JPS63305082A - Attitude controlling method in coaxial two wheeler - Google Patents

Abstract

PURPOSE:To secure such a coaxial two wheeler that is travelable in a stable state by tilting a control arm in the reverse direction where a car body is tilted, and making it so as to give a restoring moment to the car body. CONSTITUTION:A pair of wheels 2, 3 are attached to both ends of an axle 1 and, in turn, a square frame-form car body 4 is tiltably supported on this axle 1. A fulcrum shaft 5 is rotatably installed and supported in an upper part of the car body 4, and in the center of the fulcrum shaft 5, an attitude control arm 6 with a weight 6a is hangingly clamped thereto. Rotary encoders 11, 14 are attached to the car body 4 and a wheel driving motor 7, detecting each turning angle of these wheels 2, 3 and a tilt angle to a vertical line. This detec tion signal is inputted into a microcomputer 16 which controls the wheel driving motor 7 and an attitude control arm driving motor 9 on the basis of these inputted signals, thus it aims at stabilization for the car body.

Description

[Detailed description of the invention]

Object of the Invention (Field of Industrial Application) The present invention relates to a method for controlling the attitude of a coaxial two-wheeled vehicle. (Prior art) Coaxial two-wheeled vehicles, which have wheels at both ends of the same shaft, are advantageous in terms of compactness compared to four-wheeled vehicles or three-wheeled vehicles, but they cannot be put to practical use unless posture stability control is overcome. It's impossible. Therefore, research has been conducted into an attitude control method in which the control arm is suspended from the vehicle body supported on the drive shaft of the coaxial two-wheeled vehicle that constitutes such an unstable attitude system, and the inclination angle of the control arm with respect to the vehicle body is controlled. has been done. (Problem to be Solved by the Invention) However, in the attitude control method in which the control arm is tilted in the opposite direction to the direction in which the vehicle body is tilted to apply a restoring moment to the vehicle body, the dead zone of the motor for driving the control arm or the gear transmission Not only do control delays occur due to nonlinear elements such as backlash in the system, but angular velocity calculations are performed based on short-term sampling of state quantities such as the vehicle body slant angle and control arm slant angle used for feedback control. There is noise that cannot be ignored, and it is extremely difficult to stably control the attitude of the vehicle body using actual feedback control. Structure of the Invention (Means for Solving Problems) Therefore, the first invention provides a vehicle body rotatably supported on an axle having a pair of wheels at both ends, and a wheel drive motor attached to the vehicle body. The target is a coaxial two-wheeled vehicle consisting of a control combiator that sends an operation command to a wheel drive motor, and an angle detection means that detects the inclination of the vehicle body, and the lateral inclination angle of the vehicle body detected by the angle detection means is shortened. Sampling is performed at time intervals, and the sampling value is substituted into the control input calculation formula that has been input and set in the control computer in advance, using the sampled lateral slope angle of the vehicle body as a state variable and the feedback gain as a coefficient. Calculating the control torque of the wheel drive motor based on the
An operation corresponding to the calculated control torque is commanded from the control combinator to the wheel drive motor to control the attitude of the coaxial two-wheeled vehicle. A second invention is directed to a coaxial two-wheeled vehicle in which a second angle detection means for detecting the rotation angle of a wheel is added to the first invention, and the lateral inclination angle of the vehicle body detected by the first angle detection means and The rotation angle of the wheel detected by the second angle detection means is sampled at short intervals, and the sampled lateral inclination angle of the vehicle body, the sampled rotation angle of the wheel, and the angular velocity calculated based on these sampling angles are used as state variables. , calculate the sampling value by substituting the feedback gain into a control input calculation formula inputted in advance into the control computer as a coefficient, calculate the control torque of the wheel drive motor based on this calculation, and calculate the control torque of the wheel drive motor. The control computer commands the wheel drive motor to perform an operation corresponding to the calculated control torque, thereby controlling the attitude of the coaxial two-wheeled vehicle. In a third invention, a posture control arm tiltably supported by a vehicle body constituting the coaxial two-wheeled vehicle in the second invention via a support shaft, a posture control arm drive motor attached to the vehicle body, The object is a coaxial two-wheeled vehicle configured by adding a third angle detection means for detecting the inclination of the control arm and incorporating a function of sending an operation command to the attitude control arm drive motor together with the wheel drive motor into the control computer, The lateral inclination angle of the vehicle body detected by the first angle detection means, the rotation angle of the wheel detected by the second angle detection means, and the lateral inclination of the attitude control arm detected by the third angle detection means. The angle is sampled at short intervals, and the sampled lateral inclination angle of the vehicle body, the sampled rotation angle of the wheels, the sampled lateral inclination angle of the attitude control arm, and the angular velocity calculated based on these sampling angles are set as state variables, and the feedback gain is set as a coefficient. Substituting the sampling value into a control input calculation formula input and set in advance into the control computer and calculating the control torque of the wheel drive motor and the attitude control arm drive motor based on this calculation. The control computer instructs the wheel drive motor and the attitude control arm drive motor to perform operations corresponding to these calculated control torques, thereby controlling the attitude of the coaxial two-wheeled vehicle. (Operation) That is, in the first invention, the lateral inclination angle of the vehicle body detected by the first angle detection means is sampled at short intervals, and the control torque of the wheel drive motor is calculated based on this sampling. Based on this calculation result, feedback control of the wheel drive motor is performed. This causes the wheels to move in the direction in which the vehicle body is tilted, and a restoring moment is applied to the vehicle body. In this invention, although the control torque is immediately calculated only from the sampled vehicle body lateral inclination angle, the attitude stability control is good. In the second invention, the lateral inclination angle of the vehicle body detected by the first angle detection means and the rotation angle of the wheel detected by the second angle detection means are sampled at short intervals, and the angular velocities thereof are The control torque of the wheel drive motor is calculated based on the sampled value and the calculated angular velocity, and the wheel drive motor is feedback-controlled based on this calculation result. This applies a restoring moment to the vehicle body. In this invention, since not only the sampling angles of the vehicle body and wheels but also the angular velocities calculated from them are used, the attitude stability control is even better. In a third invention, the lateral inclination angle of the vehicle body is detected by the first angle detection means, the rotation angle of the wheel is detected by the second angle detection means, and the rotation angle is detected by the third angle detection means. The lateral inclination angle of the attitude control arm is sampled at short intervals, and based on this sampling, the control torque of the wheel drive motor and the attitude control arm drive motor is calculated, and the wheel drive motor is adjusted based on the calculation results. and performs feedback control of the attitude control arm drive motor. As a result, the wheels move toward the tilting direction of the vehicle body, and the control arm rotates in the opposite direction to the tilting direction of the vehicle body, thereby applying a restoring moment to the vehicle body. In this invention, the control of the attitude control arm enables more stable attitude control than in the above-mentioned invention 1.2. (Example) Hereinafter, an example embodying the present invention will be described based on the drawings. As shown in Figure 1, there are a pair of wheels 2.3 at both ends of the axle 1.
is fixedly attached to the axle 1, and a rectangular frame-shaped vehicle body 4 is tiltably supported on the axle 1. A support shaft 5 is rotatably supported on the upper part of the vehicle body 4. An attitude control arm 6 is suspended and fixed at the center of the support shaft 5, and a weight is attached to the lower end of the attitude control arm 6. 6a is attached. Weight 6
A wheel drive motor 7 capable of forward and reverse rotation is mounted on the vehicle body 4 directly below a.
is mounted on the drive shaft 7a as shown in FIG.
A reduction gear train 8 is interposed between the axle 1 and the axle 1 . As a result, the rotational drive of the wheel drive motor 7 is decelerated and transmitted to the axle 1, causing the wheels 2.3 to rotate in forward and reverse directions. Directly above the support shaft 5, a posture control arm drive motor 9 that is capable of forward and reverse rotation is mounted on the vehicle body 4, and a reduction gear train 10 is interposed between the drive shaft 9a and the support shaft 5. . As a result, the rotational drive of the attitude control arm drive motor 9 is decelerated and transmitted to the support shaft 5, and the attitude control arm 6 swings back and forth. A first rotary encoder 11 is provided on one side of the vehicle body 4, and its rotation axis 11a is set on an extension of the axle 1. A pair of contact pieces 12.
13 are mounted at right angles, and their tips are slidably in contact with the floor surface. As a result, the lateral inclination angle of the vehicle body 4 with respect to the vertical line is detected. Wheel drive motor 7
is equipped with a second rotary encoder 14, and a third rotary encoder 15 is mounted on the posture control arm drive motor 9, which determines the rotation angle of both motors 7.9, that is, the wheels 2.3. The angle of rotation and the angle of lateral inclination with respect to the vertical line are detected. A control combination 16 consisting of a microcomputer is mounted on the lower part of the vehicle body 4, and detection signals from the rotary encoders 11, 14, and 15 are input to the control computer 16. The control combinator 16 calculates control torques for the wheel drive motor 7 and attitude control arm drive motor 9 based on these input signals, and controls the wheel drive motor 7 and attitude control arm drive motor 9 to perform operations corresponding to these control torques. command.

