Modeling, Validation and Firing-On The - Move Control of Armored Vehicles Using Active Front-Wheel Steering
Modeling, Validation and Firing-On The - Move Control of Armored Vehicles Using Active Front-Wheel Steering
Modeling, Validation and Firing-On The - Move Control of Armored Vehicles Using Active Front-Wheel Steering
Technology
Abstract
It is a well-known fact that an armored vehicle will lose its directional stability when firing a large-caliber gun while mov-
ing. The instability is caused by the impulse force from firing, acting at the center of a weapons platform that produces a
yaw moment at the center of gravity of the armored vehicle. In order to improve the stability, this paper introduces a fir-
ing-on-the-move technology for armored vehicles using an active front-wheel steering (AFS) system. The AFS system is
proposed to maintain the directional stability of the armored vehicle by providing an electronically controlled correction
to the steering mechanism. The steering correction is designed to reject the unwanted yaw motion and bring the vehicle
back to its intended direction of travel after firing. The proposed control strategy of the AFS system in this study con-
sists of yaw rate feedback with lateral force rejection control. The AFS system controller is developed on a validated
10-degrees-of-freedom armored vehicle. The results indicate that the developed control strategy can effectively maintain
the directional stability, in terms of yaw and lateral motions, of the armored vehicle after firing. The superiority of the
proposed AFS system controller is also evaluated by comparing its performance to an AFS system without lateral force
rejection control as well as to a conventional armored vehicle without AFS.
Keywords
10-degrees-of-freedom armored vehicle model, firing on the move, active front-wheel steering, lateral force rejection
control
1. Introduction
From a vehicle dynamics point of view, vehicle yaw unwanted yaw rejection mechanisms has been conducted
motion can be divided into two categories, the desired yaw in both academic communities and automotive indus-
motion and the unwanted yaw motion. Desired yaw motion tries.1–3 Various methods and actuators in yaw stability
occurs when the direction of travel of the vehicle follows systems have been developed, such as the traction-control
the steering input from the driver, for example in a corner- system,4,5 anti-lock braking system,6,7 four-wheel steering
ing maneuver. In contrast, an unwanted yaw motion occurs
when a vehicle begins to move out of its lane without any 1
Department of Mechanical Engineering, Faculty of Engineering, Universiti
steering action from the driver. Side wind force, uneven
Pertahanan Nasional Malaysia, Malaysia
braking or throttle torques in all four wheels as well as 2
Malaysia-Japan International Institute of Technology, Universiti Teknologi
non-uniform tire grip in all four tires are the major factors Malaysia, Malaysia
causing the vehicle to yaw unintentionally. Unwanted yaw
motion can cause vehicle accidents, as the directional sta- Corresponding author:
Zulkiffli Abd Kadir, Department of Mechanical Engineering, Faculty of
bility of the vehicle decreases abruptly and the driver may Engineering, Universiti Pertahanan Nasional Malaysia, Kem Sungai Besi,
lose control of the vehicle. Considering the importance of 57000, Kuala Lumpur, Malaysia.
yaw stability in a vehicle, research on the development of Email: zulkiffli@upnm.edu.my
controls,8–11 electronic stability program12,13 and active In this study, the proposed control strategy of the AFS
front-wheel steering (AFS) system.14 system for firing on the move consists of an outer loop
In an armored vehicle, unwanted yaw motion can be controller and inner loop controller. The aim of designing
caused by the firing impulse acting on the center of the the outer loop controller is to reduce the magnitude of
weapon platform. The firing impulse will generate yaw unwanted motions due to firing force, namely, the yaw
moment and lateral force at the body center of gravity and lateral motions. The inner loop controller is used to
(CG), causing the armored vehicle to move out of its provide a steering correction angle using the stepper motor
intended path, as shown in Figure 1. The technology that based on the instruction obtained from an outer loop con-
is used in most armored vehicles requires static condition troller. The proposed control strategy is developed using a
during firing because it is unable to maintain the vehicle validated 10-degrees-of-freedom (10-DOF) four-wheeled
directional stability if firing is executed during moving armored vehicle (4WAV) model. The developed model of
condition. Unfortunately, firing in static condition during the armored vehicles comprises of the 3-DOF 4WAV han-
battle reduces agility and potentially makes the armored dling model engaged with a nonlinear tire model—the
vehicle an easy target for a counterattack. Therefore, in Calspan tire model and the 7-DOF 4WAV ride model.
