Determination of Dynamically Possible Driving Maneuvers

Abstract

The present disclosure relates to a computer-implemented method for calculating a trajectory of a mobile platform. The method calculates an exact or approximate solution of an optimization problem, which minimizes the travel time from a predetermined starting state to a predetermined end state, wherein the jerk of the mobile platform is restricted in absolute value to a maximum jerk and wherein the acceleration of the mobile platform is restricted, wherein the limit of the acceleration can be dependent on the velocity of the mobile platform.

Claims

1. A method for calculating a trajectory for a mobile platform, the method comprising: calculating, with a computer, the trajectory for the mobile platform as a solution of an optimization problem having a cost function, a jerk secondary condition, and an acceleration secondary condition, the cost function being a travel time of the mobile platform from a starting state to an end state, the jerk secondary condition being configured to restrict a jerk of the mobile platform in absolute value to a maximum jerk, the acceleration secondary condition being a limit for an acceleration of the mobile platform, the solution being one of an exact solution and an approximate solution.

2. The method according to claim 1, wherein the limit for the acceleration of the mobile platform is dependent on a velocity of the mobile platform.

3. The method according to claim 1, wherein the limit for the acceleration of the mobile platform is a polynomial function of the velocity of the mobile platform.

4. The method according to claim 1 further comprising: calculating a first switching point at which a first state curve touches a second state curve, the first state curve being dependent on the starting state, the jerk secondary condition being active over the first state curve, the acceleration secondary condition being active over the second state curve.

5. The method according to claim 4, the calculating the first switching point further comprising: calculating the first switching point by solving a polynomial equation.

6. The method according to claim 4 further comprising: calculating a second switching point at which the second state curve touches a third state curve and a third switching point at which the third state curve touches a fourth state curve, the jerk secondary condition being active over the third state curve and the fourth state curve with different signs, the fourth state curve being dependent on the end state.

7. The method according to claim 6, the calculating the second switching point and the third switching point further comprising: calculating the second switching point and the third switching point by solving an equation system.

8. The method according to claim 1, wherein the starting state includes at least one of a starting position of the mobile platform, a starting velocity of the mobile platform, and a starting acceleration of the mobile platform.

9. The method according to claim 1, wherein the end state includes at least one of an end position of the mobile platform, an end velocity of the mobile platform, and an end acceleration of the mobile platform.

10. The method according to claim 1, wherein the trajectory is a one-dimensional trajectory.

11. The method according to claim 1 further comprising at least one of: providing, based on the calculated trajectory, a control signal configured to activate at least one of a drive system of the mobile platform and a braking system of the mobile platform; and providing, based on the calculated trajectory, a warning signal configured to warn an occupant of the mobile platform.

12. A data processing system for calculating a trajectory for a mobile platform, the data processing comprising: a computer configured to calculate the trajectory for the mobile platform as a solution of an optimization problem having a cost function, a jerk secondary condition, and an acceleration secondary condition, the cost function being a travel time of the mobile platform from a starting state to an end state, the jerk secondary condition being configured to restrict a jerk of the mobile platform in absolute value to a maximum jerk, the acceleration secondary condition being a limit for an acceleration of the mobile platform, the solution being one of an exact solution and an approximate solution.

13. The method according to claim 1, wherein the method is performed by a data processing system that executes a computer program comprising commands.

14. The method according to claim 13, wherein the computer program is stored on a non-transitory machine-readable storage medium.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Further explanations are represented in greater detail hereinafter together with the description of preferred exemplary embodiments of the disclosure on the basis of figures.

[0059] FIG. 1 shows a method for calculating a trajectory of a vehicle according to an exemplary embodiment of the disclosure.

DETAILED DESCRIPTION

[0060] FIG. 1 shows a method 100 for calculating a trajectory of a vehicle according to an exemplary embodiment of the disclosure. In a first step S1, a sign sequence for the jerk is calculated, for which purpose the method described in [Walther et al.] can be used. In addition to the sign of the solution for u(t) in the constant sections, it is thus also implicitly determined how many switching points the solution has without consideration of the acceleration secondary condition. The sign sequence can be calculated without consideration of the acceleration secondary condition. The sign of the jerk in the first section of the vehicle trajectory calculated according to the disclosure with consideration of the acceleration secondary condition is preferably the same as the sign of the jerk in the first section of the solution without consideration of the acceleration secondary condition.