[1] FIG. 3 is a dynamic model that is a simplified version of FIG. A wheel portion 17 consisting of the vehicle body 4 is represented as a mass point at a distance 11 from the axle 1, and the attitude control arm 6 and the weight 6
An arm portion 18 consisting of a is shown as a mass point at a distance of 12 from the support shaft 5. The wheel portion 19 consisting of the axle 1 and wheels 2 and 3 is assumed to have its center of gravity on the axle 1, and the distance between the axle 1 and the support shaft 5 is E. The kinetic energy of this dynamic model is 1 for the kinetic energy of the vehicle body 17 and 2 for the kinetic energy of the arm 18.
and the kinetic energy of the wheel part 19 is the sum of 3, and each kinetic energy K1 and 2° K3 is the mass of the vehicle body part 17, m1, the mass of the arm part 18, m2, and the mass of the wheel part 19, ma. It is expressed by the coordinate components of the x-y coordinates shown in FIG. 2 as follows. However, regarding K3, the quality is ff1m
First, assume that the mass point of a is on the center of gravity. Kl = (1/2) mt(xt2+yt2)K2
=(1/2) m2(x22+ )'22)K3 =(
1/2) ma xa2 - and shi represent the first-order differential of X and y. The inclinations of the vehicle body part 17 and the arm part 18 with respect to the vertical line are each θ1. θ2, the rotation angle of the wheel portion 19 is δ3, the wheel 2.
If the radius of 3 is r, the moment of inertia of the vehicle body 17 around the axle 1 is J1, and the moment of inertia of the arm 18 around the support shaft 5 is J2, then Kt = (1/2) m I X ((r a3 + 181・cosθri2+l12θ1
2・5in2θ1)=(1/2) mx ×(r2δ32+2rj!1 δ3 /71 ・CO
3θ1+ 112e 12)=(1/2) ml r
2 θ32 +ml r211 a3θ1・CO3θt+(1/2)
J t δ12 2 = (1/2) m2 = (1/2) m2r219a2 + m2rθa(lθ1 °cos θ1−12θ2'C
O5δ2)−m2j! 12 θ1θ2 °cos (θ
1-θ2)+ (1/2) m2120 t"+(1/2)
2) J 2 e 2” However, ■1, ■2.b3 is θ1
．． θ2. This is the first differential of θ3. Regarding 3, the kinetic energy of the wheel portion 19 includes rotational energy based on the moment of inertia around the center of gravity.If this moment of inertia is J3, the kinetic energy 3 is as follows. Therefore, the kinetic energy is: K, = Kl + 2 + 3 + (1/2)・(ml r”+m2 r”4m3 r
”+J3) δ32-m2 N21 #1 #2 ・C
O3(θ1-02)+< m211+m2 jri r
810B ・cosθ1-m2 ff12 rf12
$3, cos δ2・・・・(1) Potential energy P is expressed as follows, where g is the gravitational acceleration. P=(m11t+m21)g-cos 01m21
2 g 'CoS 02 (2) Loss energy D is the viscous friction coefficient related to the rotation of the vehicle body part 17 f1, the viscous friction coefficient related to the rotation of the arm part 18 f2, and the viscous friction related to the rotation of the wheel part 19. coefficient f
3, it is expressed as follows. Torque T2 is applied to the arm portion 18 and wheel portion 19. The following Lagrange equation of motion holds true due to the operation of T3. d/d t *δ/δit1 *to δ/δθl*+
δ/δθl *P+δ/δθl *D=TlO=1.
2. 3) ・ ・ ・ (4) However, d/d t is an ordinary differential operator, and δ/δθi. δ/δθi is a partial differential operator. By substituting equations (1), (2), and (3) into equation (4), we get the following. B1 'C03 (θ1-02) θ1 + B2 θ2 + B2
°sinθ2+f2θ2−T2... (6) C1°cos O1θ1+C2°cos O2θ2
+C3θ3=T3 ・ ・ ・ (7) However, Al −J1+m2 12 f31=−m2 12 12 C1= (ml 1 +m2 1)rpl =−
m2 12 1 El = (ml 1!1+m2 1) g
2-J2 C2=-m2 12 r p2 =-m2 12 1! B2”-m2 12 g Ca-(ml + m2 + m3) r2+J
3D3= −(ml 11 +m2 N) r
Eel --m2 l1i2 r

