- Email: [email protected]
Braking Control of Articulated Vehicle for Small Turning
Steering/Braking Control of Articulated Vehicle for Small Turning Michihisa Iida*. Hiroki Tomiyama**. Toho Oh***. Hiroshi Nakashima****
*Graduate School of Agriculture, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan (Tel: +81-75-753-6168; e-mail: [email protected]). **Graduate School of Agriculture, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan (Tel: +81-75-753-6167; e-mail: [email protected]). ***Graduate School of Agriculture, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan (Tel: +81-75-753-6167; e-mail: [email protected]). ****Graduate School of Agriculture, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan (Tel: +81-75-753-6164; e-mail: [email protected]).
Abstract: A wheel loaders is a kind of articulated-frame steered vehicles and is used in narrow workspaces such as livestock barns. Its small-radius turning performance is important for improving operating efficiency in narrow workspaces. An integral steering/braking control system for small-radius turning was developed in this study. In this system, braking force acts on the inside tires to make a yawmoment around the vehicle centre of gravity. The braking force acting on the inside tires is controlled by a feedback control system of hydraulic pressure using an electro-magnetic relief valve. The relief valve is controlled by pulse width modulation to produce a desired hydraulic pressure. The control of braking force is only active when the articulation angle and vehicle speed are appropriate. Experimental results showed that the yaw-moment control allowed the articulated vehicle to turn in a smaller radius. The turning radius by the steering system with the yaw-moment control became at least 1.2 m smaller than the normal system on the wet unpaved road. Keywords: active brake control, global positioning systems, gyroscopes, integral control, vehicle dynamics, yaw rate.
1. INTRODUCTION A wheel loader is a kind of earth-moving machine that has an articulated steering mechanism to minimize its turning radius. The articulated steering mechanism can steer by bending front and rear frame parts around a vertical pivot joint in a plane. Such a vehicle generally has four tires of the same size, front and rear axles of the same tread, and a differential gear between left and right tires. As an articulated vehicle takes advantages of turning in a small radius with the same rut for front and rear tires, it is often used in narrow workspaces such as livestock barns. Oida (1983) and Iida et al. (2010) reported about turning behavior of the articulated vehicle such as yaw rate and side-slip angle. Turning performance with small radius and small side-slip angle is very important for articulated vehicles to enhance operating efficiency in narrow workspaces. Although an effective way to improve a vehicle’s turning performance can be increasing its articulation angle, the articulation angle is limited because of construction and stability requirements. Therefore, a direct yaw-moment control (DYC) to impose a desired vehicle turning performance is proposed in this study. In fact, the direct yaw-moment controls in automobiles can be realized through different technologies such as active braking actions employed in anti-locked braking system
(ABS), vehicle dynamic control system (VDC), and electronic stability program (ESP). Canale et al. (2007) also reported robust control of vehicle yaw rate dynamics using an active differential gear. Cheouat et al. (2005) simulated in integrated braking/traction and steering control system to control vehicle stability in cornering. Kiencke et al. (1997) studied the lateral motion behavior of a vehicle by measuring lateral and longitudinal acceleration, yaw rate and wheel speeds, as the vehicle moved at high speed on a paved road. They calculated its lateral motions, including tire side-slip angle. Chen et al. (1995) proposed an independent braking control system for articulated vehicle such as tractorsemitrailers to help avoid rollovers and jack-knifings on the high-way. Eisele et al. (2000) also reported that vehicle dynamics control by differential braking helps prevent heavy tractor-trailer rollovers and jack-knifings. However, they determined lateral motions and side-slip angles not by measurement but by simulations. This study aims to enhance turning performance of the articulated vehicle by the direct yaw-moment control. In other words, the objective is to control vehicle yaw-moment generated by means of unsymmetrical force distributions in left-right sides in order for the articulated vehicle to turn in a small radius.
2. PROBLEM FORMULATION AND REQUIREMENT In this study, the direct yaw-moment control aim is to let an articulated vehicle turn in small radius under safe and stable conditions when the articulation angle handled by driver is more than 25°. As to the yaw-moment generation, an unsymmetrical braking force distribution system (UBFDS) in left-right tires developed and patented at Caterpillar Japan Co., Ltd., and Kyoto University is used. In order to consider vehicle turning performance, it is useful to compare the articulated steering mechanism with Ackermann steering mechanism with respect to the turning radius. Figure 1 shows the relationship between steering angle (articulation angle in the case of the articulated vehicle) and turning radius simulated using the same kinematic and dynamic parameters at a constant speed (10 km/h). At a glance, the articulated steering mechanism is superior to the Ackermann steering mechanism with respect to the smallradius turning. In addition, the figure shows the expected turning radius in the case that the direct yaw-moment control is applied when the articulation angle is more than 25°. In addition, in order to control the magnitude of yaw-moment, the fluid pressure of the brake is controlled by an electroproportional relief valve corresponding to the desired pressure that the driver commands. The desired pressure is set at a constant value using a volume dial of a controller.
