JP7553413B2 - Autonomous driving method - Google Patents

Description

The present invention relates to an autonomous driving method that detects changes in the vehicle's state variables, i.e., total vehicle weight (weight), gradient, center of gravity position, and tire cornering coefficient (tire load), in real time in response to changes in passengers and luggage, and controls the vehicle while updating the state variables of a control model that correspond to those changes.

The motion of a vehicle is governed by Newton's second law. In other words, it is governed by the relationship between force, mass, and acceleration, or torque, moment of inertia, and rotational acceleration. It is governed by the relationship between action and reaction, that is, the relationship between the "actions of the vehicle to run, turn, and stop" and the "reactions from the road surface."

Self-driving vehicles are controlled by controlling the relationship between action and reaction. PID control, which is tuned by control engineers using their experience while observing the control response, is the most widely used method.

The control of autonomous vehicles involves changes in state quantities such as mass, center of gravity, and tire load due to changes in passengers, luggage, etc. These changes occur suddenly when passengers get on and off at stations and bus stops, and when luggage is loaded and unloaded at logistics terminals, so there is no time to tune the PID control.

Tuning is the process of correcting the deviation from the target based on given characteristics. There are limitations to tuning a control object whose state quantities change. Rather than tuning without using a model, or using a fixed specification model, it is necessary to use a control model (mathematical model) described in state quantities and adapt to the changes by rewriting (replacing) the state quantities of the model according to the changes in the state quantities.

In Chapter 9, State Feedback Control and Observers, Non-Patent Document 1 states that state feedback control is possible on the premise that all states of the controlled object can be observed, but that it is rare that all states of an actual controlled object can be observed, and in such cases, it is necessary to estimate the state using an observer, but there is no actual description of this.

Non-Patent Document 2 reports a method for modeling the longitudinal motion of large trucks, but does not mention estimating state quantities such as changes in vehicle weight.

Non-patent document 3 introduces a method for estimating changes in the load and center of gravity by detecting the natural frequencies of bouncing and pitching of a truck, but this method lacks versatility because it depends on the specifications of the suspension system.

Patent document 1 shows a calculation diagram of the accelerator opening, vehicle weight, and generated acceleration, but does not include the effect of road gradient. In addition, it is limited to the state quantity of power performance.

Patent document 2 shows a formula for calculating the change in the center of gravity position derived from the vehicle motion equation, and shows a method for calculating the change in the center of gravity position from the vehicle speed, yaw rate, and sideslip angle detected by GPS, but it is related to two-axle vehicles and does not mention multi-axle vehicles with three or four axles, and does not show a method for estimating the change in the vehicle's own weight, which is the cause of the change in the center of gravity position.

Patent document 3 shows a method for detecting the center of gravity of a four-axle vehicle using a wheel speed sensor and a yaw angle sensor without using GPS, but does not show a method for estimating the change in the vehicle's own weight, which is the cause of the change in the center of gravity.

JP 2020-011555 A JP 2021-70377 A JP 2021-84587 A

Kenzo Nonami (ed.) and Hidekazu Nishimura (co-author); Fundamentals of Control Theory Using MATLAB (registered trademark) Fujio Momiyama et al.; “Identification and modeling of longitudinal motion of large trucks” Journal of Automotive Technology, Vol. 43, No. 2, March 2012, No. 20124209, pp. 211-216 Fujio Momiyama et al.; Loading State Estimation Using Lateral Motion Model for Autonomous Large Trucks, Transactions of the Society of Automotive Engineers of Japan, Vol. 44, No. 6, November 2013, No. 20134847, p. 1377-1382.

The above-mentioned conventional technology is unable to accurately estimate the amount of change in the parameters (state quantities) of the control model of an autonomous vehicle, which changes from moment to moment while the vehicle is traveling, and is unable to reflect the amount of change in the control model in real time to enable continuous autonomous driving.

In order to solve the above problems, the present invention provides an automatic driving method in which equations for controlling driving described by vehicle state quantities are incorporated into an on-board computer (ECU), the vehicle state quantities estimated in real time are input while being updated into the equations, and a signal for controlling driving calculated by the equations is output from the on-board computer, wherein the state quantities are the vehicle's own weight, slope gradient, center of gravity position, and tire cornering coefficient, the vehicle's own weight and slope are estimated from an equation for acceleration generated in response to accelerator input, the center of gravity position and tire cornering coefficient are estimated from GPS and wheel speed, and the center of gravity position is estimated by calculating the lateral slip angle of each wheel from GPS and wheel speed, and determining the amount of movement of the center of gravity position from an equation for determining the amount of movement of the center of gravity position to estimate the center of gravity position.