[2] Next, the design of the linear control system for the dynamic model shown in FIG. 3 will be explained. The following approximation is made assuming that the dynamic model of FIG. 3 is controlled so that O1 and O2 do not always become too large. sin θ1#θ1 sin θ2#θ2cos
θl = CO3θ2xcos(01-O2)-1=s
in (θ1-θ2)B22=0 Based on the above approximation, equations (5), <6), and (7) are linearized as follows. ... (8) 'tiz -A21θ1+A22θNA23' i+A
24&2+B2+T2... (9) However, A11-EI B2/Δ A12--B2 Bt/
ΔA13- f IB2/Δ A14-- f 2
Bt/ΔA21--EI Bl/ΔA22--B
2 At/ΔA23--rl Bl/ΔA24--
r 2 As/ΔB! ! =B1/ΔBz
t--ks/ΔΔ-B12-, AI B2 X1 ”O1・x2 =θ2・x3-O1・×4-B2
The following vector and matrix representations are performed as . u=T2 Using the vector and matrix representations, the following state and output equations are obtained. X (t) = τ−X (t) +B−u, (1)
・ ・ ・ (10) Y (t) Ride・X (t) ・ ・ ・ ・ (11) When the equation of state (10) is Laplace transformed, it becomes as follows. = sX (s)=A・X (s)+B=u (s) Therefore, ---1→
... (12) 1-1 However, T is a unit matrix, and (sl-A) is an inverse matrix of (sl-τ). Substituting equation (12) into output equation (11) yields the following. Y (s) = τ(sl-τ)B-u(s)Y (
The function represented by S) /u (s) is called a transfer function in control theory, and is expressed in the following polynomial form. Y (s) /u (s) =k (s-1Fl)(S-σ2)(s-σ3)(5
-a4>÷(S-A1)(s-A2)(S-A3)(3
-A4)... (14) (S-A1)(S-A2)(S-A3)( of formula (14)
S-A4) is the characteristic polynomial, k is the gain, and A1 (i=1.
2, 3.4) are called poles. When the pole λi is on the right half plane on the complex plane, that is, when the real value is positive, Equation (10), (
It is well known in control theory that the system expressed by For example, when the parameters take the following values, it is confirmed that the pole exists on the right half of the complex plane. mx-2,59kg 1 =0.318mm2
-1.52kg 11=0.17 mm3=
0.36kg [2-0,20mJs-0,10
8kgm J2-7.01X10kgm Ja =5. OOxlOkgm fl”6.OXiONms f2”4.40X1ONms fa-4,40xlONms To stabilize the dynamic model in Fig. 3, control human power u (t
) must be added to transition from an unstable state to a stable state, but in order to do so, the existence of U(t) must be guaranteed.If U(1) exists, equation (1
0), (11) is controllable, and the necessary and sufficient condition for this is that the rank (rank) of the matrix [B, AB, A2 B, 13B] called the controllable matrix is Equation 0 (1
0) and (11) satisfy this necessary and sufficient condition and are controllable. The system expressed by equations (10) and (11) is converted into a system to which state feedback control is added as follows. However, K is a vector called state feedback gain, and C is a scalar. By substituting equation (15) into equations (10) and (11), the following state equation and output equation are obtained. +cB-V(t) ・ ・ ・ (16) Y (t) ■C-X (t) ・ ・ ・ ・ (17) When the equation of state (16) is Laplace transformed, it becomes as follows. X (s) = (s I -A-BK) cB-V
(s)... (18) Substituting equation (1 day) into output equation (17) yields the following. Y (s) -C(s I -A-BK) cB-V
(s)... (19) Therefore, the characteristic polynomial of the matrix (τ + BK> matches the characteristic polynomial, and the eigenvalue of the matrix (A + B K) corresponds to the pole. The characteristic polynomial of equation (19)' is arbitrary. The necessary and sufficient condition for matching the Monik polynomial given by , that is, for arbitrarily setting the eigenvalues of the matrix (τ0BK), is shown in equation (16).
It is well known in control theory that (17) is controllable. Thereby, by appropriately setting the state feedback gain K, the pole can be placed at an appropriate position on the left half of the complex plane, and the system can be stabilized. The state equation (16) representing the controllable system in FIG. N) Desired four different symmetrical poles 5t (i=1.2
, 3.4). (2) When all poles St are real numbers, select a real number gi and calculate the following equation. ft ” (Si −1 − 1 in 1) Bgl 3〉When all the poles Si are complex numbers α+βj (j is an imaginary number), let S i+1 be the conjugate plate αl−βij of St, and the real number g
t, g i+l are selected appropriately and the following formula is calculated. fi=((αl I −A) Bgl+βlBg++
11+((αII-τ)2+β12 units) ÷((αII-τ)2+β12 units) With this calculation, the feedback gain is as follows. ” [gl l g2, g3+g4 ko [
f 1+ f 2+ f 3+ f 4
]... (21)