30
Turning radius of vehicle center [m]
Ackermann steering
25
3. MATERIALS 3.1 Test Vehicle Test vehicle is a wheel loader, Caterpillar 910G, whose dimensions and specifications are shown in Table 1. It has a vertical pivot joint in articulated steering system and a fourwheel-drive system with differential gears in front and rear axles. The pivot joint is located at the centre of the vehicle wheelbase. The maximum articulation angle of this vehicle is 36°. The test vehicle has two speed ranges. The direct yawmoment control is applied to the vehicle only in the lowspeed range. It is supposed that the vehicle centre of gravity (COG) is on a line connecting the centre of front axle and the centre of rear axle. Table 1. Test vehicle’s dimension and specification Mass, kg Length, mm Width, mm Height, mm Wheel base Tread, mm Engine output, kW Transmissions Speed (low), km/h Speed (high), km/h Maximal articulation angle, º
6,500 5,490 2,185 3,060 2,335 1,725 63 HST & high/low-range 0–10.5 0–34.5 36
Articulated steering
20
Articulated steering with DYC
15 10 5 0 0
10 20 30 Steering (articulation) angle [°]
The vehicle speed is measured with a speed sensor that is installed at the transmission. The articulation angle of the vehicle is determined from measuring the distance between the front and rear frames by a displacement sensor (Tokyo Sokki Kenkyujyo Co., Ltd., DP-500E). The vehicle yawrate was measured with a low-cost gyro sensor (Panasonic Co., Ltd., EWTS53CB). Two GPSs (Trimble Co., Ltd., MS750) measure the track and direction of the vehicle in real time. An inertia measurement unit (IMU) with fibre optic gyro sensors and accelerometers is also installed at the vehicle to precisely measure the orientation and yawrate of the vehicle.
40
Fig.1. Example of relationship between steering angle and turning radius. When the articulation angle, the vehicle speed and the braking pressure are given by the driver as input signals, the vehicle yawrate, the vehicle side-slip angle and the turning radius are determined from the data that are measured by the sensors such as global positioning system (GPS), gyro sensors, and speed sensor. The vehicle side-slip angle is estimated with an observer. Experiments using a wheel loader are conducted to evaluate the turning performance of the articulated steering system with the direct yaw-moment control.
3.2 Vehicle Dynamics Modelling Vehicle dynamics will be worked out on the basis of a twowheel vehicle model as shown in Fig.2, with tire dynamic force generation description. The employed model is based on the following assumptions: a) Flat road surface. b) Longitudinal motion resistances are ignored compared to wheel lateral forces. c) Wheel self aligning moments are ignored. d) Steering angle and vehicle side-slip angles are small enough to linearize their trigonometrical functions.
e) Vehicle speed is a known parameter, vehicle longitudinal acceleration is low or equal to zero.
xˆ
A xˆ Bu K y - ˆy
ˆy
C xˆ
(14) (15)
where:
G2 x
Front
G lf
E
O
R
V m, I
y
COG
ld
J
>Eˆ
ˆy
Jˆ
Jˆ
@T
(16) (17)
Eˆ and Jˆ are the vehicle side-slip angle and vehicle yawrate that are estimated by the observer. The observer can estimate these state parameters from the detectable signals such as V, G and J, that are measured with low-cost sensors, and the known parameters such as m, I, lf, and lr. Observer gain K is determined from the pole displacement method. Table 2 shows the parameters of the vehicle for the observer.
lr
G2
xˆ
Table 2. Parameters of vehicle
Rear
m [kg] 6,500
Fig.2. Two-wheel vehicle model.