In the above, the gradient and vehicle weight are estimated using the vehicle longitudinal motion model equation, i.e., the "equation of acceleration generated by accelerator input" derived from the balance equation of engine output and running resistance. Specifically, the road gradient is estimated from the deceleration that occurs when the accelerator is released, and the vehicle weight is estimated from the acceleration that occurs when the accelerator is subsequently released.
In the present invention, a "formula for change in center of gravity position" derived from the vehicle lateral motion model formula is provided, and the previously determined weight and the "first and second front axle sideslip angles" and "first and second rear axle sideslip angles" obtained by GPS are substituted into this formula to determine the change length of the center of gravity position, and the loaded center of gravity position is determined by adding the determined "change length of the center of gravity position" to the "unloaded center of gravity position." In addition, the center of gravity position is also estimated by wheel speed sensors provided on the steered and non-steered wheels.
The tire cornering coefficient equation derived from the vehicle's lateral motion model equation is prepared, and the vehicle's own weight and center of gravity position obtained above are substituted into this equation, and the stability factor and side slip angle coefficient obtained by turning in a steady circle are substituted to estimate the implemented tire cornering coefficient. Thus, automatic driving control of longitudinal acceleration/deceleration motion and lateral motion/rotational motion in the lateral direction, adapted to the conditions at that time, is made possible.

In addition, there is a very short time lag between detecting changes in state quantities (weight, gradient, center of gravity position, and tire cornering coefficient) and substituting them into the control model equations to reflect the changes in autonomous driving. It is preferable to perform autonomous driving at a speed where this time lag does not cause any problems.

The present invention makes it possible to realize a control model required for controlling the longitudinal and lateral movements of an autonomous vehicle and state feedback control that adapts to changes in the state quantities of that model.

FIG. 2 is an explanatory diagram of a longitudinal motion model and weight estimation and gradient estimation. FIG. 13 is an explanatory diagram of a change in load on a power performance diagram expressed in terms of acceleration. FIG. 2 is an explanatory diagram of a lateral motion model and internal state quantities. FIG. 1 is an explanatory diagram of a method for estimating changes in center of gravity position by equipping a vehicle with a GPS and detecting changes in tire sideslip angle due to a loaded vehicle. FIG. 11 is an explanatory diagram of the change in axle load due to the shift in the center of gravity (Δl) associated with a change from an empty vehicle to a loaded vehicle. 5 is an explanatory diagram of an approximation of the actual front wheel steering angle and the center of gravity position estimated from the wheel speed. FIG. 4 is a graph showing a change in turning characteristic of a vehicle relative to vehicle speed; FIG. FIG. 13 is an explanatory diagram of how to set the "turning steering path" to the "planned route." FIG. 11 is an explanatory diagram of a flow of state estimation.

An embodiment of the present invention will be described with reference to FIGS.
Figure 1 shows the longitudinal motion model and the vehicle weight and gradient estimation. (A) is a simplified diagram of the drive system with the vehicle's equivalent moment of inertia around the drive shaft as Ieq. T _E is the engine torque, ω is the engine speed, imn is the gear ratio of the transmission, if is the final reduction ratio, ωw is the wheel rotation speed, v is the vehicle speed, r is the wheel rotation radius, and Rr, Rd, and R _θ are the rolling resistance, air resistance, and gradient resistance, respectively. The balance relationship between engine output and running resistance can be simply expressed by ignoring transmission efficiency and other factors, and is expressed as equation (1) in (B) in the figure.

From equation (1), we obtain equation (2) for the generated acceleration in response to accelerator input, as shown in (C) in the figure.
The left side is the vehicle acceleration α, and the first term on the right side is the acceleration generated by the engine, calculated by multiplying the engine torque T _E by the gear ratio imn and the final reduction ratio if of the transmission and dividing the result by the tire radius r, and dividing it by the vehicle mass converted into the rotational axis. The second term on the right side is the deceleration equivalent to rolling resistance αr, the air resistance deceleration αd, and the gradient resistance deceleration _αθ .

