Method and apparatus for lateral movement control
A method and apparatus that control lateral movement of a vehicle are provided. The method includes receiving vehicle information and path information of the vehicle, determining a center of vehicle rotation from the vehicle information, minimizing a path tracking error based on the path information of the vehicle, determining a road wheel angle command or a steering torque command using non-linear optimization based on the minimized path tracking error, and controlling an actuator according to the road wheel angle command or steering torque command.
1. A method that controls lateral movement of a vehicle, the method comprising:
receiving vehicle information and path information of the vehicle;
determining a center of vehicle rotation from the vehicle information;
minimizing a path tracking error based on the path information of the vehicle;
determining a road wheel angle command or a steering torque command based on the minimized path tracking error by using non-linear optimization; and
controlling an actuator according to the determined road wheel angle command or steering torque command;
wherein the determining the center of vehicle rotation is performed based on quasi steady-state approximation according to an equation:
O
(
-
b
+
MV
2
a
LC
r
,
L
+
K
us
V
2
δ
)
,
where O is a center of vehicle rotation, a is the vehicle length, b is the vehicle width, M is the vehicle mass, V is the vehicle forward velocity, L is a +b, K us is an understeer gradient, C r is constant corresponding to rear cornering stiffness, and δ corresponds to a road wheel angle command or a steering torque command.
2. The method of claim 1 , wherein the vehicle information comprises one or more from among a vehicle length, a vehicle width, a vehicle mass, a vehicle forward velocity, an understeer gradient, vehicle cornering stiffness, suspension compliance, a current road wheel angle command, and a current steering torque command.
3. The method of claim 1 , wherein the path information comprises coordinates of one or more waypoints the vehicle is to follow for a predetermined distance ahead of the vehicle.
4. The method of claim 1 , wherein the understeer gradient is
K
u
s
=
M
L
(
b
C
f
-
a
C
𝓇
)
,
determined according to the equation where C f corresponds to front cornering stiffness.
5. The method of claim 1 , wherein the minimizing the path tracking error comprises setting a control goal according to a cost function J(δ)=J L +J φ →min, where J L corresponds to a cost associated with a radial distance error, J φ corresponds to a cost associated with heading error, and δ corresponds to a road wheel angle command or a steering torque command.
6. The method of claim 1 , wherein the determining the road wheel angle command or the steering torque command based on the minimized path tracking error comprises using one-dimensional scalar function minimization.
7. The method of claim 1 , wherein the controlling the actuator according to the road wheel angle command or the steering torque command comprises setting an electronic power steering module according to the road wheel angle command or according to the steering torque command.
8. A method that controls lateral movement of a vehicle, the method comprising:
receiving vehicle information and path information of the vehicle;
determining a center of vehicle rotation from the vehicle information;
minimizing a path tracking error based on the path information of the vehicle;
determining a road wheel angle command or a steering torque command based on the minimized path tracking error by using non-linear optimization; and
controlling an actuator according to the determined road wheel angle command or steering torque command;
wherein the minimizing the path tracking error comprises setting a control goal according to a cost function J(δ)=J L +J φ →min, where J L corresponds to a cost associated with a radial distance error, J 100 , corresponds to a cost associated with heading error, and δ corresponds to a road wheel angle command or a steering torque command;
wherein J L is determined according to an equation
1
N
∑
j
=
1
N
w
j
Δ
L
i
2
,
where N is a total number of waypoints, j corresponds to a waypoint, w j corresponds to a weight for a radial distance error, ΔL i corresponds to a radial distance error.
9. A method that controls lateral movement of a vehicle, the method comprising:
receiving vehicle information and path information of the vehicle;
determining a center of vehicle rotation from the vehicle information;
minimizing a path tracking error based on the path information of the vehicle;
determining a road wheel angle command or a steering torque command based on the minimized path tracking error by using non-linear optimization; and
controlling an actuator according to the determined road wheel angle command or steering torque command;
wherein the minimizing the path tracking error comprises setting a control goal according to a cost function J(δ)=J L +J φ →min, where J L corresponds to a cost associated with a radial distance error, L φ , corresponds to a cost associated with heading error, and δ corresponds to a road wheel angle command or a steering torque command;
wherein J φ is determined according to an equation
1
N
∑
j
=
1
N
w
j
ϕ
Δϕ
i
2
,
where N is a total number of waypoints, j corresponds to a waypoint, w j ϕ corresponds to a weight for the heading error, Δϕ i corresponds to the heading error.
