System and methods of integrating vehicle kinematics and dynamics for lateral control feature at autonomous driving
An apparatus includes at least one camera configured to capture an image of a traffic lane in front of a vehicle. The apparatus also includes a path tracking controller configured to detect lane boundaries and a path curvature for the traffic lane from the image, determine a lateral offset of the vehicle from a reference path for the traffic lane and a heading offset for the vehicle from the path curvature, determine a yaw rate maintaining the vehicle within the traffic lane using a kinematics control, determine a steering angle maintaining the vehicle within the traffic lane using a dynamics control and the yaw rate determined by the kinematics control, and activate a steering control based on the determined steering angle.
1. An apparatus, comprising:
at least one camera configured to capture an image of a traffic lane in front of a vehicle; and
a path tracking controller configured to:
detect lane boundaries and a path curvature for the traffic lane from the image,
determine a lateral offset of the vehicle from a reference path for the traffic lane and a heading offset for the vehicle from the path curvature,
using a kinematics control, determine a yaw rate that will maintain the vehicle within the traffic lane based on one or more of a vehicle forward velocity, a relative course angle based on a heading offset for the vehicle, the path curvature, the lateral offset of the vehicle, or feedback from a dynamics control,
using the dynamics control and the yaw rate determined by the kinematics control, determine a steering angle that will maintain vehicle within the traffic lane, and
activate a steering control based on the determined steering angle.
2. The apparatus according to claim 1 , wherein the yaw rate ω d maintaining the vehicle within the traffic lane is determined from:
ω
d
=
η
v
cos
(
θ
)
+
v
κ
cos
(
θ
)
1
-
κ
r
,
where v is the vehicle forward velocity, θ is the relative course angle based on the heading offset for the vehicle, κ is the path curvature, r is the lateral offset of the vehicle, and η is the feedback from the dynamics control.
3. The apparatus according to claim 2 , wherein the determined steering angle is derived from:
{dot over (χ)}= A χ +B 1 u+B 2 ω d +B 3 sin(ϕ),
where {dot over (χ)} is the first derivative of χ=[e 1 ė 1 e 2 ė 2 ], e 1 =r is the lateral offset of the vehicle, ė 1 is the first derivative of e 1 , e 2 is a relative yaw angle of the vehicle, ė 2 is the first derivative of e 2 , and A, B 1 , B 2 and B 3 are parameters determined by one of pole placement or linear-quadratic regulation.
4. The apparatus according to claim 1 , wherein the kinematics control is configured to receive, as inputs, the lateral offset r of the vehicle from the reference path and the heading offset Δψ of vehicle heading from the path curvature.
5. The apparatus according to claim 4 , wherein the dynamics control is configured to receive, as inputs, the lateral offset r, the first derivative {dot over (r)} of the lateral offset r, the heading offset Δψ, and the first derivative Δ{dot over (ψ)} of the heading offset Δψ.
6. The apparatus according to claim 1 , wherein the dynamics control is configured to output a steering angle δ f to the steering control, and wherein the steering control is configured to generate a steering command.
7. The apparatus according to claim 1 , wherein the path tracking controller is configured to generate a braking command based on a speed of the vehicle and the determined steering angle.
8. The apparatus according to claim 7 , wherein the path tracking controller is configured to generate the braking command when the speed of the vehicle exceeds a predetermined safety limit for the determined steering angle.
9. A vehicle comprising the apparatus according to claim 1 , the vehicle further comprising:
a motor configured to drive wheels of the vehicle;
a chassis supporting axles on which the wheels are mounted, the steering control configured to generate a steering command controlling the wheels based on the determined steering angle; and
a brake actuator configured to actuate brakes for one or more of the wheels, the brake actuator configured to receive a braking control signal based on an output of the path tracking controller.
10. The vehicle according to claim 9 , wherein the vehicle is an electric vehicle and the motor is an electric motor.
11. A method, comprising:
capturing an image of a traffic lane in front of a vehicle using at least one camera; and
detecting lane boundaries and a path curvature for the traffic lane from the image;
determining a lateral offset of the vehicle from a reference path for the traffic lane and a heading offset for the vehicle from the path curvature;
using a kinematics control, determining a yaw rate that will maintain the vehicle within the traffic lane based on one or more of a vehicle forward velocity, a relative course angle based on a heading offset for the vehicle, the path curvature, the lateral offset of the vehicle, or feedback from a dynamics control;
using the dynamics control and the yaw rate determined by the kinematics control, determining a steering angle that will maintain the vehicle within the traffic lane; and
activating a steering control based on the determined steering angle.
12. The method according to claim 11 , wherein the yaw rate ω d maintaining the vehicle within the traffic lane is determined from:
ω
d
=
η
v
cos
(
θ
)
+
v
κ
cos
(
θ
)
1
-
κ
r
,
where v is the vehicle forward velocity, θ is the relative course angle based on the heading offset for the vehicle, κ is the path curvature, r is the lateral offset of the vehicle, and η is feedback from the dynamics control.
13. The method according to claim 12 , wherein the determined steering angle is derived from:
{dot over (χ)}= A χ +B 1 u+B 2 ω d +B 3 sin(ϕ),
where {dot over (χ)} is the first derivative of χ=[e 1 ė 1 e 2 ė 2 ], e 1 =r is the lateral offset of the vehicle, ė 1 is the first derivative of e 1 , e 2 is a relative yaw angle of the vehicle, ė 2 is the first derivative of e 2 , and A, B 1 , B 2 and B 3 are parameters determined by one of pole placement or linear-quadratic regulation.
14. The method according to claim 11 , wherein the kinematics control is configured to receive, as inputs, the lateral offset r of the vehicle from the reference path and the heading offset Δψ of vehicle heading from the path curvature.
15. The method according to claim 14 , wherein the dynamics control is configured to receive, as inputs, the lateral offset r, the first derivative {dot over (r)} of the lateral offset r, the heading offset Δψ, and the first derivative Δ{dot over (ψ)} of the heading offset Δψ.
16. The method according to claim 11 , wherein the dynamics control is configured to output a steering angle δ f to the steering control, and wherein the steering control is configured to generate a steering command.
17. The method according to claim 11 , further comprising:
generating a braking command based on a speed of the vehicle and the determined steering angle.
18. The method according to claim 17 , further comprising:
generating the braking command when the speed of the vehicle exceeds a predetermined safety limit for the determined steering angle.
19. The method according to claim 11 , further comprising:
driving wheels of the vehicle with a motor;
supporting axles on which the wheels are mounted with a chassis, the steering control configured to generate a steering command controlling the wheels based on the determined steering angle; and
actuating brakes for one or more of the wheels based on the speed of the vehicle.
20. The method according to claim 19 , wherein the vehicle is an electric vehicle and the motor is an electric motor.