If the vehicle acceleration α on the left side of equation (2) is Y, the part in brackets on the right side is A, accelerator opening X = engine torque _TE , and the deceleration in brackets in the second term on the right side is B, then the relationship between accelerator opening (X) and vehicle acceleration (Y) is a linear equation: Y = AX - B. A corresponds to the acceleration resistance in Figure 2, which will be described later, and B corresponds to the coasting resistance (however, since this is flat ground data, gradient resistance is not included).

In other words, the acceleration generated in response to accelerator input is expressed as a linear equation Y = AX-B, and the change in the vehicle equivalent mass meq, i.e., the change in vehicle weight, can be detected from the gradient A of the line, and the gradient resistance _αθ can be detected from the Y-axis intercept B (see Figure 2).

(D) in the figure shows how to obtain acceleration and deceleration during actual driving. A vehicle speed at which the AMT does not shift gears (25km/h in this case) is selected, and the deceleration when the accelerator is released and the acceleration when an accelerator opening pulse input of, for example, 80% is input are obtained, and a graph of the generated acceleration versus accelerator opening shown in (E) in the figure is obtained.
The vehicle's weight is calculated from the ratio of the obtained A value to the empty vehicle A value (see Figure 2), and the current gradient is recognized from the difference between the B value on flat ground and the current location B value. The linear equation Y = AX-B, which connects the DCC average and the ACC average, is used to obtain X = (Y + B)/A, and the accelerator opening X for the required acceleration Y can be determined.

Figure 2 shows the load change of the power performance diagram expressed in terms of acceleration. An example of a fully automatic electronic mechanical 12-speed transmission is shown. The left side of the figure shows an example of an empty load (total vehicle weight 11.7 tons), and the right side shows an example of a 12-ton load (total vehicle weight 23.7 tons). The figure shows the acceleration generated at each gear position from 1st to 12th in the process of accelerating with the accelerator pedal at 100% to a vehicle speed of 90 km/h, and the deceleration in the process of releasing the accelerator pedal from a vehicle speed of 80 km/h to zero. The relationship between vehicle speed and acceleration is a hyperbolic relationship of xy=a, where y is the acceleration and x is the vehicle speed, and it can be seen that the hyperbolic constant a is inversely proportional to the change in the total vehicle weight (weight).
It can also be seen that deceleration is inversely proportional to the square of the vehicle speed and is not dependent on changes in the total vehicle weight (but macroscopically). a/x corresponds to A in the above Y=AX-B. That is, changes in vehicle weight can be detected from A. Also, in the figure, y= ^{-0.0003449x2-0.006} can be interpreted as 0.0003449 being the drag coefficient of air resistance, and 0.06 being the rolling resistance. That is, changes in gradient can be detected from the rolling resistance .

Figure 3 shows the lateral motion model and its internal state quantities. On the left side of the figure is a plan view of a four-axle vehicle consisting of the first front axle, the second front axle, the first rear axle, and the second rear axle, in an ISO coordinate system with the front of the vehicle as the x-axis and the left side of the vehicle as the y-axis, and on the right side is a simplified diagram in which the left and right wheels of each axle are represented as a single wheel on the x-axis. The simplified diagram is explained below.

The x and y coordinates are moving coordinates with the origin at the center of gravity of the vehicle. The equation for balance of motion in this case is as follows.

Here,
where m is the vehicle mass, I is the moment of inertia, v is the vehicle speed, r is the yaw rate, β is the vehicle side slip angle, _CF1 , _CF2 , _CF3 , _CF4 are the cornering forces of the first front axle, second front axle, first rear axle, and second rear axle, _Kf1 , _Kf2 , _Kr1 , _Kr2 are the cornering powers of the first front axle, second front axle, first rear axle, and second rear _axle , _βf1 , βf2, _βr1 , _βr2 are the tire side slip angles of the first front axle, second front axle, first rear axle, and second rear axle, Ccf, Ccr are the cornering coefficients of the first front axle and second front axle tires and the first rear axle and second rear axle tires, and _Nf1 , _Nf2 , _Nr1 , _Nr2 , are the axle loads of the first front axle, second front axle, first rear axle, and second rear axle, δ ₁ and δ ₂ are the actual steering angles of the first front axle and second front axle, and a _k is the angle ratio of δ ₁ to δ _2. Setting lf1 to zero makes it possible to apply the model to a four-axle vehicle with two front axles and two rear axles, or a three-axle vehicle with one front axle and two rear axles, setting lf1 to zero makes it possible to apply the model to a three-axle vehicle with two front axles and one rear axle, and setting lf1 and lf1 to zero makes it possible to apply the model to a two-axle vehicle with one front axle and one rear axle.

