The actuator controller  1606  controls the lean actuator  1600  based on neither the steering torque T nor the roll angle θ. In more detail, in the leaning vehicle  1   b , since there is a correlation between the lean torque Tl and the roll rate ω, neither the steering torque T nor the lean torque Tl needs to be detected if the roll rate ω is detected. Thus, the actuator controller  1606  can control the lean actuator  1600  not based on the steering torque T, which is conventionally used for control of the lean actuator  1600 . 
     Also, for the following reason, the actuator controller  1606  controls the lean actuator  1600  not based on the roll angle θ. In order to change the roll angle θ of the vehicle body frame  1021 , it is necessary to tilt the left front wheel  1031  and the right front wheel  1032  while these front wheels are rotating. An angular momentum is occurring on the rotating left front wheel  1031  and the rotating right front wheel  1032 . Therefore, the rider applies external force to the left front wheel  1031  and the right front wheel  1032  to change the direction of the angular momentum occurring on the left front wheel  1031  and the right front wheel  1032  without largely changing the absolute value of the angular momentum occurring thereon. The absolute value of the moment caused by the external force to change the direction of the angular momentum occurring on the left front wheel  1031  and the right front wheel  1032  is affected by the roll rate ω but not affected by the roll angle θ. For example, the absolute value of a moment required to change the roll angle θ of the left front wheel  1031  and the right front wheel  1032  from 45 degrees to 50 degrees in a unit time is equal to the absolute value of a moment required to change the roll angle θ of the left front wheel  1031  and the right front wheel  1032  from 50 degrees to 45 degrees in the unit time. Therefore, the present inventors had an idea that there is not a high correlation between the lean torque Tl and the roll angle θ. Accordingly, there is not a high correlation between the roll angle θ and the roll rate ω. Then, if the roll rate ω is detected, the actuator controller  1606  can control the lean actuator  1600  that outputs a posture control torque Td to control the posture of the vehicle body frame  1021  not based on the roll angle θ. 
     For the reasons above, the actuator controller  1606  can control the lean actuator  1600  based on the roll rate ω, neither the steering torque T nor the roll angle θ. Thus, the actuator controller  1606  can control the lean actuator  1600  in an unconventional manner. 
     In the leaning vehicle  1   b , the roll rate sensor  1602  is supported by the vehicle body frame  1021  in such a manner as not to be displaceable relative to the vehicle body frame  1021 . This inhibits a great delay of a posture change of the roll rate sensor  1602  from a posture change of the vehicle body frame  1021 . As a result, the detection accuracy of the roll rate ω by the roll rate sensor  1602  can be improved. 
     Other Embodiments 
     The embodiments and modifications described herein and/or illustrated by the drawings are to make the present teaching easier to understand and not to limit the concept of the present teaching. It is possible to adapt or alter the embodiments and modifications described above without departing from the gist thereof. 
     The gist includes all equivalent elements, modifications, omissions, combinations (for example, combination of features of the embodiments and modifications), adaptations and alterations as would be appreciated by those skilled in the art based on the embodiments and modifications disclosed herein. The limitations in the claims are to be interpreted broadly based on the language employed in the claims and not limited to the embodiments and modifications described in the present specification or during the prosecution of the present application. Such embodiments and modifications are to be understood as non-exclusive. For example, the terms “preferable” and “good” in the present specification are to be understood as non-exclusive, and these terms mean “preferable but not limited to this” and “good but not limited to this”, respectively. 
     The leaning vehicles  1 ,  1   a  and  1   b  each may include a torque sensor configured to detect the steering torque T. However, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  not based on the steering torque T detected by the torque sensor. The actuator controller  1606  controls the lean actuator  1600  not based on the steering torque T detected by the torque sensor. 
     The leaning vehicles  1 ,  1   a  and  1   b  each may include a roll sensor configured to detect the roll angle θ. However, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  not based on the roll angle θ detected by the roll sensor. The actuator controller  1606  controls the lean actuator  1600  not based on the roll angle θ detected by the roll sensor. 
