System and method in lane departure warning with full nonlinear kinematics and curvature

1. An apparatus, comprising:

at least one camera configured to capture an image of a traffic lane in front of a vehicle; and

a vehicle behavior prediction controller configured to:

determine lane boundaries for a segment of a traffic lane occupied by the vehicle from the captured image of the traffic lane in front of the vehicle and prior captured images of the traffic lane in front of the vehicle,

determine a rate of road curvature for the segment of the traffic lane occupied by the vehicle from the captured image of the traffic lane in front of the vehicle and prior captured images of the traffic lane in front of the vehicle,

determine lateral distances of the vehicle from the lane boundaries and a rate of departure of the vehicle from the occupied traffic lane that is accurate for the determined road curvature,

determine a time to line crossing for the vehicle from the lateral distances and the rate of departure, and

activate a lane departure warning indicator based on the determined time to line crossing.

2. The apparatus according to claim 1 , wherein the vehicle behavior prediction controller is configured to determine the rate of departure using first and second terms for effect of road curvature on lane departure for different radii of curvature.

3. The apparatus according to claim 2 , wherein the vehicle behavior prediction controller is configured to determine the rate of departure V depart from:

V depart =v ·sin(θ)+ c l ·{dot over (θ)},

where v is a speed of the vehicle, θ is a heading offset for the vehicle, {dot over (θ)} is a first derivative of θwith respect to traveled distance, c l is a length of the vehicle, v·sin(θ) represents effect of road curvature on lane departure for a first range of radii of curvature, and c l ·{dot over (θ)} represents effect of road curvature on lane departure for a second range of radii of curvature.

4. The apparatus according to claim 3 , wherein the vehicle behavior prediction controller is configured to determine {dot over (θ)} from:

θ

˙

=

ω

-

v

⁢

κ

⁢

cos

⁡

(

θ

)

1

-

κ

⁢

r

,

where ω is vehicle yaw rate, κ is the road curvature, and r is a lateral offset of the vehicle to a lane boundary.

5. The apparatus according to claim 1 , wherein the vehicle behavior prediction controller is configured to activate the lane departure warning indicator based on the lateral distances, the rate of departure, and a road curvature.

6. The apparatus according to claim 5 , wherein the vehicle behavior prediction controller is configured to activate the lane departure warning indicator based on:

LDW=function( D threshold , V threshold , κ threshold ),

where D threshold is a threshold for distance of the vehicle from a lane boundary being approached, V threshold is a threshold for vehicle speed, and κ threshold is a threshold for road curvature.

7. The apparatus according to claim 1 , wherein the vehicle behavior prediction controller is configured to determine the time to line crossing TTLC from a lateral distance d L , to a left lane boundary, a lateral distance d R to a right lane boundary, and the rate of departure V depart based on:

if

⁢

d

L

<

d

R

,

TTLC

=

d

L

V

depart

,

else

⁢

d

L

>

d

R

,

TTLC

=

d

R

V

depart

.

8. The apparatus according to claim 1 , further comprising:

a vehicle motion controller configured to activate at least one of a braking control and a steering control based on the lane departure warning indicator.

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;

a steering control configured to generate a steering command to control the wheels based on activation of the lane departure warning indicator;

a brake actuator configured to actuate brakes for one or more of the wheels; and

a braking control configured to generate a braking command to control the brake actuator based on activation of the lane departure warning indicator.

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;

determining lane boundaries for a segment of a traffic lane occupied by the vehicle from the captured image of the traffic lane in front of the vehicle and prior captured images of the traffic lane in front of the vehicle;

determining a rate of road curvature for the segment of the traffic lane occupied by the vehicle from the captured image of the traffic lane in front of the vehicle and prior captured images of the traffic lane in front of the vehicle;

determining lateral distances of the vehicle from the lane boundaries and a rate of departure of the vehicle from the occupied traffic lane that is accurate for the determined road curvature;

determining a time to line crossing for the vehicle from the lateral distances and the rate of departure; and

activating a lane departure warning indicator based on the determined time to line crossing.

12. The method according to claim 11 , further comprising:

determining the rate of departure using first and second terms for effect of road curvature on lane departure for different radii of curvature.

13. The method according to claim 12 , further comprising:

determine the rate of departure V depart from:

V depart =v ·sin(θ)+ c l ·{dot over (θ)},

where v is a speed of the vehicle, θ is a heading offset for the vehicle, {dot over (θ)} is a first derivative of θwith respect to traveled distance, c l is a length of the vehicle, v·sin(θ) represents effect of road curvature on lane departure for a first range of radii of curvature, and c l ·{dot over (θ)} represents effect of road curvature on lane departure for a second range of radii of curvature.

14. The method according to claim 13 , further comprising:

determining {dot over (θ)} from:

θ

˙

=

ω

-

v

⁢

κ

⁢

cos

⁡

(

θ

)

1

-

κ

⁢

r

,

where ω is vehicle yaw rate, κ is the road curvature, and r is a lateral offset of the vehicle to a lane boundary.

15. The method according to claim 11 , further comprising:

activating the lane departure warning indicator based on the lateral distances, the rate of departure, and a road curvature.

16. The method according to claim 15 , further comprising:

activating the lane departure warning indicator based on:

LDW=function( D threshold , V threshold , κ threshold ),

where D threshold is a threshold for distance of the vehicle from a lane boundary being approached, V threshold is a threshold for vehicle speed, and κ threshold is a threshold for road curvature.

17. The method according to claim 11 , further comprising:

determining the time to line crossing TTLC from a lateral distance d L to a left lane boundary, a lateral distance d R to a right lane boundary, and the rate of departure V depart based on:

if

⁢

d

L

<

d

R

,

TTLC

=

d

L

V

depart

,

else

⁢

d

L

>

d

R

,

TTLC

=

d

R

V

depart

.

18. The method according to claim 11 , further comprising:

activating at least one of a braking control and a steering control based on the lane departure warning indicator.

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;

generating a steering command to control the wheels based on activation of the lane departure warning indicator; and

actuating brakes for one or more of the wheels based on activation of the lane departure warning indicator.

20. The method according to claim 19 , wherein the vehicle is an electric vehicle and the motor is an electric motor.