FIG. 4 illustrates a method of estimating the change in the center of gravity position by detecting the tire side slip angle change associated with a loaded vehicle using a GPS. A GPS is installed at an arbitrary position on the front-rear axis (X-axis) of the vehicle. The speed V _GPS and side slip angle β _GPS output from the GPS at that arbitrary position are recorded. Multiplying the vehicle speed V _GPS by the cosine of the side slip angle β _GPS gives Vx _GPS , and multiplying the vehicle speed V _GPS by the sine of the side slip angle β _GPS gives Vy _GPS . Vx _GPS is the front-rear speed in the front-rear direction (x-axis direction) of the vehicle body, and is equal to the wheel speed Vwheel of the non-steered wheel. Vy _GPS is the lateral speed in the lateral direction (y-axis direction) of the vehicle body at the position where the GPS is installed. From these GPS output values V _GPS , β _GPS and Vx _GPS , Vy _{GPS ,} the speeds and side slip angles at the front first axle position, front second axle position, rear first axle, and rear second axle can be calculated as shown in Equations (13) to (18).

Here, _Vf1 is the speed at the front first axle position, _Vf2 is the speed at the front second axle position, _Vr1 is the speed at the rear first axle position, _Vr2 is the speed at the rear second axle position, _βf1GPS is the side slip angle at the front first axle position, _βf2GPS is the side slip angle at the front second axle position, _βf1 is the side slip angle of the front first axle tires, _βf2 is the side slip angle of the front second axle tires, _βr1 is the side slip angle of the rear first axle tires, and _βr2 is the side slip angle of the rear second axle tires.
The side slip angle when the vehicle changes from an empty to a loaded state can also be calculated using the same formula with the suffix L. In other words, the change in tire side slip angle when the vehicle changes from an empty to loaded state means the change in cornering force generated by the tire according to formulas (5) to (8), so the changes in tire load (axle load) from an empty vehicle to a loaded vehicle, _Nf1 → N _Lf1 , _Nf2 → N _Lf2 , _Nr1 → N _Lr1 , _Nr2 → N _Lr2 , contained in these formulas, are calculated and used to calculate the change length (Δl) from the empty vehicle center of gravity position to the loaded vehicle center of gravity position, which will be described later. δ2, δ1, and ak contained in formulas (19) and (20) will be described later with reference to FIG. 6.

Using Figure 5, we will explain the change in axle load due to the shift in the center of gravity (Δl) associated with changing from an empty vehicle to a loaded vehicle, and then connect this to the explanation of the identification of the tire cornering coefficient in Figure 7. In Figure 5, the empty vehicle mass m becomes the loaded vehicle mass m _L , and the acceleration g of gravity acts on it, turning it into a load mg and a load m _L g. This is supported by being equally divided between the first and second front axles and equally divided between the first and second rear axles. The equal division on the front axles is achieved by an equalizer mechanism, and the equal division on the rear axles is achieved by connecting the air springs of the air suspension. Thus, the front axle load is expressed by equation (23), and the rear axle load is expressed by equation (24).

If the center of gravity position (lf1,lf2,lr1,lr2) of the empty vehicle mass (m) in Figure 3 mentioned above is known, and the loaded mass (m _L ) and the loaded vehicle side slip angle of each axle (β _Lf1 , β _Lf2 , β _Lr1 , β _lr2 ) are known, the loaded vehicle center of gravity position can be calculated from the lateral motion balance equation. The calculation method is as follows.
First, by substituting the formulas (5) to (8) into the above formula (3), we obtain formula (25).

When loading causes state changes such as m→ _mL , r→ _rL , β→ _βL , _βf1 → _βLf1 , and _βf2 → _βLf2 , and the center of gravity position moves back by Δl, the above equations (23), (24), and (26) are obtained.

Here, β _L in the formula is the sideslip angular velocity. Since it is zero in a steady state, the movement distance Δl of the center of gravity position can be calculated by actually measuring the yaw rate rL and tire sideslip angles (β _Lf1 , β _Lf2 , β _Lr1 , β _lr2 ) while maintaining the steady state using GPS and substituting them into formula (32).

