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Simulation of emergency obstacle avoidance situations using genetic algorithm
158
Technical Notes/JSAE Review 18 (1997) 143-173
Technical Notes
Simulation of emergency obstacle avoidance situations using genetic algorithm Masao Nagai, Minom Onda, Tadahiro Katagiri Tokyo University of Agriculture and Technology, Naka-cho 2-24-16, Koganei-shi, Tokyo, 184 Japan Received 1 October 1996
1. Introduction
When running at high speeds, drivers may panic if they suddenly encounter an obstacle placed on the road. In these situations, drivers react rapidly acting on the brakes and the steering wheel. This paper analyzes the braking and handling characteristics of drivers in emergency situations of obstacle avoidance using a Genetic Algorithm. Depending on the initial distance at which the driver detects the obstacle, the changes of the characteristics of the obstacle avoidance action are analyzed considering the intensity of braking and the non-linearities of tires.
In emergency situations such as emergency obstacle avoidance, the drive steering gain G h and driver preview time Tp are not constant but change with time. Figure 1 shows the structure of the closed-loop vehicle system including the vehicle and driver models. This also shows the process to adapt the varying parameters G h and Tp of the driver model using the Genetic Algorithm. X r represents the relative distance between the vehicle and the obstacle, and it is the variable which determines the present value of parameters G h and Tp.
4. Conditions for emergency obstacle avoidance 2. Vehicle model
The vehicle has been modeled as a three-degrees-offreedom vehicle moving on the horizontal plane. The vehicle has 4 tires (front and rear) each of which develops the longitudinal and lateral forces to generate the dynamical forces and moments acting on the center of gravity of the vehicle. In order to consider the non-linearities of the tires, the well-known "magic formula" for tire modeling has been adopted.
3. Driver model
The driver controlling the motion of the vehicle has been modeled as a first-order transfer function with preview effect as expressed by the following equations:
~d
I + T2S --GhY,, 1 +TIS
y,=ya-(y+VTpO).
The conditions for the simulation of the vehicle in an emergency obstacle avoidance situation are depicted in Fig. 2. The car is running at a speed of 100 k m / h (27.8 m / s ) and suddenly the driver detects an obstacle. It is assumed the driver reacts and controls the vehicle so that the following cost function J is minimized: J = payoff
= f [ a ( Yd-- y)2+ bTw2 + c~2 + db2+ e~Z] d,.
(3)
In Eq. (3), a, b, c, d, and e are positive weighting coefficients, ( Y d - Y) represents the error between the desired trajectory Yd and actual trajectory y, Tw represents the tire working rate and b and fi represent the vehicle lateral and longitudinal accelerations.
5. Genetic algorithm
(1)
(2)
In this study, the relationship between the distance X0, at which the driver first detects the obstacle, the driver steering gain G h, preview time Tp, the intensity of brake
0389-4304/97/$17.00 © 1997 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved PH S 0 3 8 9 - 4 3 0 4 ( 9 6 ) 0 0 0 7 7 - X
JSAE9730713
Technical Notes / J S A E Review 18 (1997) 143-173 Gh,Tp
~ yd + .
I
Gh, Tp and ~ _ _ braking controller trained by GA
Bs. Bt
Or, er mo e,
Isteerin~l
(controller)
Y
Vehicle
o
Fig. 1. Block diagram of the vehicle control system.
V = 27.8m/sec VehicleI,~
Obstacle
Xo m
>[
Fig. 2. Simulation conditions for obstacle avoidance.
B~. and braking time B t are identified individually using
the Genetic Algorithm to minimize the cost function of Eq. (3).
6. Results and discussion
Figures 3(a), (b) and (c) show the trajectory of the vehicle for situations when the driver detects the obstacle at distances X 0 of 28 m, 35 m and 45 m, respectively.
159
From these results it is clear that as the initial distance X 0 is shorter, in order to avoid collision with the obstacle, the trajectory of the vehicle presents overshoot. As the distance X 0 is increased, the overshoot disappears and the trajectory of the vehicle turns to be smooth with fast convergence. Figure 4 shows the working rate of each tire during obstacle avoidance for different initial conditions. From these results it is clear that as the initial distance X 0 is larger, the working rates of tires become smaller. Therefore it is clear that by using the learning method of the Genetic Algorithm to minimize the payoff function of Eq. (3), the security margins of the tires are broadened and at the same time the obstacle is avoided without collision. Figures 5(a), (b) and (c) show the influence of the initial distance X 0 on the driver characteristics during emergency obstacle avoidance. From Figs. 5(a) and (b) it is clear that as the initial distance X 0 is shorter, the driver controls the vehicle with high gain G h and short preview time T~, at the beginning of the collision avoidance action, but controls the vehicle with low gain and long preview time at the end of the action. Also it can be noted that the driver gain G h and preview time Tp almost converge to a fixed value after a short period of time. Therefore the driver controls the vehicle with low gain G h and high preview time Tp for most of the time after the obstacle is detected and the initial obstacle avoidance action is implemented.
