Granted Patent B2

US 12,637,105 · App. 17/801,221 · Granted May 26, 2026

Inventors: Alexandre Silva (Edinburgh, GB); Steffen Jaekel (Edinburgh, GB); Majd Hawasly (Edinburgh, GB); Alejandro Bordallo (Edinburgh, GB)

Assignee: Five AI Limited

B60W60/0013B60W2520/10B60W2520/105B60W2720/10B60W2720/106

Abstract

Claims (58)

1 . A computer-implemented method of determining a series of control signals for controlling an autonomous vehicle, the method comprising:

selecting a first or higher order derivative of acceleration with respect to time;

determining a parameterized stepwise kinematic function, the parameterized stepwise kinematic function being defined by a set of function parameters, and expressed as the set of function parameters comprising one or more timing parameters and one or more magnitude parameters defining a respective magnitude of said first or higher order derivative of acceleration with respect to time;

determining, by analytically integrating the parameterized stepwise kinematic function, a final acceleration, speed and position embodied as a set of parameterized closed form final acceleration, speed and position functions of the function parameters;

receiving from a maneuver planner a position target for a planned speed change maneuver;

optimizing the parameterized stepwise kinematic function in respect of the planned speed change maneuver by computing values of its function parameters in a constrained optimization process that optimizes a cost function defined over the set of function parameters, wherein the constrained optimization process imposes:

(i) a hard constraint that the final acceleration, speed and position corresponding to the parameterized stepwise kinematic function satisfy, respectively, an acceleration target, a speed target and the position target, given an initial speed and acceleration of the autonomous vehicle, wherein the hard constraint pertaining to the final acceleration, speed and position is embodied as the closed form final acceleration, speed and position functions of the function parameters, and is imposed without numerically integrating the parameterized stepwise kinematic function, and

(ii) a hard constraint that a jerk magnitude does not exceed an upper limit;

using the parameterized stepwise kinematic function to determine the series of control signals configured to control the autonomous vehicle to implement the planned speed change maneuver; and

controlling the autonomous vehicle to implement the planned speed change maneuver based on the series of control signals.

2 . The method of claim 1 , wherein the constrained optimization process hard constraints also imposes at least one acceleration and/or speed magnitude limit on the parameterized stepwise kinematic function.

3 . The method of claim 1 , wherein each the parameterized stepwise kinematic function is a jerk function, jerk being the first order derivative of acceleration with respect to time.

4 . The method of claim 3 , wherein the parameterized stepwise kinematic function exhibits a first interval of sustained jerk followed by a second interval of zero jerk, followed by a third interval of sustained jerk of opposite sign to the first interval, wherein the function parameters comprise:

one or more timing parameters defining respective durations of each of the first, second and third intervals, and

one or more jerk magnitude parameters defining respective magnitudes of the sustained jerk in the first and third intervals.

5 . The method of claim 4 , wherein the set of function parameters comprises:

multiple timing parameters and/or multiple jerk magnitude parameters, which may be adapted to set different durations for the first, second and third time intervals and/or different jerk magnitudes in the first and third time intervals.

6 . The method of claim 5 , wherein the set of function parameters consists only of the three timing parameters and the two jerk magnitude parameters.

7 . The method of claim 4 , wherein the jerk remains constant and non-zero throughout the first and third time intervals.

8 . The method of claim 1 , wherein the parameterized stepwise kinematic function is a snap function, jerk being a rate of change of acceleration and snap being a second order derivative of acceleration with respect to time.

9 . The method of claim 8 , wherein the parameterized stepwise kinematic function is defined by a set of function parameters, over which the cost function is defined, and the parameterized stepwise kinematic function is optimised by computing values of the function parameters that substantially optimize the cost function subject to the set of hard constraints; wherein the parameterized stepwise snap function exhibits a first interval of sustained snap followed by a second interval of zero snap, followed by a third interval of sustained snap of opposite sign to the first interval, followed by a fourth interval of zero snap, followed by a fifth interval of sustained snap of same sign as the first interval, followed by a sixth interval of zero snap, followed by a seventh interval of sustained snap of opposite sign to the first interval, wherein the set of function parameters comprises:

one or more timing parameters defining respective durations of each of the seven intervals, and

one or more snap magnitude parameters defining respective magnitudes of the snap in each of the first, third, fifth and seventh intervals.

10 . The method of claim 1 , wherein the cost function embodies a completion time objective, which encourages a reduction in at least one of:

overall time taken to reach the final acceleration, speed and position, or

duration of each of multiple time intervals over which the parameterized stepwise kinematic function is defined.

11 . The method of claim 10 , wherein the cost function embodies at least one of:

a timing cost for each of the one or more intervals of the parameterized stepwise kinematic function claim 4 or 9 , which encourages a reduction in the duration of that time interval, or

a jerk magnitude objective, which encourages a reduction in jerk magnitude.

12 . The method of claim 1 , wherein the hard constraints also impose a jerk magnitude lower limit on the parameterized stepwise kinematic function.