[3] A special case of the dynamic model of FIG. 3, ie, a coaxial two-wheeled vehicle with the attitude control arm 6 removed, is shown in FIG. 4, and its dynamic model is shown in FIG. The Lagrange equation of motion of the dynamic model in Figure 5 is expressed by Equation (5), (
6) and (7) can be obtained as follows. +fl θ1=0... (22) C1° cos θ! θ1+C3θ3 +D3 ・sin gl θ12+f3 θ3=T3
... (23) The following approximations are made to equations (8) and (9). sin θ1#θ1 cosθ1 #1sin gl
θ1250 Using this approximation, equations (22), (23)
is linearized as follows. ... (24) θ3 ”A21θ1+ A 23θl+ A 24θ
3+B21Ta・・・・(25) However, A11−EI C3/Δ Ata−−ft
Ca/ΔA14=f3 Ct/ΔA21=EI
C1/ΔA23- f I Ct/ΔA24
= -f a Al/ΔBtt=-C1/Δ
B21=AI/ΔEl=+'lJ g 11C1
=m1 11 rC3= (m1+m3)r2 +J
3 Al = J1Δ = A, C3-C32 xl-θ1.8□ = θ3, x3 = δ1, X4 = δ3
The following vector and matrix representations are performed as . u-T3 Using the above vector and matrix representations, the following state equation and output equation are obtained. ... (26) ... (27) Formula (21) calculated and set according to 1) to 3) above
Formula (26) using feedback gain K expressed as
, (27) are shown in FIGS. 6(a) and 6(b), and the numerical differential method described later is used in this simulation. A curve C1 in FIG. 6(a) shows a change in the lateral inclination angle θ1 of the vehicle body portion 17, a curve C2 shows a change in the rotation angle θ3 of the wheel portion 19, and a curve C3 in FIG. The curve C4 shows the change in the inclination angular velocity b1, and the curve C4 shows the change in the rotational speed b3 of the wheel portion 19. The parameters and conditions at this time are set as follows. mt-2,79kg l =0.318mm2
”Okg j!1 = 0.19 mm3
=0.36kg 12 =OmJl-0,122
37kgm J2 = Okgm J3 = 5.00xlQkgm fz = 6.86X1ONms f2=Q Nm5 f3 = 4.40X1ONms Si = (-5±4j, -6±5j) (i-1, 2, 3, 4) K-[ 4,88,1,31,5,37,6,00]X
(0)-[0,0,π/10.01 Note that X (0)
−[0, O, π/10.0] represents the initial condition, a disturbance of π/10 (rad/s) is applied to the vehicle body 17, and the simulation time interval Δt is 5 as has been adopted. Figure 6 (a), (b)
The simulation results shown in FIG. 4 show that the vehicle body 17 can be returned to the equilibrium position (θ1-0) shown by the chain line in FIG. 4, and that this equilibrium state can be maintained thereafter. It has also been found that in this equilibrium control, the further the pole is placed to the left of the left half of the complex plane, the thicker the control input becomes, but the faster the control system stabilizes.

[4] In the dynamic model expressed by equations (22) and (23), remove the attitude control arm 6, assume that the wheel 1 is almost stationary, ignore the motion related to the wheel 1, and calculate sinθl! The equation of motion when approximating =Iθ1 is as follows. A1θ1+f1θ1+E1 ・sinθ1=Jt θ
1+f1θ1−m1g1θ1=0 (59) Feedback control of u (t) =T3 is applied to the system expressed by equation (59). Jl θ1+f1 θt−mtgj! θs −u
(t) - 1ξ θ1 (t) . . . (60) However, this is a constant determined by the torque coefficient of the wheel drive motor 7, the reduction ratio of the drive system, etc. Detection of lateral inclination angle θ1, calculation time in control computer 16, command input to wheel drive motor 7, reduction gear train 8
The overall control delay time consisting of transmission delay etc. at Δ
Considering T, equation (60)%Formula % Snow - ξ is θ1 (t-ΔT)... (61) θl (t-ΔT) is expanded by Taylor and minute quantities of second order or higher are ignored. Then it becomes as follows. θ1 (−ΔT) #θ1(t)−ΔTθ1(t) Accordingly, equation (61) becomes as follows. + (Kξ−mtgl) θ1=0 (62) The characteristic equation obtained by Laplace transform of equation (62) is as follows. Jl s2+ (fl-1(ξΔT) s+ (K
ξ−ml gl)=0 (63) The stability condition of the control system expressed by equation (63) is the well-known Reuth-Hur in control theory.
Based on the stability conditions of ml gl/ξ<K<ξΔT (64) According to equation (64), it can be seen that the lower limit of the feedback gain is constant, but the upper limit changes depending on the delay time ΔT. That is, if the delay time ΔT is small, the selection range for the feed bank gain is expanded, and the degree of freedom in selecting an appropriate feedback gain is increased. The computer simulation results performed on equation (62) using the feedback gain K selected from equation (64) show attitude stability control that is almost the same as the stable attitude control in the linear control system in [3], For example, Δ
Postural stability is extremely good when T = 3 ms and T = 10°0. Note that it has been made clear from the experimental results of the control system expressed by equation (62) that the same inconvenience does not occur even if the sampling time Δt is adopted as the delay time ΔT.

[5] The feedback control described so far is based on the pole placement method, but feedback control based on the optimal control method will be explained next. The control system in FIG. 3 is expressed by equation (10). □ → X (mu)=A-X (t)+B-u (t)...
- (10) Determine control human power u (t) so as to minimize the following evaluation function J (u) for equation (10). +u (t) RU (t) ) d t... (2
8) However, i is a 4×4 and R is a 1×1 fixed symmetric matrix. Minimizing J (u) means bringing the initial state as close to a stable state as possible with as little control energy as possible. The optimal human power UO(t
) is the following Ri c cat i equation (
29), formula (30) is obtained. It is obtained as (31). T, -1-+-- A P+PA-PBRBP+Q 0... (29) uo(t)=-X (t)... (31)
Therefore, by determining K, the optimal human power uO(t) can be generated in the form of state feedback. The feedback gain of the state equation (16) representing the controllable system in FIG. 3 is determined as follows. <1> Select diagonal matrices Q and R appropriately. (2) Select K when i-0 so that A+BK becomes stable (for simplicity, use K calculated by the above-mentioned pole placement method). (3) As τl −A+BKl, the following Ryapunov (L
Find a 4×4 positive semi-definite symmetric matrix solution of equation (32). ... (32) -1-*T- (4) Ki+1 =-RB Pl, i-i
Return to (3) as +1. It will be done. The present invention shows that how to take the weights Q and H in the evaluation function formula (28) has a strong influence on the control performance of the control system, and the smaller R is compared to 100, the more quickly the control system can be stabilized. It has been discovered by the person. Furthermore, in the dynamic model shown in Fig. 3, the stability of the vehicle body part 17 is more important than the stability of the arm part 18, so a hundred choices are possible, such as giving greater weight to the diagonal element of i corresponding to xl than others. It is. In this sense, it can be said that the optimal control method is superior to the pole placement method. The simulation results based on this optimal control method are the same as the simulation results using the pole placement method described above.
This shows that it is possible to restore this state of equilibrium and maintain this equilibrium state thereafter.