order to improve the mobility of the armored vehicle, the Validation was performed using a Ferret Scout Car for
involvement of yaw stability control that makes the vehi- several driving conditions such as the step steer test,
cle able to shoot during moving is a necessity. This paper single-lane change test and double-lane change test. The
investigates a firing-on-the-move method using an AFS responses obtained from actual handling tests are used as a
system in order to reject the unwanted yaw motion and lat- benchmark for model validation of the 10-DOF armored
eral motion subject to gun disturbance. The goal of imple- vehicle model. Then, the proposed control strategy for fir-
menting the AFS system is to maintain the handling ing on the move, namely, the yaw rate feedback with lat-
quality and directional stability of the armored vehicle by eral force rejection control (LFRC), is developed on this
retaining the armored vehicle in its direction of travel dur- validated model.
ing firing on the move. This paper is structured as follows: the next section
The AFS system maintains the conventional mechani- focuses on the mathematical derivation of the 10-DOF
cal link between the front wheels and the steering wheel. 4WAV model. Section 3 shows the development of the
A planetary gear set, which has two input shafts connected proposed control strategy for firing-on-the-move technol-
to the steering shaft and a stepper motor, is the one that ogy with AFS. Section 4 discusses the model validation
delivers the variation of the steering ratio in the AFS sys- results of the 10-DOF 4WAV model, followed by the ben-
tem. The final steering ratio of the AFS system is basically efits of the proposed AFS system in an armored vehicle in
the superposition between the driver input delivered via a Section 5. Overall conclusions are discussed in Section 6.
steering shaft and the steering input actuated by the step-
per motor. The AFS system is also able to generate a cor-
rective steering response, directly enhancing the vehicle 2. The 10-degrees-of-freedom armored
yaw motion. The basic concept of AFS for firing on the vehicle model
move in an armored vehicle is to provide an immediate
steering correction to reject the unwanted yaw motion due The 10-DOF model of a 4WAV presented in this study
to firing force. The steering correction, which is electroni- contains the 7-DOF 4WAV ride model and the 3-DOF
cally controlled using a direct current (DC) motor, is then 4WAV handling model. The 7-DOF 4WAV ride model
overlapped with the conventional steering input via the contains the 3-DOF armored vehicle body motions, which
planetary gear set. allow the vehicle to pitch, roll and heave. The armored
ms Z€s = Fsfl + Fdfl + Fsfr + Fdfr + Fsrl + Fdrl + Fsrr + Fdrr ð1Þ
where
Figure 2. A two-dimensional view of a four-wheeled armored
vehicle. ms = weight of sprung mass;
Z€s = vertical acceleration of sprung mass at the CG;
Fsfr = front right spring force = Ksfr (Zufr Zsfr );
Fsrl = rear left spring force = Ksrl (Zurl Zsrl );
Fsrr = rear right spring force = Ksrr (Zurr :
Zsrr);
:
Fdfl = front left damper force = Csfl ( Z ufl :
Z sfl);
:
Fdfr = front right damper force = Csfr:( Z ufr : Z sfr);
Fdrl = rear left damper force = Csrl ( Z url :
Z srl);
:
Fdrr = rear right damper force = Csrr ( Z urr Z srr);
Ksfl , Ksfr , Ksrl , Ksrr = spring stiffness at the front left,
front right, rear left and rear right;
Csfl , Csfr , Csrl , Csrr = damping stiffness at the front left,
front right, rear left and rear right;
Zsfl , Zsfr , Zsrl , Zsrr = sprung masses displacement at the
front left, front right, rear left and rear right;
Figure 3. A 7-degrees-of-freedom four-wheeled armored
vehicle ride model.