The above-mentioned tire side slip angle and yaw rate are measured by GPS, and substituted into equation (32) for the center of gravity position movement distance developed from the lateral motion model equation to calculate and obtain the center of gravity position associated with loading, and control is continued. In addition, a method for obtaining the actual front wheel steering angle and approximate center of gravity position estimated from the wheel speed is explained with reference to Figure 6.

Each axle wheel is equipped with a wheel speed sensor for ABS, ASR or EBS. From the wheel speed obtained by this wheel speed sensor, the yaw rate can be obtained using equation (33), the longitudinal speed using equation (34), the actual steering angle of the second front axle using equation (35), the distance from the vehicle's longitudinal axle to the turning center using equation (36), the turning radius of the center of gravity using equation (37), the side slip angle of the center of gravity using equation (38), and the distance from the center between the two rear axles to the center of gravity using equation (39).

Here, vrR and vrL in equation (33) are the wheel speeds of the right and left rear wheels, Tr is the rear axle tread, _a1 is a correction coefficient as a matching adjustment term with the vehicle speed detected by GPS, _a2 in equation (34) is a correction coefficient as a matching adjustment term with the vehicle front/rear axle component of the actual ground speed detected by GPS, and _a3 in equation (35) is a correction term as a matching adjustment term with the wheel speed of the non-steered axle and the actual steering angle calculated from the wheel speed of the steering axle and its cosine, calculated from the tie rod stroke of the steering axle.

When the vehicle's weight can be estimated from the equation Y = Ax-B, which is the relationship between the accelerator opening and the generated acceleration in (E) of Figure 1, and the center of gravity position can be estimated from Δl in Figures 4 and 5, i.e., equations (32) and (39), the state quantities (values of elements) of the state equations in equations (3) and (4) above become known, except for the tire cornering coefficients (Ccf, Ccr). The estimation of Ccf and Ccr is carried out by assuming that the turning characteristics calculated from equations (3) and (4) are equal to the turning characteristics obtained from actual vehicle testing, and determining the values of Ccf and Ccr included in the calculation equations.

FIG. 7 shows the change in the turning characteristics of a vehicle with respect to the vehicle speed. A circle with a radius of _R0 is made. When the vehicle turns at a slow speed and the steering angle (steering angle) that allows the vehicle to turn at a constant radius R0 is determined, and the vehicle speed is gradually increased (Vlow→Vhigh), the turning radius changes (Rv_low→Rv_high) as shown in the figure, and the vehicle side slip angle changes ( _β0 → _βv ). This change is plotted as the square of the vehicle speed on the horizontal axis and _βv / _β0 and Rv/ _R0 on the vertical axis, and the change characteristics of the side slip angle and the turning radius are obtained, and the side slip angle coefficient _Kβ0 and the stability factor Ksf are obtained. Here, the "1.0" point at zero vehicle speed for _βv / _β0 and Rv/ _R0 is uniquely determined, so the side slip angle coefficient and the stability factor are obtained by obtaining at least one level of the actual measurement point ^v2 indicated by the cross mark and connecting it to the "1.0" point.

The sideslip angle coefficient and stability factor are derived from the state equations (3) and (4) by expanding (see attached document) them into equations (40) and (41).

In both equations (40) and (41), by setting lf1 to zero, it is possible to apply the formula to a four-axle vehicle with two axles at the front and two at the rear, or to a three-axle vehicle with one axle at the front and two at the rear, by setting lr1 to zero, it is possible to apply the formula to a three-axle vehicle with two axles at the front and one at the rear, and by setting both lf1 and lr1 to zero, it is possible to apply the formula to a two-axle vehicle with one axle at the front and one at the rear.

As described above, the tire cornering coefficients of the rear axle and the front axle can be estimated by substituting the experimentally identified values for the sideslip angle coefficient _Kβ0 included in equation (42-2) and the stability factor Ksf in equations (43-1) and (43-2) and substituting these values into equations (46) and (47) together with equations (42-1) and (43-3).

Fig. 8 shows how to set the "turning steering path" to the "planned route". This shows the "turning steering path" for obtaining the side slip angle coefficient _Kβ0 and the stability factor Ksf by drawing the "turning steering path" while shifting lanes on a public road, not limited to the wide area where turning is possible as shown in Fig. 7, and a method for setting the "turning steering path" at an arbitrary position on the operation planned route.

