Game-theoretic planning for risk-aware interactive agents

1. A method for risk-aware game-theoretic trajectory planning, the method comprising:

modeling an ego vehicle and at least a first vehicle and a second vehicle as risk-aware agents in a game-theoretic driving environment;

exchanging risk-sensitivity information of the ego vehicle, the first vehicle, and the second vehicle using vehicle-to-vehicle (V2V) communication between the ego vehicle, the first vehicle, and the second vehicle;

ranking upcoming planned trajectories according to a risk-aware cost function of the ego vehicle based on both a driving maneuver risk-sensitivity of the ego vehicle and a driving maneuver risk-sensitivity of the first vehicle and the second vehicle associated with each of the upcoming planned trajectories; and

selecting a vehicle trajectory to enter a merge gap between the first vehicle and the second vehicle according to the ranking of the upcoming planned trajectories according to the risk-aware cost function and a determined padding distance based on both the driving maneuver risk-sensitivity of the ego vehicle and the driving maneuver risk-sensitivity of the first vehicle and the second vehicle associated with the selected vehicle trajectory to enter the merge gap including the determined padding distance between the first vehicle and the second vehicle and reach a target destination according to a mission plan.

2. The method of claim 1 , in which modeling comprises:

approximating a feedback Nash equilibria of a risk-aware game-theoretic trajectory planning;

deriving, at each iteration, a linearized approximation of system dynamics and a quadratic approximation of the risk-aware cost function; and

solving a backward recursion for finding the feedback Nash equilibria of the risk-aware game-theoretic trajectory planning.

3. The method of claim 1 , in which ranking the upcoming planned trajectories comprises:

computing risk-sensitive cost functions associated with the upcoming planned trajectories relative to both the driving maneuver risk-sensitivity of the ego vehicle and the driving maneuver risk-sensitivity of the first vehicle and the second vehicle; and

planning the vehicle trajectory of the ego vehicle based on the risk-sensitive cost functions associated with the planned trajectories relative to the ego vehicle and the first vehicle and the second vehicle and the driving maneuver proximity-sensitivity of the ego vehicle and the first vehicle and the second vehicle.

4. The method of claim 3 , further comprising accelerating a speed of the ego vehicle to successfully merge into a target lane of a multilane roadway including the first vehicle and the second vehicle.

5. The method of claim 3 , further comprising decelerating a speed of the ego vehicle to successfully merge into a target lane of a multilane roadway including the first vehicle and the second vehicle.

6. The method of claim 5 , in which the ego vehicle is on an on-ramp of the multilane roadway and the target lane is a first lane of the multilane roadway.

7. The method of claim 1 , further comprising discarding an upcoming planned trajectory if the risk-aware cost function of the upcoming planned trajectory is greater than a predetermined value.

8. The method of claim 1 , further comprising discarding an upcoming planned trajectory if the driving maneuver risk-sensitivity of the ego vehicle and the first vehicle and the second vehicle corresponding to the upcoming planned trajectory are less than a predetermined value.

9. A non-transitory computer-readable medium having program code recorded thereon for risk-aware game-theoretic trajectory planning, the program code being executed by a processor and comprising:

program code to model an ego vehicle and at least a first vehicle and a second vehicle as risk-aware agents in a game-theoretic driving environment;

program code to exchange risk-sensitivity information of the ego vehicle, the first vehicle, and the second vehicle using vehicle-to-vehicle (V2V) communication between the ego vehicle, the first vehicle, and the second vehicle;

program code to rank upcoming planned trajectories according to a risk-aware cost function of the ego vehicle based on both a driving maneuver risk-sensitivity of the ego vehicle and a driving maneuver risk-sensitivity of the first vehicle and the second vehicle associated with each of the upcoming planned trajectories; and

program code to select a vehicle trajectory to enter a merge gap between the first vehicle and the second vehicle according to the ranking of the upcoming planned trajectories according to the risk-aware cost function and a determined padding distance based on both the driving maneuver risk-sensitivity of the ego vehicle and the driving maneuver risk-sensitivity of the first vehicle and the second vehicle associated with the selected vehicle trajectory to enter the merge gap including the determined padding distance between the first vehicle and the second vehicle and reach a target destination according to a mission plan.