I [kgm2] 13,500
l [m] 2.335
Cf and Cr [N/rad] 20,000
The mathematical model is:
mV E J IJ
E
(1)
2C f E f 2C r E r
2C f l f E
f
Er ld
f
2C r l r E r M
z
E lfJ /V G / 2
(3)
E lr J / V G / 2
(4) (5)
l cos G / 2
where m is the vehicle mass [kg], I is the moment of inertia around the vertical axis [kg-m2], l is the distance between the centres of the front and rear axles, and lf and lr are the distances between the centre of gravity and the front and rear axles, respectively (lf : lr = 3 : 2). Cf and Cr are the front and rear tires cornering stiffness, G is the articulation angle, E is the vehicle side-slip angle, J is the vehicle yaw rate and V is the vehicle speed. Ef and Er are the tire side-slip angles. Mz is the yaw moment generated by the braking force. Equations (1) and (2) can change into a state-space model as follows: x
Ax Bu
y
Cx
3.3 Active Brake Control System
(2) The brake system of the test vehicle was modified to apply the braking force on either left or right tires in response to its articulation angle G. Figure 3 illustrates the outline of the modified brake system. This figure shows the valve position to drive in the same way as the normal brake system. It includes four electric poppet valves (V1-V4), an electroproportional relief valve (V5), and a controller. Right front tire Left front tire Pick-up sensor Master cylinder
V1
V2
P1
(6) (7)
P3
H.M
V3
where: u
>E >G
y
J
x
A
B
C
J @T Mz@
ª 2 C f C r / mV 2 C f l f C r l r / mV 2 1º » « «¬ 2 C f l f C r l r / I 2 C f l f 2 C r l r 2 / IV »¼ 0 º ª C f C r / mV « C l C l / I 1/ I» r r ¬ f f ¼
Foot brake pedal
Brake friction plate
>0 1@
(8) (9) (10) (11)
(13)
An observer to estimate the vehicle side-slip angle for the articulated vehicle is designed as follows:
V5
P2 Pump Differential gear Left rear tire
(12)
V4
Right rear tire
Fig. 3. Brake system in test vehicle. Normally, all the brakes of four tires were actuated by the foot brake pedal and master cylinder (normal mode). On the other hand, in the case of turning in small radius (control mode), each pair of the left or right brakes was operated by
pressured fluid from the hydraulic pump. The V1-V4 valves switch from normal mode to control mode. Table 3 shows the relationship among articulation angle, valve position, and operation mode. The trigger signal to switch the mode is the articulation angle of the vehicle. The brake system works under normal mode in the articulation angle range of –25° - 25°. If the articulation angle increases more than 25°, the brake system switches to the control mode and applies the left brakes automatically. In the same way, in the case that the articulation angle is less than –25°, the brake system actuates only the right brakes. Table 3. Valve Operation depending on articulation angle Operation Control mode (right turn) Normal mode Control mode (left turn)
Articulation angle Less than –25° –25° to 25° More than 25°
Valve position V1&V2 V3 V4 OFF OFF ON ON OFF
OFF ON
OFF OFF
3.4 Actuation System Modelling The pressures (P1-P3) of the left/right brakes and pump are individually measured by pressure sensors (Kyowa Electric Works Co., Ltd., PG-KU). The braking force acting on the tire is proportional to the pressure controlled by the relief valve V5. In the control mode, the relief valve regulates the fluid pressure from the pump at a desired pressure by pulse width modulation. For this purpose, the pressure P3 was used as a feedback signal to control the relief valve (Fig.4). The desired value (reference) of the braking pressure is given by setting a volume dial of the controller.
P3d(s) +
PI
Relief valve
P3(s)
– Pressure sensor Fig. 4. Pressure control by electro-proportional relief valve. 3.5 Yaw-moment by Braking Force The brake piston pinches the brake friction plate in proportion to the braking pressure and it generates the braking force on either left or right tire. The braking force decreases the traction force of the inner tire. At the same time, as the differential gear is between the left and right tires, the inner tire’s traction force decreased by the braking force adds the outer tire’s traction force by means of the differential gear. Therefore, the yaw-moment Mz (t) around the vehicle centre of gravity is described as
M z s
K m P3 s
(18)
where Km is the gain of yaw-moment by the brake pressure and is defined as Km
(19)
4 P G m A p dr B / r
where Ap is the effective brake piston area, P is the friction efficient of the brake friction plate, rB is the radius of the pitch circle of the brake friction plate, r is the radius of tire, Gm is the final gear ratio between brake and tire, d is the tread between left and right tires, respectively. Though Km can be calculated by measured parameters, it has the errors and uncertainty in practice. B
The maximal pump pressure is 19MPa. However, the pressure limit of hoses and seals is lower than the pump pressure and the tire is locked at the braking pressure of 3 MPa. The braking pressure range as the input is defined from 0 MPa to 3 MPa. Therefore, the yaw-moment that can be mechanically generated is ± 20550 Nm theoretically. 4. EXPERIMENTAL METHODS 4.1 Zigzag Line Travelling Experiments of zigzag line travelling were conducted to evaluate the actuation of the active brake control system. Road condition was wet concrete surface because of rain. The vehicle travelled at a constant speed and the driver steered from side to side. The experiments were conducted in two ways: 1) zigzag line travelling without direct-yaw-moment control, 2) zigzag line travelling with direct yaw-moment control. The direct yawmoment control was applied when the articulation angle was more than 25°. The braking pressure was set at 2.3 MPa. The track of the vehicle was measured by two real-time kinematic global positioning systems (RTK-GPS). The vehicle side-slip angle was estimated by the observer. 4.2 Constant Circle Turning In order to measure the actual turning radius, experiments of constant circle turning were conducted. The road condition was a wet unpaved road. In the same way, the tracks of the vehicle were measured by the RTK-GPS and the vehicle sideslip angle was estimated by the observer. 5. RESULTS AND DISCUSSION 5.1 Zigzag Line Travelling Figure 5 shows the tracks of the vehicle travelling in zigzag line measured by the GPS. The average speeds were about 1.7 m/s (without direct yaw-moment control) and 1.2 m/s (with direct yaw-moment control), respectively. Figure 6 shows the actual articulation angles steered by the driver.