[6] Next, the design of the nonlinear control system of the dynamic model shown in FIG. 3 will be explained. When designing the linear control system, it was assumed that the dynamic model shown in FIG. 3 would be controlled so that θ1 and θ2 would not become too large, but when designing the nonlinear control system, the following assumptions were made. (2) The lateral inclination angle θ1 of the vehicle body portion 17 is always controlled so as not to become too large. (2) The rotational acceleration θ3 of the wheel portion 19 is very small. (2) When the lateral inclination angle θ1 of the vehicle body portion 17 is large, its angular velocity θ1 is small. (2) When the lateral inclination angle θ2 of the arm portion 18 is large, its angular velocity θ2 is small. ■When the angular velocity bl of the vehicle body part 17 is large, the lateral inclination angle θ1
is small. ■When the angular velocity b2 of the arm portion 18 is large, the lateral inclination angle θ
2 is small. Equation (5) expressing the dynamic model in Figure 3 based on the assumptions of ■～■
, (6) and (7) are slightly simplified as follows. B1 °cos θ2 θ1+B2 θ2+E2 l
5in θ2+r2 θ2=T2 (34) (35) Rewrite equations (33) and (34) as follows.・・・ (36) However, ・ ・ ・ (37) T2°=T2−B2 ・sinθ2−f2#2・ ・
(38) Furthermore, perform vector and matrix display as follows. As a result, equation (34) is rewritten into the following state equation (39). θ(t)=A・θ(t)+B-72' (t)・
... (39) Since τ in equation (39) is a time-varying (time-varying) coefficient, the poles change over time and at least one pole is on the right half of the complex plane, and the equation ( The system represented by 39) is known to be very unstable. In order to stabilize the system by fixing the time-varying pole in such an unstable system at a desired position on the left half of the complex plane, the formula (
The following feedback control is performed on the system represented by 39). T2 “−[kll k2+ ka+ k+ ] [
θ1. θ2. θ3. θ4]− to θ (40) As a result, equation (39) becomes as follows. The characteristic polynomial of equation (41), that is, the characteristic polynomial of (A+BK), is as follows. D (λ) = det(λI-(A+BK)1 = 1λI-A-BKI =λ' + (a f 1-b k2-c k4)
λ3+ (aEl-bJ-ck3-[1k4/Δ)λ
2-(ft k3+E1 k4)λ/Δ-Etka
/Δ・・・・(42) However, Δ=ac−b2. Since it is assumed that all the rods of the system expressed by equation (4) are fixed, the coefficients of equation (42) must be time-invariant (time-invariant), and A, B Since is a time-varying coefficient, K is also necessarily time-varying. In order to obtain this time-varying K (hereinafter referred to as KL), we will select one desirable stable linear time-invariant model expressed by the following equation (43). X(t)=A' −X (t) ・−・ (43)
The control system expressed by equation (41) should always match equation (43), that is, the poles of the system expressed by equation (41) should be made to match equation (43).
), it is possible to stabilize the control system expressed by equation (41).
43) is expressed as follows. -α1 +βij (α>O, t-1, 2, 3, 4) This characteristic polynomial is expressed as follows. D(λ)-1λI-A'1 = λ4+d 3 λ8+d2 λ2+d 1
λ + d. ... (44) If we always make the coefficients of the characteristic polynomial (42) in equation (41) match the coefficients of the characteristic polynomial in equation (43), then Kt
1 for each element. 2. 3. 4 becomes as follows. kr -11b ・(aEl-d2+fl dx/Ex
-CΔdo/El-f 12dO/E12)... (
45) k2 = l/b ・(a f 1-d3+cΔdl/E
l+rl cΔd o/E x2) ... (46) k3 = -Δd o/Et ... (47) k4-(Δ/Er) ・(ft do/Et-dt)
... (48) Through these operations, the pole of equation (39) representing the time-varying system is always the pole of the stable linear time-invariant model (41) (-αl+β
lj), and the feedback coefficient Kt of the time-varying system (39) becomes a time variable at each sampling time according to equations (45) to (48). That is, this feedback is a type of adaptive control, which is model matching for time-varying system parameters. The control human power T2 of the arm portion 18 can be obtained from equation (38) as follows. T2 =72' +E2 -5in θ2+f2θ
2-KLθ+E2 ・sin θ2+f2θ2...
(49) The control human force T3 of the wheel portion 19 is obtained from the force 1 of equation (35) as follows. By substituting equations (37) and (40), we get...
50) To move the wheels 2.3 at a constant speed, it is sufficient to apply a control input that causes the angular velocity b3 of the wheels 2.3 to approach the target angular velocity δ3°. Therefore, the control input for the wheel section 19 is as follows. Sampling state quantity θ1 at each time. θ2. The time-varying feedback gain Kt was calculated from θ3, and the computer simulation results performed for equation (39) using this calculated value are shown in FIGS. 7(a), (b), and (C). . Curve C5 in Fig. 7 (a), (b), (c),
C17 and C9 indicate the change in the lateral inclination angle θ1 of the vehicle body part 19, and curves C6 and C8° CIO indicate the lateral inclination angle θ1 of the arm part 18.
2 shows the transition. The parameters and conditions at this time are set as follows. ml = 2.79kg j! =0.318m
m2=1.40kg ls=0.17mm
a = 0.36 kg 12 = 0.20 mJ
l=0.108 kgm J2 ”7. OIXlokgm J3 ”5. OOXlokgm r =4. 5 xto・m fl=6.0XIONm5 f2=4.40xlONms fa=4.40xlONms Kt=[4,8B, 1,31.5.37.6.0
0 1X (0) = [0, π/10.0.01
X (0) = [0, π/10. O and OF represent initial conditions, and π/10(r a d /
A disturbance of s ) is given, and 10+ms is adopted as the simulation time interval Δt. The pole Si in Fig. 7(a) is 5t-(-3±4j, -4±5
3) (i = 1. 2. 3. 4) The pole St in Fig. 7(b) is Si rich (-5±4j, -6±53) The pole Si in Fig. 7(c) is 5t-(- 7±43.-8±53). The simulation results shown in FIGS. 7(a), (b), and (c) indicate that the vehicle body 17 can be returned to the equilibrium position (θ1-〇) shown by the chain line in FIG. 2, and that this equilibrium state can be maintained thereafter. It shows. It has also been found that in this equilibrium control, the further the pole is placed to the left of the left half of the complex plane, the greater the control input becomes, but the control system stabilizes more quickly. that's all