(n) whe~l X,=28m
(b) when Xo=35m
f--] (c) whcll X0=45m Fig. 3. Vehicle trajectories during obstacle avoidance.
~-100
- -
b-. "
---
100
front right tire - front left tire - rear right tire rearleft tire
10(3 i i
~" 50
50
,
r r.i .~
5C
'' i t ..,
oi t [secJ (a) when XO= 28m
' 5
0 t [secl (b) when XO = 35m
5
t [sec] (c) when X0 = 45m
Fig. 4. Tire working ratios during obstacle avoidance under different initial conditions.
5
Technical Notes/JSAE Review 18 (1997) 143-173
160
(a)
'il i i i i i i i
Q.140.12-
~
0.I0.08-
From the braking characteristics shown in Fig. 5(c), it is clear that as the initial distance X 0 is shorter, the intensity of braking is high at the beginning of the collision avoidance action. However, if the initial distance X 0 is longer, the intensity of braking is low. This means that the driver takes less care of braking as the initial distance of the obstacle is longer.
0.060.04-
7. Conclusions
0.02
¢5 5 Time
5G
Xo [m]
[sec]
(b)
.,
•
•
:
:
•
2.s
g ~
i
":
.
2 1.5 1 0.5 5 50
]3me
[sac] Obstacle
3O
0
This paper has analyzed the characteristics of drivers in emergency situations of collision avoidance, considering the initial distance X 0, at which the driver discovers the obstacle, as a variable parameter. (1) When the initial distance X 0 is quite short, the collision avoidance action becomes a difficult operation. To overcome this emergency situation, the driver controls the vehicle with high steering gain G h and with low preview time Tp. In this case, both a h and TI, show experiment significant variations. (2) It has been found that for emergency situations (short initial distance X0), appropriate braking can improve the steering characteristics of the collision avoidance action. (3) For situations when the initial distance X 0 is long, it is possible to avoid collision with steering action only.
References
Xo Ira]
[1] N a g a i , M. et al., Simulation of Urgent Obstacle Avoidance Using
(c)
Genetic Algorithm (in Japanese with English summary). Proceedings of J S A E , No. 962 (1996).
101..¸ i 8 ....
~
i
6
"
4
:
i
i
5 T~me [sec]
5O
Xo [m]
Fig. 5. Influences of initial distance on driver characteristics during the emergency obstacle avoidance. (a) Steering gain G h vs. initial distance and time. (b) Preview time Tp vs. initial distance and time. (c) Intensity of braking B s vs. initial distance and time.
Technical Notes/JSAE Review 18 (1997) 143-173
Technical Notes
Simulation of emergency obstacle avoidance situations using genetic algorithm Masao Nagai, Minom Onda, Tadahiro Katagiri Tokyo University of Agriculture and Technology, Naka-cho 2-24-16, Koganei-shi, Tokyo, 184 Japan Received 1 October 1996
1. Introduction
When running at high speeds, drivers may panic if they suddenly encounter an obstacle placed on the road. In these situations, drivers react rapidly acting on the brakes and the steering wheel. This paper analyzes the braking and handling characteristics of drivers in emergency situations of obstacle avoidance using a Genetic Algorithm. Depending on the initial distance at which the driver detects the obstacle, the changes of the characteristics of the obstacle avoidance action are analyzed considering the intensity of braking and the non-linearities of tires.
In emergency situations such as emergency obstacle avoidance, the drive steering gain G h and driver preview time Tp are not constant but change with time. Figure 1 shows the structure of the closed-loop vehicle system including the vehicle and driver models. This also shows the process to adapt the varying parameters G h and Tp of the driver model using the Genetic Algorithm. X r represents the relative distance between the vehicle and the obstacle, and it is the variable which determines the present value of parameters G h and Tp.
4. Conditions for emergency obstacle avoidance 2. Vehicle model
The vehicle has been modeled as a three-degrees-offreedom vehicle moving on the horizontal plane. The vehicle has 4 tires (front and rear) each of which develops the longitudinal and lateral forces to generate the dynamical forces and moments acting on the center of gravity of the vehicle. In order to consider the non-linearities of the tires, the well-known "magic formula" for tire modeling has been adopted.
3. Driver model
The driver controlling the motion of the vehicle has been modeled as a first-order transfer function with preview effect as expressed by the following equations:
~d
I + T2S --GhY,, 1 +TIS
y,=ya-(y+VTpO).
The conditions for the simulation of the vehicle in an emergency obstacle avoidance situation are depicted in Fig. 2. The car is running at a speed of 100 k m / h (27.8 m / s ) and suddenly the driver detects an obstacle. It is assumed the driver reacts and controls the vehicle so that the following cost function J is minimized: J = payoff
= f [ a ( Yd-- y)2+ bTw2 + c~2 + db2+ e~Z] d,.
(3)
In Eq. (3), a, b, c, d, and e are positive weighting coefficients, ( Y d - Y) represents the error between the desired trajectory Yd and actual trajectory y, Tw represents the tire working rate and b and fi represent the vehicle lateral and longitudinal accelerations.