Zufl , Zufr , Zurl , Zurr = unsprung masses displacement at
the front left, front right, rear left and rear right;
vehicle body is mounted to four unsprung masses at each Z_ sfl , Z_ sfr , Z_ srl , Z_ srr = sprung masses velocity at the front
corner. Each unsprung mass is permitted to heave in the left, front right, rear left and rear right;
vertical direction. The 3-DOF 4WAV handling model con- Z_ ufl , Z_ ufr , Z_ url , Z_ usrr = unsprung masses velocity at the
siders the vehicle longitudinal, lateral and yaw motions at front left, front right, rear left and rear right.
the respective axes. The equation of motion for roll moment is given as
w
2.1 Ride model for armored vehicle € = Fsfr + Fsrr + Fdfr + Fdrr
Ir u
2 ð2Þ
w
The 4WAV considered in this study, as illustrated in Fsfl + Fsrl + Fdfl + Fdrl + ms ay hCG
Figure 2, is based on a category of a movable weapon sys- 2
tem that has four wheels and can fire a 75-mm projectile where
from the gun turret, while the 4WAV ride model is shown
in Figure 3. There are several assumptions that need to be u
€ = angular acceleration of roll at the body CG;
considered in developing the 7-DOF 4WAV ride model. Ir = moment inertia of the roll axis;
The first assumption is that the suspensions system is hCG = distance from the roll axis to the CG;
modeled simply as a combination of spring and damper w= vehicle track width;
elements. The second assumption is that the effect of the ay = lateral acceleration.
passive anti-roll bar for vehicle rolling resistance is taken Similarly, the moment balance equation for pitch
into account in the mass moment of inertia in the x-axis. motion is given as
The tire behavior is also assumed as a linear spring and
the vehicle remains grounded at all times so that each tire Ip θ€ = (Fsrl + Fdrl + Fsrr + Fdrr )b
is constantly touching the road surface during maneuver- ð3Þ
(Fsfl + Fdfl + Fsfr + Fdfr )a + ms ax hCG
ing. The last assumption is that the position of the suspen-
sion system is always in vertical direction. where
The 4WAV ride model contains the armored vehicle
body, four suspension systems and the corresponding tires. θ€ = angular acceleration of pitch at the body CG;
The 3-DOF body motions are the armored vehicle heave, Ip = moment inertia of the pitch axis;
w w
Zsfr = Zs + u aθ Z_ sfr = Z_ s + u_ aθ_
2 2
w w
Zsfl = Zs u aθ Z sfl = Z s u_ aθ_
_ _
2 2 ð4Þ
w w
Zsrr = Zs + u + bθ Z_ srr = Z_ s + u_ + bθ_
2 2
w w
Zsrl = Zs u + bθ Z srl = Z s u_ + bθ_
_ _
2 2
where u and θ are armored vehicle roll angle and body Figure 4. Armored vehicle handling model with firing
pitch angle at the CG, respectively. The equation of motion disturbance.
for unsprung masses at each corner can be obtained using
force balance analysis as follows: surface where the gradient is equal to zero. Secondly, the
military vehicle is assumed to capable of moving along the
mufl Z€ ufl = Ftfl Fsfl Fdfl longitudinal and lateral directions and to rotate in the
z-axis. Thirdly, the steering wheel angle and the wheel
mufr Z€ ufr = Ftfr Fsfr Fdfr steer angle are modeled as a constant ratio, while the steer-
ð5Þ
murl Z€ url = Ftrl Fsrl Fdrl ing inertia is neglected in the model. Lastly, the effect of
murr Z€ urr = Ftrr Fsrr Fdrr aerodynamic in the horizontal direction is ignored and the
armored vehicle is assumed to travel with constant speed,
where while the effect of longitudinal slip is ignored. The longi-
tudinal acceleration and lateral acceleration in the x- and
Ftfl = tire force at the front left = Ktfl Zrfl Zufl ; y-axes are written as ax and ay, respectively, and the yaw
Ftfr = tire force at the front right = Ktfr Zrfr Zufr ; acceleration as €r. Acceleration in the longitudinal direction
Ftrl = tire force at the rear left = Ktrl ðZrrl Zurl Þ; is written as
Ftrr = tire force at the front left = Ktrr ðZrrr Zurr Þ;
Ktfr , Ktfl , Ktrr , Ktrl = tire stiffness at the front right, front v_ x = ax + vy r_ ð6Þ
left, rear right and rear left;
mufr , mufl , murr , murl = unsprung masses at the front The longitudinal acceleration can be obtained by con-
right, front left, rear right and rear left. sidering the forces acting at each tire in the x-axis as
0 1
w2 Fxfr cos δ + w2 Fxfl cos δ w2 Fxrr + w2 F xrl + w2 Fyfl sin δ