[2]～

The computer simulation results for the control system design in [6] all show the control effectiveness of the dynamic models shown in Figures 3 and 5, and the coaxial two-wheeled vehicle shown in Figure 2 was constructed based on this theoretical basis. There is. The block circuit diagram of the control system in this coaxial two-wheeled vehicle is the first one.
0, and the control computer 16 has an 11th
A control program shown in a flowchart in FIG. 11(a), FIG. 11(b), or FIG. 11(C) is incorporated. The control programs shown in FIGS. 11(a) and 11(b) correspond to a linear control system, and the control program shown in FIG. 11(C) corresponds to a nonlinear control system. In the linear control program shown in FIG. 11(a), the control computer 16 initializes each control circuit such as the count circuit, output interface circuit, and data latch circuit shown in FIG.
The control computer 16 takes in the detection signal outputted from the sampling value θ via the counting circuit.
The control torque T3 is calculated using equation (60) consisting of 1 and the feedback gain K inputted in advance, and the calculated control torque T3 is sent to the drive unit via the data launch circuit and D/A converter shown in FIG. Output to. The data launch circuit has a function of holding output data from the control computer 16 until the next sampling point. In the linear control program shown in FIG. 11(b), the control computer 16 initializes each control circuit such as the count circuit, output interface circuit, and data latch circuit shown in FIG. The detection signal output from the encoder 11.14゜15 is taken in through a counting circuit, and a predetermined set of n (θl. θ2.θa) (11 (i= 1.2...n) is Differential value of the n-th sampling value (θ1.θ2.θ3) (n), hitting angular velocity (δ1, 112.8 a) (nl
Calculate by numerical differentiation. Then, the control computer 16 controls the sampling value (θ1
．． θ2. θ3)(n), calculated value (θ1.θ2.θa)(
The control torque T2. Ta is calculated, and this calculated control torque T2. T3 is outputted to the drive unit via the data launch circuit and D/A converter shown in FIG. In the nonlinear control program shown in FIG. 11(c), the control computer 16 performs calculation of angular velocity by numerical differentiation in the same manner as in the linear control program, and then calculates the time-varying feedback gain Kt. Then, the control computer 16 controls the sampling angle (θ
1, θ2. θa) (n), calculated angular velocity ("l+'j2+
”3(n) and pre-calculated time-varying feedback gain Kt
The control torques T2, T
a is calculated, and the calculated control torque T2°Ta is output to the drive unit via the data latch circuit and D/A converter shown in FIG. The numerical differentiation method performed in the linear control program and the nonlinear control program will be described below. Sampling time Δt1, that is (θ1.θ2.θa) (
1) Intake time and (θ1, θ2.θa) +t rn
If the interval with the capture time is sufficiently small, the angle 7i (
i=1.2.3) can be approximated by a second-order polynomial as follows. Tt (t) #a+bt+ct2・ ・ ・ (
52) By differentiating equation (52), the angular velocity i
(B is calculated. Ti (t) = b + 2ct... (53) n sampling time points (5 (fixed) in this example) tl = -
2Δt t2−−Δt t3=Qt4=Δt
Observation angles θ1(1), δ1(2), δ1(
31, δ1(4). The sum of squares ε of the difference between δ1(5) and Ti in equation (52) is expressed as follows. ε−(Tl (1)−θi (1))+(Ti (2)
-θ1f2))+(Ti (3)-θi f31)+(
Ti (4)-θi (4))+(7-i (5)-θ
i (5)) = (θ1(11(a+2bΔ, t + 4 cΔt2
))2+(θ1(2)-(a+bΔt+cΔt2))2
+ (θ1(3)-a)2 + (θ1(4) (a+bΔt+cΔt2))2
+ (θ1(5)-(a+2bΔt+4cΔt2))2
The coefficient a of equation (52) is set so as to minimize this ε. b and c are determined as follows. a = (1/70) ・(-6θi (1)+24
θ1(2)+34 θi(3)+24 θ1(41-
60(5))b = (1/10Δt)・(-2θi
(1)-θ1(2)÷θ1(41+2θ1(5)) c = (1/14Δt2) ・(2θi 11)-
θ1(2)-2θ1(3)-θ1(4)-2θi (5
1) By substituting a, b, and c determined in this way into equation (53), the angular velocity θt (nl(n
=1.2.3.4.5) can be obtained. For example, the angular velocity at sampling time t is expressed as follows. θi (5) = b + 2 c・2Δt-(1/1
0 Δt)・(26θi (1)−27θ1(2)−4
0θi (31-13θi (4)+54 θ
i (5) )... (54) That is, the past five sampling angles θi 11) ~ θ
1(5), the angular velocity θi at the sampling time t is calculated while smoothing the angle θi at the sampling time t, and by this smoothing, the calculated angular velocity accurately matches the actual angular velocity. The size of the sampling time interval Δt affects the stable control of the control system, and the smaller the interval Δt, the better; however, the calculation speed of the control computer 16 performed between one sampling point and the next sampling point may Left and right. Therefore, equations (45) to (48) for calculating each element of the time-varying feedback gain Kt in the nonlinear system are rewritten as follows. kl ”(1/b) ・(aEl−a2+rl d
l/El-CΔdo/El-f I"do/E1" (
1/ b) ・(aEl-d2-fl k4/Δ-c
k3)... (55) k2=(1/b) (a fl-d3+cAd1
/El+rl cΔdo/E12) = (1/ b) ・(a fl-d3-c ka )
... (56) k3 = -Δd o/ E 1 ... (57) k4 = (Δ/Es)・(ft do/E1-dt)
=-(1/Et)・(d1Δ+fxka)... (5
8) Formulas (55) to (58) instead of formulas (45) to (48)
By using , it is possible to significantly shorten the calculation time of the time-varying feedback gain Kt. The state feedback gain obtained for the system parameter values, initial disturbance, and various set 5i = (-3 ± j, -4 ± 23) similar to the linear control simulation for the dynamic model shown in Figure 5. −[4,8B, 1
．． 31.5.37.6.00 Based on 1, the feedback control results for the coaxial two-wheeled vehicle shown in Fig. 4 are shown in Fig. 8 (a).
), (b), (c). Figure 8 (
The curve C1l in a) represents the change in the lateral inclination angle θ1 of the vehicle body portion 17;
A curve C12 indicates a change in the rotation angle θ3 of the wheel portion 19.
A curve C13 in FIG. 8(b) shows the change in the angular velocity δ1 of the vehicle body 17, and a curve C14 in FIG. 8(c) shows the change in the control torque T.
The results in Figures 8(a)-(c) showing the transition of wheel 2
．． The vehicle body 1 exhibits robust stability due to the movement of 3, and even in the face of quite large disturbances, the vehicle body 1 returns to the equilibrium position shown by the chain line in Figure 4.
7's reinstatement will take place immediately. Figure 9 (a) shows the feedback control results when the coaxial two-wheeled vehicle in Figure 2, which has the same system parameter values as the nonlinear control simulation target for the dynamic model in Figure 3, travels to the target value θ3 w3rad. ), (b). Curve C15 in FIG. 9(a) indicates the vehicle body portion 17.
The curve C16 in FIGS. 9(a) and (b) shows the change in the rotation angle θ3 of the wheel portion 19, and the curve C16 in FIGS.
The curve C17 in b) shows the change in the angular velocity θ1 of the vehicle body portion 17. According to FIGS. 9(a) and 9(b), initially the vehicle body part 17