10. An apparatus that controls lateral movement of a vehicle, the apparatus comprising:
at least one memory comprising computer executable instructions; and
at least one processor configured to read and execute the computer executable instructions, the computer executable instructions causing the at least one processor to:
receive vehicle information and path information of the vehicle;
determine a center of vehicle rotation from the vehicle information;
minimize a path tracking error based on the path information of the vehicle;
determine a road wheel angle command or a steering torque command based on the minimized path tracking error by using non-linear optimization; and
control an actuator according to the determined road wheel angle command or steering torque command;
wherein the path information comprises coordinates of one or more waypoints the vehicle is to follow for a predetermined distance ahead of the vehicle; and
wherein the computer executable instructions cause the at least one processor to determine the center of vehicle rotation is performed based on quasi steady-state approximation according to an equation:
O
(
-
b
+
MV
2
a
LC
r
,
L
+
K
us
V
2
δ
)
,
where O is a center of vehicle rotation, a is the distance between vehicle center of gravity and front axle, b is the distance between vehicle center of gravity and rear axle, M is the vehicle mass, V is the vehicle forward velocity, L is a +b, K us is an understeer gradient, C r is constant corresponding to cornering stiffness, and δ corresponds to a road wheel angle command or a steering torque command.
11. The apparatus of claim 10 , wherein the vehicle information comprises one or more from among a vehicle length, a vehicle width, a vehicle mass, a vehicle forward velocity, an understeer gradient, vehicle cornering stiffness, a suspension compliance, a current road wheel angle command, and a current steering torque command.
12. The apparatus of claim 10 , wherein the understeer gradient is determined according to the equation
K
u
s
=
M
L
(
b
C
f
-
a
C
𝓇
)
,
where C f corresponds to front cornering stiffness.
13. The apparatus of claim 12 , wherein the computer executable instructions cause the at least one processor to minimize the path tracking error by setting a control goal according to a cost function J(δ)=J L +J φ →min, where J L corresponds to a cost associated with a radial distance error, J φ corresponds to a cost associated with heading error, and δ corresponds to a road wheel angle command or a steering torque command.
14. The apparatus of claim 13 , wherein J L is determined according to an equation
1
N
∑
j
=
1
N
w
j
Δ
L
i
2
,
where N is the total number of waypoints, j corresponds to a waypoint, w j corresponds to a weight for a radial distance error, ΔL i corresponds to a radial distance error.
15. The apparatus of claim 13 , wherein J φ is determined according to an equation
1
N
∑
j
=
1
N
w
j
ϕ
Δϕ
i
2
,
where N is the total number of waypoints, j corresponds to a waypoint, w j ϕ corresponds to a weight for the heading error, Δϕ i corresponds to the heading error.
16. The apparatus of claim 10 , wherein the computer executable instructions cause the at least one processor to determine the road wheel angle command or the steering torque command based on the minimized path tracking error by using one-dimensional scalar function minimization.
17. The apparatus of claim 10 , further comprising an electronic power steering module,
wherein the computer executable instructions cause the at least one processor to set the electronic power steering module according to the road wheel angle command or the steering torque command.
18. A method that controls lateral movement of a vehicle, the method comprising:
receiving vehicle information and path information of the vehicle;
determining a center of vehicle rotation from the vehicle information based on a quasi steady-state approximation;
minimizing a path tracking error based on the path information of the vehicle;
determining a road wheel angle command or a steering torque command based on the minimized path tracking error by using non-linear optimization; and
controlling an actuator according to the determined road wheel angle command or steering torque command;
wherein the minimizing the path tracking error comprises setting a control goal according to a cost function J(δ)=J L +J φ →min, where J L corresponds to a cost associated with a radial distance error, J φ corresponds to a cost associated with heading error, and δ corresponds to a road wheel angle command or a steering torque command;
wherein J L is determined according to an equation
1
N
∑
j
=
1
N
w
j
Δ
L
i
2
,
where N is a total number of waypoints, j corresponds to a waypoint, w j corresponds to a weight for a radial distance error, ΔL i corresponds to a radial distance error; and
wherein J φ is determined according to an equation
1
N
∑
j
=
1
N
w
j
ϕ
Δ
ϕ
i
2
,
where N is a total number of waypoints, j corresponds to a waypoint, w j ϕ corresponds to a weight for the heading error, Δϕ i corresponds to the heading error.