4
Y [m]
3 2 1 0 -1 0
10
20
X [m]
30
40
50
applied. When the articulation angle to the left was more than 25°, the left brake pressure increased and became about 2.3 MPa. Oppositely, when the articulation angle to the right was less than –25°, the right brake pressure became about 2.3 MPa. In addition, it was showed that the relief valve regulated the brake pressure at 2.3 MPa. As the result, it was confirmed that the active brake control system developed in this study was actuated in right operational way corresponding to the articulation angle as the trigger. 3 Pressure [MPa]
a) Exp.1: without direct yaw-moment control. 4
Y [m]
3 2 1
Left Right
2
1
0 0
0
10
20
30 Time [s]
-1 0
10
20
30
50
40
X [m]
40
50
60
Fig. 7. Brake pressure changes by articulation angle (Exp. 2). Figure 8 shows the vehicle yawrates measured by the lowcost gyro sensor. Though the speed of the Exp. 2) was lower than that of the Exp. 1), the vehicle yawrate of the Exp. 2) was higher than that of the Exp. 1). In the Exp. 2), the yawmoment generated by the active brake control caused the higher yawrate.
b) Exp.2: with direct yaw-moment control. Fig. 5. Tracks of the vehicle travelling in zigzag line. 40
20
60
10
40
0 Yawrate[°/s]
Articulated angle [°]
30
-10 -20 -30 -40 0
10
20
Time [s]
30
40
20 0 -20 -40
50
-60 0
a) Exp.1: without direct yaw-moment control. 40
10
20
Time [s]
30
40
50
a) Without direct yaw-moment control (Exp. 1). 60
20 10
40
0 Yawrate[°/s]
Articluated angle [°]
30
-10 -20 -30 -40 0
10
20
30 Time [s]
40
50
60
b) Exp.2: with direct yaw-moment control. Fig. 6. Articulation angles steered by the driver. Figure 7 shows the variations of the left and right brake pressures according to the articulation angle input by the driver in the case that the direct yaw-moment control was
20 0 -20 -40 -60 0
10
20
30 Time [s]
40
b) With direct yaw-moment control (Exp. 2). Fig. 8. Yawrates measured by gyro sensor.
50
60
5.2 Constant Circle Turning
20
Actual Observer
Side-slip angle [°]
10
Figure 10 shows the comparison of the turning radius when the different braking pressures were applied to the inner tires. The vehicle speed was about 1.2 m/s. The turning radius at the braking pressure 2.4 MPa became at least 1.2 m smaller than that at 0 MPa. Experimental results proved that the yawmoment control could make the turning radius smaller.
0 -10 -20 0
10
20
30
50
40
Time [s]
a) Without direct yaw-moment control (Exp. 1). 20
Actual Observer
Side-slip angle [°]
10 0 -10 -20 0
10
20
30
40
50
60
Time [s]
6. CONCLUSIONS A direct yaw-moment control system was applied in order for an articulated vehicle to turn in a smaller radius. An active brake control system using an electro-proportional relief valve was developed to generate the yaw-moment. This brake control system was controlled by the articulation angle determined by the driver. An observer to estimate the vehicle side-slip angle was designed and employed. This observer could estimate the vehicle side-slip angle by the yawrate measured with a low-cost gyro sensor. Experimental results of constant circle turning showed that the direct yaw-moment control allowed the articulated vehicle to turn in a smaller radius. The turning radius at the braking pressure 2.4 MPa became at least 1.2 m smaller than that of 0 MPa on a wet unpaved road.
b) With direct yaw-moment control (Exp. 2).
ACKNOWLEDGEMENT
Fig.9. Side-slip angles estimated by observer.
This research was financially supported by Caterpillar Japan Co., Ltd.
Figure 9 shows the comparisons of the actual and estimated side-slip angles. Without the DYC, both actual and estimated side-slip angles were almost same magnitude and variation. On the other hand, there were some differences of peak values between actual and estimated slide-slip angles with DYC. However, the observer could estimate almost the sideslip angle by using the low-cost yaw rate sensor. 4 R=2.89m (1.6MPa)
R=3.27m (0MPa) 3 2
Y [m]
1 R=2.04m (2.4MPa)
0 -1 -2 -3 -4 -4
-3
-2
-1
0 X [m]
Fig. 10. Comparison of turning radius.