is slightly oscillating, the control based on the movement of the wheels 2.3 acts in a direction that prioritizes the stability of the attitude of the vehicle body 17, and performs small control operations. For a while after the wheel 2.3 starts moving, the arm part 18 also swings little by little in almost the same phase as the car body part 17, and the swings of the car body part 17 and the arm part 18 synchronize around 7 seconds. , the arm portion 18 swings significantly. At this point, the wheels 2.3 rapidly approach the target position, but the stability of the vehicle body 17 due to this acceleration suppresses the swinging of the arm 18. At around 9 seconds, the wheels 2.degree. 3 begin to decelerate, and the instability of the vehicle body 17 due to this deceleration is compensated for by the moderate rocking of the arm 18. The coaxial two-wheeled vehicle stopped slightly before the target position θ3 = 3 rad, but this seems to be caused by solid friction in the wheel drive system. The control results when the target position is set to θ3-0 are shown in Figure 9 (a
) and (b), the situation was exactly the same as after the coaxial two-wheeled vehicle stopped. The rocking of the vehicle body 17 in the stationary state of the coaxial two-wheeled vehicle is
Comparing FIG. 9(a) and FIG. 9(a), wheel portion 1
9 and the arm portion 18 at the same time, the attitude control method that simultaneously drives the vehicle body portion 17
In this sense, the coaxial two-wheeled vehicle with the attitude control arm 6 shown in FIG. 2 has better attitude control than the coaxial two-wheeled vehicle without the attitude control arm 6 shown in FIG. 4. is judged. Incidentally, the inventor of the present application conducted an attitude control experiment using only the attitude control arm 6, but found that the vehicle body 17 could not be stably maintained at an equilibrium position in either the linear control system or the non-linear control system. . This is due to the occurrence of control delays due to non-linear factors such as the dead zone of the attitude control arm drive motor 9 or the backlash of the gear transmission system, as well as the lateral inclination angle of the vehicle body and the lateral inclination angle of the attitude control arm 6 used for feedback control. This seems to be caused exclusively by the noise present in the calculation of angular velocity based on the short-time sampling of the state quantity, which explains the difficulty in applicability of the conventional attitude control method using only the attitude control arm 6. The present invention is, of course, not limited to the above-mentioned embodiments. For example, a coaxial two-wheeled vehicle can be provided with a steering function by connecting a pair of wheels 2 and 3 and a wheel drive motor 7 via a differential gear mechanism. Alternatively, it is also possible to drive the pair of wheels 2.3 independently of each other to provide a steering function. (Effects of the Invention) As detailed above, according to the first invention of the present application, the lateral inclination angle detected by the angle detection means for detecting the inclination of the vehicle body is sampled at short intervals, and the sampling lateral inclination of the vehicle body is Calculate the sampling value by substituting the angle and feedback gain into a control input calculation formula input and set in advance in the control computer as coefficients, calculate the control torque of the wheel drive motor based on this calculation, and calculate the control torque of the wheel drive motor. Since the control computer commands the wheel drive motor to perform an operation corresponding to the calculated control torque to control the attitude of the coaxial two-wheeled vehicle, feedback control of the wheel drive motor is performed based on the calculation result, and the vehicle body When the vehicle tilts, the wheels immediately move in the direction in which the vehicle body is tilted, ensuring that the vehicle body is restored to its original position. According to the second invention of the present application, the lateral inclination angle detected by the first angle detection means for detecting the inclination of the vehicle body and the rotation angle detected by the second angle detection means for detecting the rotation angle of the wheels are shortened. Control inputs that are sampled at time intervals and input into the control computer in advance using the sampled lateral inclination angle of the vehicle body, the sampled rotation angle of the wheels, and the angular velocity calculated based on these sampled angles as state variables and the feedback gain as a coefficient. Substituting the sampling value into a calculation formula, calculating the control torque of the wheel drive motor based on this calculation, and instructing the wheel drive motor to perform an operation corresponding to the calculated control torque from the control computer. Since the posture of the coaxial two-wheeled vehicle is controlled by using the same axis, feedback control of the wheel drive motor is performed based on the above calculation result, and when the vehicle body tilts, the wheels immediately move in the direction of the tilting direction of the vehicle body, thereby restoring the vehicle body. will be carried out reliably. Furthermore, in the third invention of the present application, the lateral inclination angle of the vehicle body detected by the first angle detection means, the rotation angle of the wheel detected by the second angle detection means, and the coaxial two-wheeled vehicle of the first invention The lateral inclination angle detected by the third angle detection means for detecting the inclination of the attitude control arm added to the body is sampled at short intervals, and the sampled lateral inclination angle of the vehicle body, the sampled rotation angle of the wheel, and the attitude control arm are sampled at short intervals. calculation by substituting the sampling value into a control input calculation formula input and set in advance in the control computer with the sampling transverse angle and the angular velocity calculated based on these sampling angles as state variables and the feedback gain as a coefficient, Based on this calculation, the wheel drive motor and attitude control arm are driven. In addition to calculating the control torque of the drive motor, the control combinator controls the attitude of the coaxial two-wheeled vehicle by instructing the wheel drive motor and the attitude control arm drive motor to perform operations corresponding to these calculated control torques. ,
Feedback control of the wheel drive motor and the attitude control arm drive motor is performed based on the above calculation results, and when the vehicle body tilts, the wheels move in the direction of the tilt of the vehicle body, and the control arm moves in the direction of the tilt of the vehicle body. It rotates to the opposite side to ensure that the vehicle body is restored. In the third aspect of the invention, the stability of maintaining the vehicle body in the equilibrium position is even better than that of the first aspect of the invention due to the attitude control action of the attitude control arm.