     In the leaning vehicles  1  and  1   a , the leaning-vehicle-steering-actuator controller  606  may calculate the roll angle θ by integrating the roll rate ω detected by the roll rate sensor  602 . The leaning-vehicle-steering-actuator controller  606  may use the calculated roll angle θ for posture control of the vehicle body frame  21 . In the leaning vehicle  1   b , the actuator controller  1606  may calculate the roll angle θ by integrating the roll rate ω detected by the roll rate sensor  1602 . The actuator controller  1606  may use the calculated roll angle θ for posture control of the vehicle body frame  1021 . 
     Each of the leaning vehicles  1  and  1   a  may be a vehicle including two front wheels and one rear wheel, like the leaning vehicle  1   b . The leaning vehicle  1   b  needs to include at least one rear wheel. 
     The link mechanism  1005  of the leaning vehicle  1   b  is a parallelogram link mechanism. However, the link mechanism  1005  does not need to be a parallelogram link mechanism, and may be a double wishbone link mechanism. 
     In the leaning vehicle  1   a , the leaning-vehicle-steering-actuator controller  606  determines an estimated steering torque T(m, n) based on the speed V and the roll rate ω, and thereafter determines a control current value I(m, n) based on the estimated steering torque T(m, n). However, the leaning-vehicle-steering-actuator controller  606  may determine a control current value I(m, n) based on the speed V and the roll rate ω. In this case, the leaning-vehicle-steering-actuator controller  606  stores a table in which control current values I(m, n) are stored in association with values of the speed V(m) and values of the roll rate ω(n). Instead of such a table, a mathematical expression or a map may be used for the determination of an estimated steering torque T(m, n) and/or the determination of a control current value I(m, n). 
     In the leaning vehicle  1   b , the actuator controller  1606  determines an estimated lean torque Tl(m, n) based on the speed V and the roll rate ω, and thereafter determines a control current value I(m, n) based on the estimated lean torque Tl(m, n). However, the actuator controller  1606  may determine a control current value I(m, n) based on the speed V and the roll rate ω. In this case, the actuator controller  1606  may store a table in which control current values I(m, n) are stored in association with values of the speed V and values of the roll rate ω. Instead of such a table, a mathematical expression or a map may be used for the determination of an estimated lean torque Tl(m, n) and/or the determination of a control current value I(m, n). 
     The above-described control method of the steering actuator  600  based on the speed V and the roll rate ω carried out in the leaning vehicle  1   a  is only an example, and the control method of the steering actuator  600  is not limited to this. In the control method of the steering actuator  600  based on the speed V and the roll rate ω, the estimated steering torque determination table and the control current determination table are not necessarily used. The leaning-vehicle-steering-actuator controller  606 , for example, stores a reference control current value that is to be used for determination of a control current value to be outputted to the steering actuator  600 . The reference control current value may be a constant value or may be a variable value that varies in association with any other parameter (for example, temperature) than the speed V and the roll rate ω. Then, the leaning-vehicle-steering-actuator controller  606  may determine a control current value by multiplying the reference control current value with a coefficient determined based on the speed V and the roll rate ω. 
     The above-described control method of the lean actuator  1600  based on the speed V and the roll rate ω carried out in the leaning vehicle  1   b  is only an example, and the control method of the lean actuator  1600  is not limited to this. In the control method of the lean actuator  1600  based on the speed V and the roll rate ω, the estimated lean torque determination table and the control current determination table are not necessarily used. The actuator controller  1606 , for example, stores a reference control current value that is to be used for determination of a control current value to be outputted to the lean actuator  1600 . The reference control current value may be a constant value or may be a variable value that varies in association with any other parameter (for example, temperature) than the speed V and the roll rate ω. Then, the actuator controller  1606  may determine a control current value by multiplying the reference control current value with a coefficient determined based on the speed V and the roll rate ω. 