1
2
3
4
REFERENCES Canale, M., Fagiano, L., Milanese, M., Borodani, P. (2007). Robust vehicle yaw control using an active differential and IMC techniques. Control Engineering Practice, 15, 923–941. Chen, C., Tomizuka, M. (1995). Steering and independent braking control for tractor-semitrailer vehicles in automated highway systems. Proceedings of the 34th conference on Decision & Control. Cheouat, H., Diop, S. (2005). An observation and an integrated braking/traction and steering control for a cornering vehicle. American Control Conference, Portland, OR, USA. Eisele, D. D., Peng, H. (2000). Vehicle dynamics control with rollover prevention for articulated heavy trucks. Proceedings of the 5th International Symposium on Advanced Vehicle Control (AVEC2000). Iida, M., Fukuta, M., Tomiyama, H. (2010). Measurement and analysis of side slip angle of articulated vehicle. Engineering in Agriculture, Environment and Food, 3(1), 1–6. Kiencke, U., Daiß, A. (1997). Observation of lateral vehicle dynamics. Control Engineering Practice. 5(8), 1145– 1150. Oida, A. (1983). Turning behavior of articulated frame steering tractor – I. Motion of tractor without traction –. Journal of Terramechanics, 20(3), 153–165.
*Graduate School of Agriculture, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan (Tel: +81-75-753-6168; e-mail: [email protected]). **Graduate School of Agriculture, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan (Tel: +81-75-753-6167; e-mail: [email protected]). ***Graduate School of Agriculture, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan (Tel: +81-75-753-6167; e-mail: [email protected]). ****Graduate School of Agriculture, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan (Tel: +81-75-753-6164; e-mail: [email protected]).
Abstract: A wheel loaders is a kind of articulated-frame steered vehicles and is used in narrow workspaces such as livestock barns. Its small-radius turning performance is important for improving operating efficiency in narrow workspaces. An integral steering/braking control system for small-radius turning was developed in this study. In this system, braking force acts on the inside tires to make a yawmoment around the vehicle centre of gravity. The braking force acting on the inside tires is controlled by a feedback control system of hydraulic pressure using an electro-magnetic relief valve. The relief valve is controlled by pulse width modulation to produce a desired hydraulic pressure. The control of braking force is only active when the articulation angle and vehicle speed are appropriate. Experimental results showed that the yaw-moment control allowed the articulated vehicle to turn in a smaller radius. The turning radius by the steering system with the yaw-moment control became at least 1.2 m smaller than the normal system on the wet unpaved road. Keywords: active brake control, global positioning systems, gyroscopes, integral control, vehicle dynamics, yaw rate.
1. INTRODUCTION A wheel loader is a kind of earth-moving machine that has an articulated steering mechanism to minimize its turning radius. The articulated steering mechanism can steer by bending front and rear frame parts around a vertical pivot joint in a plane. Such a vehicle generally has four tires of the same size, front and rear axles of the same tread, and a differential gear between left and right tires. As an articulated vehicle takes advantages of turning in a small radius with the same rut for front and rear tires, it is often used in narrow workspaces such as livestock barns. Oida (1983) and Iida et al. (2010) reported about turning behavior of the articulated vehicle such as yaw rate and side-slip angle. Turning performance with small radius and small side-slip angle is very important for articulated vehicles to enhance operating efficiency in narrow workspaces. Although an effective way to improve a vehicle’s turning performance can be increasing its articulation angle, the articulation angle is limited because of construction and stability requirements. Therefore, a direct yaw-moment control (DYC) to impose a desired vehicle turning performance is proposed in this study. In fact, the direct yaw-moment controls in automobiles can be realized through different technologies such as active braking actions employed in anti-locked braking system
(ABS), vehicle dynamic control system (VDC), and electronic stability program (ESP). Canale et al. (2007) also reported robust control of vehicle yaw rate dynamics using an active differential gear. Cheouat et al. (2005) simulated in integrated braking/traction and steering control system to control vehicle stability in cornering. Kiencke et al. (1997) studied the lateral motion behavior of a vehicle by measuring lateral and longitudinal acceleration, yaw rate and wheel speeds, as the vehicle moved at high speed on a paved road. They calculated its lateral motions, including tire side-slip angle. Chen et al. (1995) proposed an independent braking control system for articulated vehicle such as tractorsemitrailers to help avoid rollovers and jack-knifings on the high-way. Eisele et al. (2000) also reported that vehicle dynamics control by differential braking helps prevent heavy tractor-trailer rollovers and jack-knifings. However, they determined lateral motions and side-slip angles not by measurement but by simulations. This study aims to enhance turning performance of the articulated vehicle by the direct yaw-moment control. In other words, the objective is to control vehicle yaw-moment generated by means of unsymmetrical force distributions in left-right sides in order for the articulated vehicle to turn in a small radius.
2. PROBLEM FORMULATION AND REQUIREMENT In this study, the direct yaw-moment control aim is to let an articulated vehicle turn in small radius under safe and stable conditions when the articulation angle handled by driver is more than 25°. As to the yaw-moment generation, an unsymmetrical braking force distribution system (UBFDS) in left-right tires developed and patented at Caterpillar Japan Co., Ltd., and Kyoto University is used. In order to consider vehicle turning performance, it is useful to compare the articulated steering mechanism with Ackermann steering mechanism with respect to the turning radius. Figure 1 shows the relationship between steering angle (articulation angle in the case of the articulated vehicle) and turning radius simulated using the same kinematic and dynamic parameters at a constant speed (10 km/h). At a glance, the articulated steering mechanism is superior to the Ackermann steering mechanism with respect to the smallradius turning. In addition, the figure shows the expected turning radius in the case that the direct yaw-moment control is applied when the articulation angle is more than 25°. In addition, in order to control the magnitude of yaw-moment, the fluid pressure of the brake is controlled by an electroproportional relief valve corresponding to the desired pressure that the driver commands. The desired pressure is set at a constant value using a volume dial of a controller.