@ w Fyfr sin δ bFyrl bFyrr + aFyfl cos δ + aFyfr cos δ aFxfl sin δ A = Iz€r ð10Þ
2
aFxfr sin δ + cFe sin β
where
where Mp is the mass of the projectile, vo is the initial
I z = moment of inertia around the z-axis; speed of the projectile, vf is the speed of the projectile
δ = wheel steer angle; leaving the muzzle and t is the time required by the pro-
m = armored vehicle mass. jectile to obtain its maximum speed at the muzzle. To
After obtaining the three main vehicle dynamic para- evaluate the performance of the proposed control strategy,
meters of the military vehicle (i.e., longitudinal accelera- the firing force is defined as a step function produced by a
tion, lateral acceleration and yaw angular acceleration), the 75-mm caliber gun, as shown in Figure 5. In this study,
parameters are then used to estimate the slip angle of front the firing angles are set in 30°, 60° and 90° to the right-
tire (αf ) and rear tire (αr ) as follows: hand side of the armored vehicle.
vy + a_r
tan αf = δ ð11Þ 3. Basic configuration and proposed
vx
control strategy of active front-wheel
and steering for a four-wheeled armored
vehicle
vy b_r
tan αr = ð12Þ The AFS for a 4WAV is built by retaining the conven-
vx
tional mechanical parts, such as the steering wheel, the
where vx , vy and r_ are the longitudinal velocity, the lateral steering shaft, the recirculating ball gearbox, the pitman
velocity and the yaw rate of the armored vehicle, arm and the steering arms. In AFS, there are two angles
which are obtained by the integration of v_ y , v_ x and €r, that need to be evaluated: the steering wheel input given
respectively. by the driver and steering correction angle produced by
the controller and actuated by the AFS actuator, as illu-
2.3 Firing force model strated in Figure 6. There is an additional gearbox between
The firing force acting at the gun platform can be the steering shaft and AFS actuator to superimpose the
explained using the relationship of impulse and momen- steering wheel angle obtained from the driver and angle of
tum. Impulse can be used as a basic concept to estimate steering correction from the AFS actuator. The combina-
the linear momentum of firing force obtained from tions of both angles provide a correction angle for wheel
the projectile based on the mass and velocity of the steer angle through the pitman arm.
projectile.15 The correlation between the impulse and The control strategy is developed using a validated 10-
momentum of the projectile leaving a muzzle can be writ- DOF 4WAV model by assuming that the armored vehicle
ten as travels in a straight direction without any steering input
given by the driver. The control strategy of AFS consists
(vf vo ) of an inner loop controller and an outer loop controller, as
Fe = M p ð13Þ
t
15000
Firing force
10000
5000
0
0 0.5 1 1.5 2 2.5
Time (s)
Figure 7. Control strategy of the active front-wheel steering for a four-wheeled armored vehicle.
100
Experiment
80 Simulation
Steering angle (deg)
0.1
40 0.05
20
0 0
0 2 4 6 8 10 0 2 4 6 8 10
Time (s) Time (s)
(a) Steering wheel angle (b) Yaw rate response
0.01
0.02
0.005
0 0
0 2 4 6 8 10 0 2 4 6 8 10
Time (s) Time (s)
(c) Lateral acceleration respons e (d) Roll angle response
reduce the roll motion response of the armored vehicle the driver in maintaining a constant speed for both actual
body. For yaw rate and lateral acceleration responses, bet- handling tests. It also can be due to the assumption in
ter similarity in the responses are shown starting from the simulation where the steering inertia is neglected. For the
initial phase until the steering input is introduced to the overall validation results, it is clear that the behaviors
armored vehicle. It also can be seen that the data of the obtained from the simulation works and the experimental
experimental results contains some chattering caused by works for the three tests have similar responses with
the effect of the actual road profile and the engine vibra- acceptable error. The validated armored vehicle model is
tions. Noise and data chattering from experimental works then used to assess the performance of the proposed con-
can be removed using a correct filtering technique. trol strategy of the AFS system in Section 5.