The "turning steering trajectory" is shown at the top of Figure 8. We are assuming a road with two or more lanes on each side. This is the driving trajectory from the right side of the figure to the left side. While driving in the driving lane, the car steers to the right between P0 and P1 at L01, switches from right to left steering between P1 and P3 at L123, determines the steering angle between P3 and P4, maintains the speed and steering angle between P4-P5-P6 at L456 and acquires data, releases the steering angle between P6-P7 at L67, steers from left to right between P7-P8-P9 at L789, and switches from right to straight at L910 between P9-P10.

The lower part of FIG. 8 shows a method of incorporating the above-mentioned "turning steering path" prepared in advance into the planned route. Although the "turning steering path" is drawn while changing lanes on a public road, the public road is not necessarily a straight line, so the "turning steering path" can be drawn even on a curved road. For a straight road (A), a right-turn circuit is assumed in (B) and a left-turn circuit is assumed in (C). The route curvatures of (A), (B), and (C) are obtained in advance. The curvature is multiplied by the vehicle speed at that location to obtain the yaw rate, and the yaw rate is integrated to obtain the course angle of the planned route, and the course angle of the "turning steering angle path" is added to it, integrated, and multiplied by the vehicle speed to obtain the "turning steering path" set to the planned route. For the "turning steering path" set to the planned route, the sideslip angle coefficient _Kβ0 and the stability factor Ksf are obtained according to FIG. 7.

FIG. 9 shows the flow of state estimation. This flow relates to the estimation of state quantities of vehicle weight, center of gravity position, and tire cornering coefficient from start to finish. The present invention does not include an explanation of the control of switching the estimated state quantities to control specifications (parameters). Step 1 is a step of confirming that the vehicle weight, center of gravity position, and tire cornering coefficient to be estimated are parameters (state quantities) required by the control model, and that their numerical values are set (set) as empty vehicle state values. Step 2 is a step of confirming that an empty vehicle identification experiment for the tire cornering coefficient has been conducted , and that the identified numerical values are installed in the model. Step 3 is a step of confirming that an operation plan and a bus schedule have been set, and that an implementation plan for the location and time of effective real-time state estimation has been prepared. Step 4 is
(1) Estimate the vehicle's own weight and gradient using the accelerator, and update the front and rear model parameters. (2) Perform a partial steady turn corresponding to the "turning steering path," estimate the center of gravity position, and update the lateral movement model parameters. (3) Perform a partial steady turn corresponding to the "turning steering path," and check and update the tire cornering coefficient. The vehicle is operated in this order.

As described above, the present invention relates to a method for detecting state quantities in order to detect changes in the state quantities of a vehicle, i.e., total vehicle weight, center of gravity position, and tire load, that accompany changes in passengers and baggage, and to perform adaptive control while updating the state quantities of a control model that correspond to those changes.
A method that uses a linear equation Y=AX-B, which is the vehicle acceleration Y relative to the accelerator opening X corresponding to equation (2), detects the change in vehicle weight from the gradient A of the straight line, and detects the gradient from the Y intercept B.
A method in which a GPS is installed, the tire side slip angle caused by the loaded vehicle is detected, and the change in the center of gravity position is estimated using equation (32).
When the change in vehicle weight and the change in center of gravity are known, the front and rear loads can be determined, and the vehicle's lateral slip angle coefficient and stability factor can be grasped by a "turning steering path." By detecting these at a location where the vehicle can be driven while maintaining steering and substituting them into equations (46) and (47), the tire cornering coefficient can be estimated.
Thus, the present invention addresses the need for adaptive control of an autonomous vehicle to accommodate changes in the vehicle's forward and backward motion characteristics and lateral motion characteristics associated with changes in passenger and load.

Claims (1)

An autonomous driving method in which an equation for controlling driving, which is described by vehicle state quantities, is incorporated into an on-board computer (ECU), the vehicle state quantities estimated in real time are input into the equation while being updated, and a signal for controlling driving calculated by the equation is output from the on-board computer, wherein the state quantities are the vehicle's own weight, slope gradient, center of gravity position, and tire cornering coefficient, the vehicle's own weight and slope are estimated by an equation for generated acceleration in response to accelerator input, the center of gravity position and tire cornering coefficient are estimated by GPS and wheel speed , and the center of gravity position is estimated by calculating the lateral slip angle of each wheel from the GPS and wheel speed, and determining the amount of movement of the center of gravity position by the following equation (32) :

Images