30
Turning radius of vehicle center [m]
Ackermann steering
25
3. MATERIALS 3.1 Test Vehicle Test vehicle is a wheel loader, Caterpillar 910G, whose dimensions and specifications are shown in Table 1. It has a vertical pivot joint in articulated steering system and a fourwheel-drive system with differential gears in front and rear axles. The pivot joint is located at the centre of the vehicle wheelbase. The maximum articulation angle of this vehicle is 36°. The test vehicle has two speed ranges. The direct yawmoment control is applied to the vehicle only in the lowspeed range. It is supposed that the vehicle centre of gravity (COG) is on a line connecting the centre of front axle and the centre of rear axle. Table 1. Test vehicle’s dimension and specification Mass, kg Length, mm Width, mm Height, mm Wheel base Tread, mm Engine output, kW Transmissions Speed (low), km/h Speed (high), km/h Maximal articulation angle, º
6,500 5,490 2,185 3,060 2,335 1,725 63 HST & high/low-range 0–10.5 0–34.5 36
Articulated steering
20
Articulated steering with DYC
15 10 5 0 0
10 20 30 Steering (articulation) angle [°]
The vehicle speed is measured with a speed sensor that is installed at the transmission. The articulation angle of the vehicle is determined from measuring the distance between the front and rear frames by a displacement sensor (Tokyo Sokki Kenkyujyo Co., Ltd., DP-500E). The vehicle yawrate was measured with a low-cost gyro sensor (Panasonic Co., Ltd., EWTS53CB). Two GPSs (Trimble Co., Ltd., MS750) measure the track and direction of the vehicle in real time. An inertia measurement unit (IMU) with fibre optic gyro sensors and accelerometers is also installed at the vehicle to precisely measure the orientation and yawrate of the vehicle.
40
Fig.1. Example of relationship between steering angle and turning radius. When the articulation angle, the vehicle speed and the braking pressure are given by the driver as input signals, the vehicle yawrate, the vehicle side-slip angle and the turning radius are determined from the data that are measured by the sensors such as global positioning system (GPS), gyro sensors, and speed sensor. The vehicle side-slip angle is estimated with an observer. Experiments using a wheel loader are conducted to evaluate the turning performance of the articulated steering system with the direct yaw-moment control.
3.2 Vehicle Dynamics Modelling Vehicle dynamics will be worked out on the basis of a twowheel vehicle model as shown in Fig.2, with tire dynamic force generation description. The employed model is based on the following assumptions: a) Flat road surface. b) Longitudinal motion resistances are ignored compared to wheel lateral forces. c) Wheel self aligning moments are ignored. d) Steering angle and vehicle side-slip angles are small enough to linearize their trigonometrical functions.
e) Vehicle speed is a known parameter, vehicle longitudinal acceleration is low or equal to zero.
xˆ
A xˆ Bu K y - ˆy
ˆy
C xˆ
(14) (15)
where:
G2 x
Front
G lf
E
O
R
V m, I
y
COG
ld
J
>Eˆ
ˆy
Jˆ
Jˆ
@T
(16) (17)
Eˆ and Jˆ are the vehicle side-slip angle and vehicle yawrate that are estimated by the observer. The observer can estimate these state parameters from the detectable signals such as V, G and J, that are measured with low-cost sensors, and the known parameters such as m, I, lf, and lr. Observer gain K is determined from the pole displacement method. Table 2 shows the parameters of the vehicle for the observer.
lr
G2
xˆ
Table 2. Parameters of vehicle
Rear
m [kg] 6,500
Fig.2. Two-wheel vehicle model.