To ensure that the developed model is valid in repre-
senting the actual 4WAV, the model validation is also
performed for the 30 km/h single-lane change test and 5. Performance evaluation of the proposed
40 km/h double-lane change test. The results of the valida- control strategy for active front-wheel
tion for the single-lane change and double-lane change steering
tests show that the results from actual data and the simula-
tion results have good correlation, as can be seen in The investigation on the performance of the proposed con-
Figures 11 and 12, respectively. Figures 11(a) and 12(a) trol strategy for AFS with an additional LFRC loop is pre-
show the actual steering input delivered by the driver in sented in this section. Responses obtained from the passive
single-lane change and double-lane change tests. The vali- armored vehicle are set as the basic benchmark for perfor-
dation results for the single- and double-lane change tests mance evaluation of the proposed control strategy. To
(i.e., the lateral acceleration, yaw rate and roll angle evaluate the benefit of additional LFRC, comparison
responses) show that the results obtained from simulation between the behaviors of the proposed control strategy and
are able to track the actual maneuver results with similar AFS without a LFRC loop is made. This section starts by
trends and magnitudes, as demonstrated in Figures 11(b)– explaining the selection of the parameters of the armored
(d) as well as 12(b)–(d), respectively. The small deviations vehicle and proposed control strategy parameter used in
in the validation results might be caused by the problem of the simulation work, as well as demonstrating the AFS
0.3 Experiment
100 Simulation
Steering angle (deg) 0.2
Simulation Simulation
0.1 0.05
0.4
100 Experiment
Steering angle (deg)
0.2 Simulation
Yaw rate (rad/s)
50
0 0
-50 -0.2
-100 -0.4
-150
-0.6
-200
0 2 4 6 8 10 0 2 4 6 8 10
Time (s) Time (s)
0 0
-0.2
-0.1
-0.4
-0.6 -0.2
-0.8 -0.3
0 2 4 6 8 10 0 2 4 6 8 10
Time (s) Time (s)
(c) Lateral acceleration response (d) Roll angle response
30 deg
performance in various firing angles at a constant speed of -10 60 deg
40 km/h. The proposed control strategy for AFS is tested 90 deg
for its performance in enhancing both lateral motion and 0 0.5 1 1.5 2 2.5
yaw motion of the armored vehicle after firing in terms of time (s)
several performance characteristics: lateral acceleration,
lateral position, yaw rate and yaw angle. Figure 13. Steering correction angles for 30°, 60° and 90°.
0 0.15
0.1
-0.1
0.05
-0.2 0
0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5
Time (s) Time (s)
(a) Lateral acceleration for 30deg firing angle (b) Lateral position for 30deg firing angle
0.5
AFS without LFRC AFS without LFRC
0.4 0.6
AFS without LFRC AFS without LFRC
Lateral displacement (m)
Lateral acceleration (g)
0 0.3
0.2
-0.2
0.1
-0.4 0
0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5
Time (s) Time (s)
(e) Lateral acceleration for 90deg firing angle (f) Lateral position for 90deg firing angle
Figure 14. Lateral motion responses of active front-wheel steering (AFS) for various firing angles.
to increase the target accuracy as well as decrease the per- angle error for AFS with LFRC is very small and can be
centage of human faults during firing on the move. neglected. The capability of AFS with LFRC to retain the
For yaw angle response, the performance of AFS with directional stability after firing with various firing angles
LFRC shows an excellent response compared to AFS is also observed. The ability of the proposed control strat-
without LFRC and the armored vehicle equipped with a egy in cancelling out the magnitude of the yaw angle can
passive steering system by canceling out the yaw angle enhance the handling quality of the armored vehicle in the
error, which has the capability to return back to its desired presence of firing disturbances while moving. Since the
direction of travel after firing. From the results obtained, it yaw rate and yaw angle responses of AFS with LFRC
also can be seen that the maximum magnitude of yaw show better improvement using the proposed control
0.025 0.012
AFS without LFRC AFS without LFRC
0.02 AFS with LFRC 0.01 AFS with LFRC
0.01 0.006
0.004
0.005
0.002
0
0
0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5
Time (s) Time (s)
(a) Yaw rate for 30deg firing angle (b) Yaw angle for 30deg firing angle
0.02 0.01
0.01
0.005
0
0
0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5
Time (s) Time (s)
(c) Yaw rate for 60deg firing angle (d) Yaw angle for 60deg firing angle
Figure 15. Yaw motion responses of active front-wheel steering (AFS) for various firing angles.