5. Genetic algorithm
(1)
(2)
In this study, the relationship between the distance X0, at which the driver first detects the obstacle, the driver steering gain G h, preview time Tp, the intensity of brake
0389-4304/97/$17.00 © 1997 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved PH S 0 3 8 9 - 4 3 0 4 ( 9 6 ) 0 0 0 7 7 - X
JSAE9730713
Technical Notes / J S A E Review 18 (1997) 143-173 Gh,Tp
~ yd + .
I
Gh, Tp and ~ _ _ braking controller trained by GA
Bs. Bt
Or, er mo e,
Isteerin~l
(controller)
Y
Vehicle
o
Fig. 1. Block diagram of the vehicle control system.
V = 27.8m/sec VehicleI,~
Obstacle
Xo m
>[
Fig. 2. Simulation conditions for obstacle avoidance.
B~. and braking time B t are identified individually using
the Genetic Algorithm to minimize the cost function of Eq. (3).
6. Results and discussion
Figures 3(a), (b) and (c) show the trajectory of the vehicle for situations when the driver detects the obstacle at distances X 0 of 28 m, 35 m and 45 m, respectively.
159
From these results it is clear that as the initial distance X 0 is shorter, in order to avoid collision with the obstacle, the trajectory of the vehicle presents overshoot. As the distance X 0 is increased, the overshoot disappears and the trajectory of the vehicle turns to be smooth with fast convergence. Figure 4 shows the working rate of each tire during obstacle avoidance for different initial conditions. From these results it is clear that as the initial distance X 0 is larger, the working rates of tires become smaller. Therefore it is clear that by using the learning method of the Genetic Algorithm to minimize the payoff function of Eq. (3), the security margins of the tires are broadened and at the same time the obstacle is avoided without collision. Figures 5(a), (b) and (c) show the influence of the initial distance X 0 on the driver characteristics during emergency obstacle avoidance. From Figs. 5(a) and (b) it is clear that as the initial distance X 0 is shorter, the driver controls the vehicle with high gain G h and short preview time T~, at the beginning of the collision avoidance action, but controls the vehicle with low gain and long preview time at the end of the action. Also it can be noted that the driver gain G h and preview time Tp almost converge to a fixed value after a short period of time. Therefore the driver controls the vehicle with low gain G h and high preview time Tp for most of the time after the obstacle is detected and the initial obstacle avoidance action is implemented.
(n) whe~l X,=28m
(b) when Xo=35m
f--] (c) whcll X0=45m Fig. 3. Vehicle trajectories during obstacle avoidance.
~-100
- -
b-. "
---
100
front right tire - front left tire - rear right tire rearleft tire
10(3 i i
~" 50
50
,
r r.i .~
5C
'' i t ..,
oi t [secJ (a) when XO= 28m
' 5
0 t [secl (b) when XO = 35m
5
t [sec] (c) when X0 = 45m
Fig. 4. Tire working ratios during obstacle avoidance under different initial conditions.
5
Technical Notes/JSAE Review 18 (1997) 143-173
160
(a)
'il i i i i i i i
Q.140.12-
~
0.I0.08-
From the braking characteristics shown in Fig. 5(c), it is clear that as the initial distance X 0 is shorter, the intensity of braking is high at the beginning of the collision avoidance action. However, if the initial distance X 0 is longer, the intensity of braking is low. This means that the driver takes less care of braking as the initial distance of the obstacle is longer.
0.060.04-
7. Conclusions
0.02
¢5 5 Time
5G
Xo [m]
[sec]
(b)
.,
•
•
:
:
•
2.s
g ~
i
":
.
2 1.5 1 0.5 5 50
]3me
[sac] Obstacle
3O
0
This paper has analyzed the characteristics of drivers in emergency situations of collision avoidance, considering the initial distance X 0, at which the driver discovers the obstacle, as a variable parameter. (1) When the initial distance X 0 is quite short, the collision avoidance action becomes a difficult operation. To overcome this emergency situation, the driver controls the vehicle with high steering gain G h and with low preview time Tp. In this case, both a h and TI, show experiment significant variations. (2) It has been found that for emergency situations (short initial distance X0), appropriate braking can improve the steering characteristics of the collision avoidance action. (3) For situations when the initial distance X 0 is long, it is possible to avoid collision with steering action only.
References
Xo Ira]
[1] N a g a i , M. et al., Simulation of Urgent Obstacle Avoidance Using
(c)
Genetic Algorithm (in Japanese with English summary). Proceedings of J S A E , No. 962 (1996).
101..¸ i 8 ....
~
i
6
"
4
:
i
i
5 T~me [sec]
5O
Xo [m]
Fig. 5. Influences of initial distance on driver characteristics during the emergency obstacle avoidance. (a) Steering gain G h vs. initial distance and time. (b) Preview time Tp vs. initial distance and time. (c) Intensity of braking B s vs. initial distance and time.