I [kgm2] 13,500
l [m] 2.335
Cf and Cr [N/rad] 20,000
The mathematical model is:
mV E J IJ
E
(1)
2C f E f 2C r E r
2C f l f E
f
Er ld
f
2C r l r E r M
z
E lfJ /V G / 2
(3)
E lr J / V G / 2
(4) (5)
l cos G / 2
where m is the vehicle mass [kg], I is the moment of inertia around the vertical axis [kg-m2], l is the distance between the centres of the front and rear axles, and lf and lr are the distances between the centre of gravity and the front and rear axles, respectively (lf : lr = 3 : 2). Cf and Cr are the front and rear tires cornering stiffness, G is the articulation angle, E is the vehicle side-slip angle, J is the vehicle yaw rate and V is the vehicle speed. Ef and Er are the tire side-slip angles. Mz is the yaw moment generated by the braking force. Equations (1) and (2) can change into a state-space model as follows: x
Ax Bu
y
Cx
3.3 Active Brake Control System
(2) The brake system of the test vehicle was modified to apply the braking force on either left or right tires in response to its articulation angle G. Figure 3 illustrates the outline of the modified brake system. This figure shows the valve position to drive in the same way as the normal brake system. It includes four electric poppet valves (V1-V4), an electroproportional relief valve (V5), and a controller. Right front tire Left front tire Pick-up sensor Master cylinder
V1
V2
P1
(6) (7)
P3
H.M
V3
where: u
>E >G
y
J
x
A
B
C
J @T Mz@
ª 2 C f C r / mV 2 C f l f C r l r / mV 2 1º » « «¬ 2 C f l f C r l r / I 2 C f l f 2 C r l r 2 / IV »¼ 0 º ª C f C r / mV « C l C l / I 1/ I» r r ¬ f f ¼
Foot brake pedal
Brake friction plate
>0 1@
(8) (9) (10) (11)
(13)
An observer to estimate the vehicle side-slip angle for the articulated vehicle is designed as follows:
V5
P2 Pump Differential gear Left rear tire
(12)
V4
Right rear tire
Fig. 3. Brake system in test vehicle. Normally, all the brakes of four tires were actuated by the foot brake pedal and master cylinder (normal mode). On the other hand, in the case of turning in small radius (control mode), each pair of the left or right brakes was operated by
pressured fluid from the hydraulic pump. The V1-V4 valves switch from normal mode to control mode. Table 3 shows the relationship among articulation angle, valve position, and operation mode. The trigger signal to switch the mode is the articulation angle of the vehicle. The brake system works under normal mode in the articulation angle range of –25° - 25°. If the articulation angle increases more than 25°, the brake system switches to the control mode and applies the left brakes automatically. In the same way, in the case that the articulation angle is less than –25°, the brake system actuates only the right brakes. Table 3. Valve Operation depending on articulation angle Operation Control mode (right turn) Normal mode Control mode (left turn)
Articulation angle Less than –25° –25° to 25° More than 25°
Valve position V1&V2 V3 V4 OFF OFF ON ON OFF
OFF ON
OFF OFF
3.4 Actuation System Modelling The pressures (P1-P3) of the left/right brakes and pump are individually measured by pressure sensors (Kyowa Electric Works Co., Ltd., PG-KU). The braking force acting on the tire is proportional to the pressure controlled by the relief valve V5. In the control mode, the relief valve regulates the fluid pressure from the pump at a desired pressure by pulse width modulation. For this purpose, the pressure P3 was used as a feedback signal to control the relief valve (Fig.4). The desired value (reference) of the braking pressure is given by setting a volume dial of the controller.
P3d(s) +
PI
Relief valve
P3(s)
– Pressure sensor Fig. 4. Pressure control by electro-proportional relief valve. 3.5 Yaw-moment by Braking Force The brake piston pinches the brake friction plate in proportion to the braking pressure and it generates the braking force on either left or right tire. The braking force decreases the traction force of the inner tire. At the same time, as the differential gear is between the left and right tires, the inner tire’s traction force decreased by the braking force adds the outer tire’s traction force by means of the differential gear. Therefore, the yaw-moment Mz (t) around the vehicle centre of gravity is described as
M z s
K m P3 s
(18)
where Km is the gain of yaw-moment by the brake pressure and is defined as Km
(19)
4 P G m A p dr B / r
where Ap is the effective brake piston area, P is the friction efficient of the brake friction plate, rB is the radius of the pitch circle of the brake friction plate, r is the radius of tire, Gm is the final gear ratio between brake and tire, d is the tread between left and right tires, respectively. Though Km can be calculated by measured parameters, it has the errors and uncertainty in practice. B
The maximal pump pressure is 19MPa. However, the pressure limit of hoses and seals is lower than the pump pressure and the tire is locked at the braking pressure of 3 MPa. The braking pressure range as the input is defined from 0 MPa to 3 MPa. Therefore, the yaw-moment that can be mechanically generated is ± 20550 Nm theoretically. 4. EXPERIMENTAL METHODS 4.1 Zigzag Line Travelling Experiments of zigzag line travelling were conducted to evaluate the actuation of the active brake control system. Road condition was wet concrete surface because of rain. The vehicle travelled at a constant speed and the driver steered from side to side. The experiments were conducted in two ways: 1) zigzag line travelling without direct-yaw-moment control, 2) zigzag line travelling with direct yaw-moment control. The direct yawmoment control was applied when the articulation angle was more than 25°. The braking pressure was set at 2.3 MPa. The track of the vehicle was measured by two real-time kinematic global positioning systems (RTK-GPS). The vehicle side-slip angle was estimated by the observer. 4.2 Constant Circle Turning In order to measure the actual turning radius, experiments of constant circle turning were conducted. The road condition was a wet unpaved road. In the same way, the tracks of the vehicle were measured by the RTK-GPS and the vehicle sideslip angle was estimated by the observer. 5. RESULTS AND DISCUSSION 5.1 Zigzag Line Travelling Figure 5 shows the tracks of the vehicle travelling in zigzag line measured by the GPS. The average speeds were about 1.7 m/s (without direct yaw-moment control) and 1.2 m/s (with direct yaw-moment control), respectively. Figure 6 shows the actual articulation angles steered by the driver.