strategy, the possibility of the developed control strategy firing at angles of 30°, 60° and 90° at 40 km/h. The com-
improving the target accuracy during firing on the move parison of armored vehicle responses is used to demon-
also can be achieved. strate the usefulness of the developed control strategy to
Figures 16 (a)–(d) show the detailed responses of the reduce unwanted yaw motion and unwanted lateral motion
proposed control strategy, namely, AFS with LFRC, in in any firing angles. It is very clear that the proposed con-
enhancing the dynamic qualities of an armored vehicle for trol strategy can improve the armored vehicle dynamic
0.4 0.2
30 deg
60 deg 60 deg
0.2 90 deg 0.15 90 deg
0 0.1
-0.2 0.05
-0.4 0
0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5
Time (s) Time (s)
(a) Lateral acceleration response (b) Lateral displacement response
-3 -3
x 10 x 10
2
30 deg 30 deg
4
Yaw rate (rad/s)
Figure 16. Active front-wheel steering with lateral force rejection control responses.
qualities during firing with various firing angles. The max- steering system. The need of LFRC to the yaw rate feed-
imum unwanted yaw moment acting on the weapon plat- back is strongly proven compared to AFS without LFRC.
form occurs at the 90° firing angle. Overall, it can be said that AFS with LFRC of the armored
vehicle application in firing-on-the-move technology sig-
nificantly improves the stability level of the armored vehi-
6. Conclusion cle by lowering the magnitudes of lateral acceleration,
lateral displacement and yaw rate, as well as eliminating
A 10-DOF 4WAV model has been developed using
the yaw angle after firing. Enhancement of armored vehi-
MATLAB-Simulink and validated experimentally through
cle stability will reduce the risk of the driver losing control
the step steer, single-lane change and double-lane change
caused by firing action, as well as increase the firing
handling tests. The validation results of yaw rate response,
accuracy.
lateral acceleration response and roll angle response show
that the responses of the developed armored vehicle model
are able to track the behaviors of an actual armored vehi- Acknowledgments
cle measured by several sensors. From the model valida- The authors would like to thank the Malaysian Ministry of
tion results, it can be said that the developed armored Education through LRGS (LRGS/B-U/2013/UPNM/
vehicle model can be used to simulate armored vehicle DEFENCE & SECURITY-P1), the Institut Kejuruteraan
responses in any maneuvering tests. In terms of armored
Tentera Darat (IJED)and the Malaysia-Japan
vehicle responses of the proposed control strategy, it can
be concluded that the performance of the AFS with LFRC International Instituteof Technology (MJIIT) for the use
is able to reduce and eliminate the unwanted yaw and of their research facilitiesfor this research.
Declaration of conflicting interest
lateral motions in all the selected firing angles compared
with the armored vehicle equipped with the passive The authors declare that there is no conflict of interest.
Regimental Workshop and Commanding Officer 73rd Nopember (ITS), Indonesia in 2007 and his master’s
Divisional Workshop. He has also held various staff posi- degree in mechanical engineering from Universiti
tions in areas including EME Staff Officer 12th Infantry Teknikal Malaysia Melaka (UTeM), Malaysia in 2010. He
Brigade, EME Staff Officer Grade One 2nd Infantry obtained his doctorate in the field of smart materials and
Division, Engineering Staff Officer Grade One of Policy actuator design from Universiti Teknologi Malaysia
Division, Defence Logistics Department in Ministry of (UTM) in 2015. He is currently a researcher in the
Defence, Malaysia, and is currently seconded from the Vehicle System Engineering Research Laboratory of the
Malaysian Armed Forces to the UPNM. His research Malaysia-Japan International Institute of Technology at
interests include armored vehicle vibrations and dynamics UTM. His research interests are in the area of advanced
modeling. actuator and intelligent system designs.