13 . The method of claim 2 , wherein the at least one acceleration and/or speed magnitude limit comprises an upper acceleration and/or speed magnitude limit and a lower acceleration and/or speed magnitude limit.

14 . The method of claim 1 , wherein prior to instigating the speed change maneuver, a speed change initiation process is performed repeatedly, to determine a time at which to initiate the speed change maneuver, the time chosen so as to encourage the constrained optimization process to satisfy an optimal comfort condition to an extent possible.

15 . The method of claim 14 , wherein the speed change initiation process comprises:

determining a preliminary speed change trajectory, by computing a preliminary kinematic function with a fixed amount of jerk until a fixed acceleration limit is reached, wherein the speed change maneuver is initiated in response to the preliminary kinematic function satisfying a predetermined initiation condition.

16 . The method of claim 1 , wherein the hard constraints impose an upper limit on the time taken to reach the final position, speed and acceleration.

17 . Non-transitory computer-readable media embodying instructions configured so as, when executed by one or more hardware processors, to cause the one or more hardware processors to perform operations for determining a series of control signals for controlling an autonomous vehicle, the operations comprising:

selecting a first or higher order derivative of acceleration with respect to time;

determining a parameterized stepwise kinematic function, the parameterized stepwise kinematic function being defined by a set of function parameters, and expressed as the set of function parameters comprising one or more timing parameters and one or more magnitude parameters defining a respective magnitude of said first or higher order derivative of acceleration with respect to time;

determining, by analytically integrating the parameterized stepwise kinematic function, a final acceleration, speed and position embodied as a set of parameterized closed form final acceleration, speed and position functions of the function parameters;

receiving from a maneuver planner a position target for a planned speed change maneuver;

optimizing the parameterized stepwise kinematic function in respect of the planned speed change maneuver by computing values of its function parameters in a constrained optimization process that optimizes a cost function defined over the set of function parameters, wherein the constrained optimization process imposes:

(i) a jerk magnitude upper limit on the computed kinematic function, and

(ii) a hard constraint that the final acceleration, speed and position meet, respectively, an acceleration target, a speed target and the position target, wherein the constrained optimization process is performed in the domain of the kinematic function, with the final acceleration, speed and position are derived from the parameterized stepwise kinematic function, given an initial speed and acceleration of the autonomous vehicle, in order to apply the hard constraints, and wherein the constraint pertaining to the final acceleration, speed and position is embodied as the closed form final acceleration, speed and position functions of the function parameters, and is imposed without numerically integrating the kinematic function;

determining, based on the constrained optimization process, a series of control signals configured to control an autonomous vehicle to implement the planned speed change maneuver; and

controlling the autonomous vehicle to implement the planned speed change maneuver based on the series of control signals.

18 . The non-transitory computer-readable media of claim 17 , wherein the form of the parameterized stepwise kinematic function is constrained such that corresponding final acceleration, velocity and distance functions are derived as closed form equations, having coefficients defined by said set of function parameters and current speed and acceleration of the autonomous vehicle, and a corresponding speed change distance is determined using the closed form equations.

19 . A computer system comprising:

memory embodying instructions; and

one or more hardware processors coupled to the memory and configured to execute the instructions, the instructions being configured so as, when executed by the one or more hardware processors, to cause the one or more hardware processors to perform operations comprising:

selecting a first or higher order derivative of acceleration with respect to time;

determining a parameterized stepwise kinematic function, the parameterized stepwise kinematic function being defined by a set of function parameters, and expressed as the set of function parameters comprising one or more timing parameters and one or more magnitude parameters defining a respective magnitude of said first or higher order derivative of acceleration with respect to time;

determining, by analytically integrating the parameterized stepwise kinematic function, a final acceleration, speed and position embodied as a set of parameterized closed form final acceleration, speed and position functions of the function parameters;

receiving a position target for a planned speed change maneuver;

optimizing the parameterized stepwise kinematic function in respect of the planned speed change maneuver by computing values of its function parameters in a constrained optimization process that optimizes a cost function defined over the set of function parameters, wherein the constrained optimization process imposes:

(i) a hard constraint that the final acceleration, speed and position corresponding to the parameterized stepwise kinematic function satisfy, respectively, an acceleration target, a speed target and the position target, given an initial speed and acceleration of an autonomous vehicle, wherein the hard constraint pertaining to the final acceleration, speed and position is embodied as the closed form final acceleration, speed and position functions of the function parameters, and is imposed without numerically integrating the parameterized stepwise kinematic function, and

(ii) a hard constraint that a jerk magnitude does not exceed an upper limit;

using the parameterized stepwise kinematic function to determine a series of control signals configured to control the autonomous vehicle to implement the planned speed change maneuver; and

controlling the autonomous vehicle to implement the planned speed change maneuver based on the series of control signals.

Assignments (1)

Priority Claims (1)

Continuity (1)

References Cited (19)