     The roll rate sensor  602  may be supported by any other component than the steering actuator  600 . When the leaning vehicle  1   a  includes an IMU (inertial measurement unit), the roll rate sensor  602  may be a roll rate sensor included in the IMU. The IMU is a unit configured to detect the inertia of the leaning vehicle  1   a . In this case, the roll rate sensor  602  is supported by the case of the IMU. The IMU is supported by the vehicle body frame  21  via a rubber mount so that noise generated by the engine vibration will not be transmitted to sensors provided in the IMU. Therefore, when the roll rate sensor  602  is included in the IMU, the roll rate sensor  602  is supported by the vehicle body frame  21  in such a manner as to be slightly displaceable relative to the vehicle body frame  21 . As with the roll rate sensor  602 , the roll rate sensor  1602  may be included in such an IMU. 
     Each of the leaning vehicles  1  and  1   a  may be a two-wheeled off-road motorcycle, a two-wheeled scooter-type motorcycle, or a moped bicycle. 
     The roll axis Ax may pass through the roll rate sensor  602  or  1602 . In this case, the roll rate sensor  602  or  1602  detects the roll rate ω still more accurately. 
     The posture control torque Td may be used for any other purpose than the posture control of the vehicle body frame  1021  around the roll axis Ax. The posture control torque Td may be used for posture control of the vehicle body frame  1021  around a yaw axis. The posture control torque Td may be used for posture control of the vehicle body frame  1021  around a pitch axis. 
     When the leaning vehicle  1   a  is running at a low speed, the supplementary steering torque Tc may be outputted to the steering shaft  62  to inhibit the vehicle body frame  21  from leaning in the leftward direction L or the rightward direction R. More specifically, the leaning-vehicle-steering-actuator controller  606  carries out such leaning inhibition control, for example, under the condition of 0 km/h&lt;V≤20 km/h. When the front wheel  3  is steered leftward while the vehicle body frame  21  is leaning in the leftward direction L, a negative roll rate ω occurs, and when the front wheel  3  is steered rightward while the vehicle body frame  21  is leaning in the rightward direction R, a positive roll rate ω occurs. 
     Therefore, the current determination section  616  outputs a positive control current value I(m, n) when the vehicle body frame  21  is leaning in the leftward direction L (when the roll rate ω is a positive value). The steering actuator  600  outputs a positive supplementary steering torque Tc to the steering shaft  62 . Accordingly, the front wheel  3  is steered leftward, and the vehicle body frame  21  is returning to the upright posture. The current determination section  616  outputs a negative control current value I(m, n) when the vehicle body frame  21  is leaning in the rightward direction R (when the roll rate ω is a negative value). The steering actuator  600  outputs a negative supplementary steering torque Tc to the steering shaft  62 . Accordingly, the front wheel  3  is steered rightward, and the vehicle body frame  21  is returning to the upright posture. In this way, the vehicle body frame  21  of the leaning vehicle  1   a  is inhibited from leaning in the leftward direction L or the rightward direction R. Further, the leaning-vehicle-steering-actuator controller  606  may control the steering actuator  600  based on a yaw rate in addition to the roll rate ω. The yaw rate is an angular rate of a rotation of the vehicle body frame  21  around an axis extending along the up-side direction UD. Also, depending on the characteristics of the leaning vehicle  1   a , the leaning-vehicle-steering-actuator controller  606  may control the steering actuator  600  to assist the leaning motion of the leaning vehicle  1   a.    
     The leaning-vehicle-steering-actuator controller  606  may carry out a control process as described below. When the speed V is, for example, greater than 20 km/h, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  with reference to the estimated steering torque determination table as shown by TABLE 1 and the control current determination table as shown by  FIG. 2 . However, when the speed V is, for example, equal to or less than 20 km/h, the leaning-vehicle-steering-actuator controller  606  controls the steering actuator  600  to perform the above-described leaning inhibition control. 