10. The non-transitory computer-readable medium of claim 9 , in which the program code to model comprises:

program code to approximate a feedback Nash equilibria of the risk-aware game-theoretic trajectory planning;

program code to derive, at each iteration, a linearized approximation of system dynamics and a quadratic approximation of the risk-aware cost function; and

program code to solve a backward recursion for finding the feedback Nash equilibria of the risk-aware game-theoretic trajectory planning.

11. The non-transitory computer-readable medium of claim 9 , in which the program code to rank the upcoming planned trajectories comprises:

program code to compute risk-sensitive cost functions associated with the upcoming planned trajectories relative to both the driving maneuver risk-sensitivity of the ego vehicle and the driving maneuver risk-sensitivity of the first vehicle and the second vehicle; and

program code to plan the vehicle trajectory of the ego vehicle based on the risk-sensitive cost functions associated with the upcoming planned trajectories relative to the ego vehicle and the first vehicle and the second vehicle and the driving maneuver risk-sensitivity of the ego vehicle and the first vehicle and the second vehicle.

12. The non-transitory computer-readable medium of claim 11 , further comprising program code to accelerate a speed of the ego vehicle to successfully merge into a target lane of a multilane roadway including the first vehicle and the second vehicle.

13. The non-transitory computer-readable medium of claim 11 , further comprising program code to decelerate a speed of the ego vehicle to successfully merge into a target lane of a multilane roadway including the first vehicle and the second vehicle.

14. The non-transitory computer-readable medium of claim 13 , in which the ego vehicle is on an on-ramp of the multilane roadway and the target lane is a first lane of the multilane roadway.

15. The non-transitory computer-readable medium of claim 9 , further comprising program code to discard an upcoming planned trajectory if the risk-aware cost function of the upcoming planned trajectory is greater than a predetermined value and/or if the driving maneuver risk-sensitivity of the ego vehicle and the first vehicle and the second vehicle corresponding to the upcoming planned trajectory are less than a predetermined value.

16. A system on chip (SoC) for risk-aware game-theoretic trajectory planning, the SoC comprising:

a game-theoretic risk model configured to model an ego vehicle and at least a first vehicle and a second vehicle as risk-aware agents in a game-theoretic driving environment;

a communications module to exchange risk-sensitivity information of the ego vehicle, the first vehicle, and the second vehicle using vehicle-to-vehicle (V2V) communication between the ego vehicle, the first vehicle, and the second vehicle;

a risk-aware cost function module configured to rank upcoming planned trajectories according to a risk-aware cost function of the ego vehicle based on both a driving maneuver risk-sensitivity of the ego vehicle and a driving maneuver risk-sensitivity of the first vehicle and the second vehicle associated with each of the upcoming planned trajectories; and

a vehicle trajectory selection module configured to select a vehicle trajectory to enter a merge gap between the first vehicle and the second vehicle according to the ranking of the upcoming planned trajectories according to the risk-aware cost function and a determined padding distance based on both the driving maneuver risk-sensitivity of the ego vehicle and the driving maneuver risk-sensitivity of the first vehicle and the second vehicle associated with the selected vehicle trajectory to enter the merge gap including the determined padding distance between the first vehicle and the second vehicle and reach a target destination according to a mission plan.

17. The SoC of claim 16 , further comprising an ego perception module to determine a current trajectory of the ego vehicle and the current trajectory of the first vehicle and the second vehicle.

18. The SoC of claim 17 , further comprising a vehicle trajectory planner to plan the upcoming planned trajectories of the ego vehicle according to the current trajectory of the ego vehicle and the current trajectory of the first vehicle and the second vehicle.

19. The SoC of claim 16 , in which the game-theoretic risk model is configured:

to approximate a feedback Nash equilibria of the risk-aware game-theoretic trajectory planning;

to derive, at each iteration, a linearized approximation of system dynamics and a quadratic approximation of the risk-aware cost function; and

to solve a backward recursion for finding the feedback Nash equilibria of the risk-aware game-theoretic trajectory planning.