[0061] In a second step S2, a first switching point is calculated according to the method described in [Walther et al.]. The acceleration secondary condition is thus not taken into consideration and the first switching point, at which the function u(t) changes its sign the first time is calculated. The time of the first switching point without consideration of the acceleration secondary condition is referred to hereinafter as τ.sub.12.

[0062] In a third step S3, a first switching point is calculated in consideration of the acceleration secondary condition. For this purpose, the switching point is calculated at which a first state curve touches a second state curve, wherein the starting point of the first state curve is given by the starting state [s.sub.0, v.sub.0, a.sub.0].sup.T, wherein the jerk u(t) is equal in absolute value to the maximum jerk over the first state curve, wherein the sign of the jerk over the first state curve is the same as the sign calculated in step S1, and wherein the acceleration secondary condition is active over the second state curve. The time of the first switching point in consideration of the acceleration secondary condition is t.sub.1.

[0063] In a fourth step S4, it is checked whether Ti is less than or equal to t.sub.1. It is thus checked whether the first switching point without consideration of the acceleration secondary condition is before the first switching point with consideration of the acceleration secondary condition.

[0064] If τ.sub.1 is less than or equal to t.sub.1, the vehicle trajectory calculated according to the disclosure is thus preferably identical to the trajectory calculated according to [Walther et al.] without consideration of the acceleration secondary condition. Further parameters of this trajectory can be determined in step S5a.

[0065] If τ.sub.1 is greater than t.sub.1, the vehicle trajectory calculated according to the disclosure thus comprises a first and a second section, wherein as described above the first section of the vehicle trajectory is given by the first state curve and wherein the second state curve is given by the second state curve.

[0066] If the solution without consideration of the acceleration secondary condition, which can be calculated according to [Walther et al.], comprises a switching point, the vehicle trajectory calculated according to the disclosure thus preferably comprises a third section. If in addition the solution without consideration of the acceleration secondary condition comprises a second switching point, the vehicle trajectory calculated according to the disclosure thus preferably has a fourth section. The number of the switching points of the solution without consideration of the acceleration secondary condition results directly from the sign sequence determined in step S1. In a step S5b, a second and a third switching point can thus be calculated, wherein the second state curve touches a third state curve in the second switching point and the third state curve touches a fourth state curve in the third switching point, wherein the jerk secondary condition is active over the third and the fourth state curve with different signs, and wherein the fourth state curve ends in the end state [s.sub.ƒ, v.sub.ƒ, a.sub.ƒ].sup.T. In particular, the sequence of the signs of the jerk over the first, the third, and the fourth state curve is identical to the sequence of the sign of the jerk of the corresponding solution according to [Walther et al.] without consideration of the acceleration secondary condition. The second and the third switching point can be calculated by solving a system of four equations having four unknowns.

[0067] In a step S6, the vehicle trajectory according to the disclosure can be generated.

[0068] After the calculation of the trajectory, which maximally utilizes the dynamic options, it can be determined, for example, whether threading into a vehicle flow is possible, whether complete deceleration is possible before an obstacle or the end of an acceleration lane, or whether overtaking a road user is possible. In particular a drive, a braking, and/or a steering system can be activated in dependence thereon, in order to follow the trajectory calculated according to the disclosure. However, it is also possible that the trajectory calculated according to the disclosure is not advantageous, since, for example, complete deceleration before an obstacle is no longer possible. In this case, for example, the trajectory calculated according to the disclosure can be modified to avoid the obstacle.

[0069] The described exemplary embodiments similarly relate to the computer-implemented method for calculating a vehicle trajectory, the data processing system for executing the method, the computer program, and the computer-readable storage medium. In other words, features which have been described with reference to the computer-implemented method can also be implemented in the data processing system, the computer program, and/or the storage medium and vice versa.

[0070] Synergy effects can result from different combinations of the exemplary embodiments, although they are not described in detail.