     When the leaning vehicle  1   b  is running at a low speed, the posture control torque Td may be outputted to the upper cross member  1051  or the lower cross member  1052  to inhibit the vehicle body frame  1021  from leaning in the leftward direction L or the rightward direction R. More specifically, the actuator controller  1606  carries out the leaning inhibition control, for example, under the condition of 0 km/h&lt;V≤20 km/h. The current determination section  1616  outputs a negative control current value I(m, n) when the vehicle body frame  1021  is leaning in the leftward direction L (when the roll rate ω is a positive value). The lean actuator  1600  outputs a negative posture control torque Td to the lower cross member  1052 . Accordingly, the lower cross member  1052  rotates clockwise relative to the vehicle body frame  1021  in a view in the backward direction b, and the vehicle body frame  21  is returning to the upright posture. The current determination section  1616  outputs a positive control current value I(m, n) when the vehicle body frame  1021  is leaning in the rightward direction R (when the roll rate ω is a negative value). The lean actuator  1600  outputs a positive posture control torque Td to the lower cross member  1052 . Accordingly, the lower cross member  1052  rotates counterclockwise relative to the vehicle body frame  1021  in a view in the backward direction b, and the vehicle body frame  1021  is returning to the upright posture. In this way, the vehicle body frame  1021  of the leaning vehicle  1   b  is inhibited from leaning in the leftward direction L or the rightward direction R. Further, the leaning-vehicle-steering-actuator controller  606  may control the lean actuator  1600  based on a yaw rate in addition to the roll rate ω. Also, depending on the characteristics of the leaning vehicle  1   b , the actuator controller  1606  may control the lean actuator  1600  to assist the leaning motion of the leaning vehicle  1   b.    
     The leaning-vehicle-steering-actuator controller  606  does not necessarily use the speed V and may use only the roll rate ω for control of the steering actuator  600 . Alternatively, the leaning-vehicle-steering-actuator controller  606  may control the steering actuator  600  based on not only the roll rate ω but also any other parameter. The actuator controller  1606  does not necessarily use the speed V and may use only the roll rate ω for control of the lean actuator  1600 . Alternatively, the actuator controller  1606  may control the lean actuator  1600  based on not only the roll rate ω but also any other parameter. 
     The lean actuator  1600  may output the posture control torque Td to the upper cross member  1051  instead of the lower cross member  1052 . Alternatively, the lean actuator  1600  may output the posture control torque Td to the left side member  1053  or to the right side member  1054 . 
     The roll rate sensor  602  and the leaning-vehicle-steering-actuator controller  606  may be connected to each other by an electrical signal line or an optical fiber. The speed sensor  604  and the leaning-vehicle-steering-actuator controller  606  may be connected to each other by an electrical signal line or an optical fiber. The roll rate sensor  602 , the speed sensor  604  and the leaning-vehicle-steering-actuator controller  606  may be connected to one another by a CAN (controller area network) or any other connection means. When a CAN is used, various kinds of information are multiplexed and transmitted through the line interconnecting the roll rate sensor  602 , the speed sensor  604  and the leaning-vehicle-steering-actuator controller  606 . A connection means other than a CAN is, for example, connecting the roll rate sensor  602  and the leaning-vehicle-steering-actuator controller  606  by a line and connecting the speed sensor  604  and the leaning-vehicle-steering-actuator controller  606  by a line. Through the line connecting the roll rate sensor  602  and the leaning-vehicle-steering-actuator controller  606 , only the roll rate ω is transmitted. Through the line connecting the speed sensor  604  and the leaning-vehicle-steering-actuator controller  606 , only the speed V is transmitted. 