[Brief explanation of the drawing]

FIG. 1 is a perspective view showing an embodiment embodying the third invention, FIG. 2 is a side view thereof, FIG. 3 is a side view showing a mechanical model that is a simplified version of FIG. 2, and FIG. 1.2 is a side view showing an embodiment embodying the invention, FIG. 5 is a side view showing a mechanical model that is a simplified version of FIG. 4, and FIGS. 6(a) and (b)
) shows the computer simulation results of the dynamic model of FIG. 5, and FIG.
1 and a graph showing changes in the rotation angle θ3 of the wheel portion 19,
FIG. 6(b) is a graph showing changes in the angular velocity θ of the vehicle body portion 17 and the rotational angular velocity θ3 of the wheel portion 19, FIG. 7(a),
(b), (C) show the computer simulation results of the mechanical model of Fig. 3, and Fig. 7(a) is based on the selected poles 5i-(-3±4j. -4±5j). A graph showing changes in the lateral inclination angles θ1 and θ2 of the vehicle body part 17 and the arm part 18, FIG. 7(b) shows the lateral inclination angle θ1 based on the selected pole 5i=(-5±4j, -6±5j) ．． Graph showing changes in θ2, Figure 7 (c
) are graphs showing changes in the lateral oblique angle θ1° θ2 based on the selected pole 5t-(-7±4j, -8±5j), FIGS. 8(a) and 8(b). (c) shows the linear control results for the coaxial two-wheeled vehicle shown in FIG. 4, and FIG. b
) is a graph showing changes in the rotational angular velocity θ3 of the wheel portion 19,
FIG. 8(c) is a graph showing the change in control torque T3, FIGS. 9(a) and (b) show the nonlinear control results for the coaxial two-wheeled vehicle of FIG. 1.2, and FIG. 9(a) is A graph showing changes in the lateral inclination angle θ1 of the vehicle body part 17 and the rotation angle θ3 of the wheel part 19, FIG. 9(b) shows the change in the rotation angle θ3 and the arm part 18.
A graph showing changes in the lateral inclination angle θ2 of 1.
The control block diagram of the coaxial two-wheeled vehicle shown in Fig. 2, and Fig. 11 (
a) is a flowchart showing a linear control program, the first
FIG. 1(b) is a flowchart showing another linear control program, and FIG. 11(C) is a flowchart showing a nonlinear control program. Axle 1, wheels 2.3, vehicle body 4, attitude control arm 6, weight 6a, wheel drive motor 7, attitude control arm drive motor 9, rotary encoder 11 as first angle detection means, second angle Rotary encoder 14 as a detection means, rotary encoder 15 as a third angle detection means, control computer 16, vehicle body part 17, arm part 1
8. Wheel portion 19, angle θ1. θ2. θ3, angular velocity "1.
"2+93, control torque T2, T3, feedback gain K. K, Kt. Patent applicant CKD Co., Ltd. Yamafuji f Pretext

Claims (1)

[Claims] 1. A pair of wheels (2, 3), an axle (1) installed between both wheels (2, 3), and a vehicle body (1) rotatably supported on the axle (1). 4), a wheel drive motor (7) mounted on the vehicle body (4), a control computer (16) that sends operating commands to the wheel drive motor (7), and an angle for detecting the inclination of the vehicle body (4). In a coaxial two-wheeled vehicle consisting of a detection means (11), the inclination angle (θ_1) of the vehicle body (4) detected by the angle detection means (11) is determined at short intervals (Δt).
The sampling inclination angle (θ_1) of the vehicle body (4) is used as a state variable, and the feedback gain (K)
is calculated by substituting the sampling value (θ_1) into the control input calculation formula (60) input and set in advance in the control computer (16) as a coefficient, and based on this calculation, the wheel drive motor (7) A posture control method for a coaxial two-wheeled vehicle, in which a control torque (T_3) of a coaxial two-wheeled vehicle is calculated, and a control computer (16) instructs the wheel drive motor (7) to perform an operation corresponding to the calculated control torque (T_3). 2 A pair of wheels (2, 3), an axle (1) installed between both wheels (2, 3), a vehicle body (4) rotatably supported on the axle (1), and a vehicle body ( 4), a control computer (16) that sends an operation command to the wheel drive motor (7), and a first angle detection means (1) that detects the inclination of the vehicle body (4). 11) and wheels (2,
3) second angle detection means (14) for detecting the rotation angle of
In a coaxial two-wheeled vehicle consisting of
_1) and the rotation angle (θ_3) of the wheels (2, 3) detected by the second angle detection means (14) are sampled at short intervals (Δt), and the sampling inclination angle ( θ_1), the sampling rotation angle (θ_3) of the wheels (2, 3), and these sampling angles (θ
Angular velocity (■_1, θ_3) calculated based on
■_3) is the state variable, feedback gain (■, ■t
) is used as a coefficient to input the control input calculation formula (20, 49, 51) into the control computer (16) in advance.
), the control torque (T_3) of the wheel drive motor (7) is calculated based on this calculation, and the operation corresponding to the calculated control torque (T_3) is controlled from the control computer (16). A posture control method in a coaxial two-wheeled vehicle that commands the wheel drive motor (7). 3 A pair of wheels (2, 3), an axle (1) installed between both wheels (2, 3), a vehicle body (4) rotatably supported on the axle (1), and a vehicle body ( An attitude control arm (6) tiltably supported by the vehicle body (4), a wheel drive motor (7) attached to the vehicle body (4), and an attitude control arm drive motor (7) also attached to the vehicle body (4). 9), a control computer (16) that sends operating commands to the wheel drive motor (7) and the attitude control arm drive motor (9), and the vehicle body (4).
a first angle detection means (11) for detecting the inclination of the wheels; and a second angle detection means (11) for detecting the rotation angle of the wheels (2, 3).
14) and a third arm that detects the tilt of the attitude control arm (6).
In the coaxial two-wheeled vehicle, the inclination angle (θ_1) of the vehicle body (4) detected by the first angle detection means (11) is determined by the second angle detection means (14). Rotation angle (θ_3) of the wheels (2, 3) detected and tilt angle (θ_2) of the attitude control arm (6) detected by the third angle detection means (15)
The vehicle body (4) is sampled at short intervals (Δt).
sampling inclination angle (θ_1) of wheels (2, 3), sampling rotation angle (θ_3) of wheels (2, 3), attitude control arm (6
) and the angular velocity (■_1, ■_3, ■_2) calculated based on these sampling angles (θ_1, θ_3, θ_2) are state variables, and the feedback gains (■, ■t) are coefficients. The sampling values (θ_1, θ_3, θ_2, ■_1, ■_3, ■_2
), and based on this calculation, the wheel drive motor (7) and the attitude control arm drive motor (9) are calculated.
The control torques (T_3, T_2) of the wheel drive motor (7) are calculated from the control computer (16) and the operation corresponding to these calculated control torques (T_3, T_2) is controlled by the control computer (16).
and a posture control method in a coaxial two-wheeled vehicle that commands a posture control arm drive motor (9).