4
Y [m]
3 2 1 0 -1 0
10
20
X [m]
30
40
50
applied. When the articulation angle to the left was more than 25°, the left brake pressure increased and became about 2.3 MPa. Oppositely, when the articulation angle to the right was less than –25°, the right brake pressure became about 2.3 MPa. In addition, it was showed that the relief valve regulated the brake pressure at 2.3 MPa. As the result, it was confirmed that the active brake control system developed in this study was actuated in right operational way corresponding to the articulation angle as the trigger. 3 Pressure [MPa]
a) Exp.1: without direct yaw-moment control. 4
Y [m]
3 2 1
Left Right
2
1
0 0
0
10
20
30 Time [s]
-1 0
10
20
30
50
40
X [m]
40
50
60
Fig. 7. Brake pressure changes by articulation angle (Exp. 2). Figure 8 shows the vehicle yawrates measured by the lowcost gyro sensor. Though the speed of the Exp. 2) was lower than that of the Exp. 1), the vehicle yawrate of the Exp. 2) was higher than that of the Exp. 1). In the Exp. 2), the yawmoment generated by the active brake control caused the higher yawrate.
b) Exp.2: with direct yaw-moment control. Fig. 5. Tracks of the vehicle travelling in zigzag line. 40
20
60
10
40
0 Yawrate[°/s]
Articulated angle [°]
30
-10 -20 -30 -40 0
10
20
Time [s]
30
40
20 0 -20 -40
50
-60 0
a) Exp.1: without direct yaw-moment control. 40
10
20
Time [s]
30
40
50
a) Without direct yaw-moment control (Exp. 1). 60
20 10
40
0 Yawrate[°/s]
Articluated angle [°]
30
-10 -20 -30 -40 0
10
20
30 Time [s]
40
50
60
b) Exp.2: with direct yaw-moment control. Fig. 6. Articulation angles steered by the driver. Figure 7 shows the variations of the left and right brake pressures according to the articulation angle input by the driver in the case that the direct yaw-moment control was
20 0 -20 -40 -60 0
10
20
30 Time [s]
40
b) With direct yaw-moment control (Exp. 2). Fig. 8. Yawrates measured by gyro sensor.
50
60
5.2 Constant Circle Turning
20
Actual Observer
Side-slip angle [°]
10
Figure 10 shows the comparison of the turning radius when the different braking pressures were applied to the inner tires. The vehicle speed was about 1.2 m/s. The turning radius at the braking pressure 2.4 MPa became at least 1.2 m smaller than that at 0 MPa. Experimental results proved that the yawmoment control could make the turning radius smaller.
0 -10 -20 0
10
20
30
50
40
Time [s]
a) Without direct yaw-moment control (Exp. 1). 20
Actual Observer
Side-slip angle [°]
10 0 -10 -20 0
10
20
30
40
50
60
Time [s]
6. CONCLUSIONS A direct yaw-moment control system was applied in order for an articulated vehicle to turn in a smaller radius. An active brake control system using an electro-proportional relief valve was developed to generate the yaw-moment. This brake control system was controlled by the articulation angle determined by the driver. An observer to estimate the vehicle side-slip angle was designed and employed. This observer could estimate the vehicle side-slip angle by the yawrate measured with a low-cost gyro sensor. Experimental results of constant circle turning showed that the direct yaw-moment control allowed the articulated vehicle to turn in a smaller radius. The turning radius at the braking pressure 2.4 MPa became at least 1.2 m smaller than that of 0 MPa on a wet unpaved road.
b) With direct yaw-moment control (Exp. 2).
ACKNOWLEDGEMENT
Fig.9. Side-slip angles estimated by observer.
This research was financially supported by Caterpillar Japan Co., Ltd.
Figure 9 shows the comparisons of the actual and estimated side-slip angles. Without the DYC, both actual and estimated side-slip angles were almost same magnitude and variation. On the other hand, there were some differences of peak values between actual and estimated slide-slip angles with DYC. However, the observer could estimate almost the sideslip angle by using the low-cost yaw rate sensor. 4 R=2.89m (1.6MPa)
R=3.27m (0MPa) 3 2
Y [m]
1 R=2.04m (2.4MPa)
0 -1 -2 -3 -4 -4
-3
-2
-1
0 X [m]
Fig. 10. Comparison of turning radius.
1
2
3
4
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