     The roll rate sensor  1602  and the actuator controller  1606  may be connected to each other by an electrical signal line or an optical fiber. The speed sensor  1604  and the actuator controller  1606  may be connected to each other by an electrical signal line or an optical fiber. The roll rate sensor  1602 , the speed sensor  1604  and the actuator controller  1606  may be interconnected by a CAN or any other connection means. When a CAN is used, various kinds of information are multiplexed and transmitted through the line interconnecting the roll rate sensor  1602 , the speed sensor  1604  and the actuator controller  1606 . A connection means other than a CAN is, for example, connecting the roll rate sensor  1602  and the actuator controller  1606  by a line and connecting the speed sensor  1604  and the actuator controller  1606  by a line. Through the line connecting the roll rate sensor  1602  and the actuator controller  1606 , only the roll rate ω is transmitted. Through the line connecting the speed sensor  1604  and the actuator controller  1606 , only the speed V is transmitted. 
     The leaning vehicle  1   b  may further include a leaning-vehicle-steering-actuator controller  606  and a steering actuator  600 . In this case, in the leaning vehicle  1   b , the leaning vehicle steering control actuator controller  606  controls the steering actuator  600 , and the actuator controller  1606  controls the lean actuator  1600 . The operations of the leaning-vehicle-steering-actuator controller  606  of the leaning vehicle  1   b  are the same as the operations of the leaning-vehicle-steering-actuator controller  606  of the leaning vehicle  1   a . Also, the leaning-vehicle-steering-actuator controller  606  and the actuator controller  1606  may change the assist rate depending on the speed V(m) and/or the roll rate ω(n). For example, when the leaning vehicle  1   b  is running at a low speed, the leaning-vehicle-steering-actuator controller  606  increases the assist rate of the steering actuator  600 , and the actuator controller  1606  decreases the assist rate of the lean actuator  1600 . On the other hand, when the leaning vehicle  1   b  is running at a high speed, the leaning-vehicle-steering-actuator controller  606  decreases the assist rate of the steering actuator  600 , and the actuator controller  1606  increases the assist rate of the lean actuator  1600 . However, how the assist rate is changed is not limited to this. 
     The leaning vehicles  1  and  1   a  may employ the drive-by-wire technology. Specifically, the handlebar  60  does not need to be mechanically connected to the front wheel  3 . The handlebar  60  does not need to be mechanically connected to the at least one steerable wheel  3   o . In this case, the steering actuator  600  steers the at least one steerable wheel  3   o  in accordance with the manipulation of the handlebar  60 . In this regard, the force applied to the handlebar  60  is not transmitted to the at least one steerable wheel  3   o . In this case, the steering actuator  600  steers the front wheel  3  in accordance with the manipulation of the handlebar  60 . In this regard, the force applied to the handlebar  60  is not transmitted to the front wheel  3 . 
     REFERENCE SIGNS LIST 
     
         
         
           
               1 ,  1   a  leaning vehicle 
               2 ,  1002  vehicle body 
               3  front wheel 
               3   o  at least one steerable wheel 
               4 ,  1004  rear wheel 
               7 ,  1007  steering mechanism 
               21 ,  1021  vehicle body frame 
               24 ,  1024  seat 
               25 ,  1025  power unit 
               60 ,  1060  handlebar 
               62 ,  1062  steering shaft 
               64  front fork 
               64 L,  1033  left shock absorber 
               64 R,  1034  right shock absorber 
               66  upper bracket 
               68  under bracket 
               211 ,  1211  head pipe 
               600  steering actuator 
               602 ,  1602  roll rate sensor 
               604 ,  1604  speed sensor 
               606  leaning-vehicle-steering-actuator controller 
               614 ,  1614  torque estimation section 
               616 ,  1616  current determination section 
               1005  link mechanism 
               1031  left front wheel 
               1032  right front wheel 
               1051  upper cross member 
               1052  lower cross member 
               1053  left side member 
               1054  right side member 
               1067  tie rod 
               1314  left front axle 
               1317  left bracket 
               1324  right front axle 
               1327  right bracket 
               1337  center bracket 
               1052 A front lower cross member 
               1052 B rear lower cross member 
               1600  lean actuator 
               1606  actuator controller 
             Ax roll axis