DE102019201124A1 - A system for a vehicle - Google Patents

Abstract

The invention provides a system for a vehicle that can be operated in an autonomous mode, the system being for planning a trajectory of the vehicle. In particular, the system includes a receiver configured to receive road segment data from at least one subsystem of the vehicle, the road segment data indicating at least one feature of a road segment proximate to the vehicle. The system also includes an achievable state module configured to determine a set of achievable vehicle states within a prescribed period of time responsive to at least one vehicle restriction, each of the achievable vehicle states including an achievable vehicle position. The system also includes an allowable position module configured to determine a plurality of allowable vehicle positions in the road segment based on the received road segment data, wherein the plurality of allowable vehicle positions are within the particular set of achievable vehicle positions. The system also includes a target state module configured to determine a target vehicle state having a target vehicle position in the road segment, the target vehicle position corresponding to one of the plurality of determined allowable vehicle positions. The system also includes a trajectory generation module configured to determine a viable trajectory on which the vehicle travels to the target vehicle position in response to the at least one vehicle constraint to plan the vehicle trajectory.

Description

TECHNICAL AREA

The present disclosure relates to a system for a vehicle, and more particularly, but not exclusively, to a system for a vehicle that can be operated in an autonomous mode. Aspects of the invention relate to a system, a method, and a vehicle.

STATE OF THE ART

The first generation of vehicles with autonomous driving modes was able to perform the following tasks: lane keeping, keeping the distance to a preceding vehicle, providing a lane departure warning, etc. This helped to increase occupant comfort and reduce the driver's workload. A human driver is still required to initiate or intervene in either more sophisticated but equally common maneuvers, such as lane change, threading traffic, overtaking, etc., while performing the same. For example, overtaking a preceding vehicle is a template for such complex maneuvers as it combines both lateral movement and longitudinal movement of an overtaking vehicle (test vehicle) while avoiding a slower moving obstacle vehicle (leading vehicle), as well as partial maneuvers of the vehicle Lane change, tracking and threading in a sequential manner.

The inherently complicated structure of overtaking derives from its dependence on a large number of factors such as road conditions, weather, traffic density, type of overtaking vehicle, type of vehicle to overtake, relative speed between vehicles, distance traveled, etc., what the classification and standardization is relatively difficult. In addition, in order to perform overtaking maneuvers, accurate information regarding the availability of roads and lanes, the trajectory of the lead vehicle, the road conditions, etc. is required.

There are a number of proposed methods for scheduling trajectories to perform a complex autonomous maneuver, such as an autonomous overtaking maneuver, by treating it as a problem to avoid a moving obstacle. For example, incremental search-based algorithms such as Rapidly Exploring Random Trees (RRT) have been proposed for planning trajectories for a complex autonomous maneuver; However, RRT algorithms are disadvantageous in that the planned trajectories may be jerky, which in turn may result in reduced occupant comfort. In addition, the computation times for most search-based algorithms are dependent on the surrounding traffic density, making them less suitable for automotive applications.

If accurate information regarding the road and the surrounding obstacles is available, it will be appreciated that techniques based on a potential field are successful in creating trajectories that avoid stationary or moving obstacles. However, these methods do not involve vehicle dynamics and therefore can not ensure how feasible it is for the vehicle to actually follow the planned trajectory.

Model Predictive Control (MPC) methods have the ability to formulate vehicle dynamics and obstacle avoidance constraints as a finite-horizon constrained optimization problem. These methods have the disadvantage that obstacle avoidance restrictions for scheduling a trajectory are generally not convex, which severely limits the feasibility and uniqueness of the solution to the optimization problem. To address this problem, techniques such as convexization, changing the frame of reference and approximation have been proposed. Nevertheless, the optimization problem formulated by these approaches often requires constraint equivalence, which changes in real time, making it difficult to implement in an electronic control unit (ECU) of a vehicle.

The concept of motion primitives included in an MPC frame structure has been proposed to plan obstacle avoidance trajectories. However, since these motion primitives are computed off-line and retrieved through a look-up table, only a subset of all feasible trajectories can be available for scheduling a trajectory.

It has been proposed to generate planned overtravel trajectories, for example, by directing the test vehicle along virtual target points which are located at sufficient distances around the lead vehicle, thereby redrafting a trajectory into a navigation problem. In such methods, however, the test vehicle is modeled as a spot mass without dynamics, and therefore these methods are not suitable for planning complex maneuver trajectories of autonomous vehicles.

The present invention aims to overcome the disadvantages associated with the prior art.

BRIEF SUMMARY OF THE INVENTION

According to one aspect of the invention, there is provided a system for a vehicle that is operable in an autonomous mode, the system being for planning a trajectory of the vehicle. The system includes a receiver configured to receive road segment data from at least one subsystem of the vehicle, the road segment data indicating at least one feature of a road segment proximate to the vehicle. The system includes an achievable state module configured to determine a set of achievable vehicle states within a prescribed period of time as a function of at least one vehicle restriction, each of the achievable vehicle states including an achievable vehicle position. The system includes an allowable position module configured to determine a plurality of allowable vehicle positions in the road segment based on the received road segment data, wherein the plurality of allowable vehicle positions are within the determined set of achievable vehicle positions. The system includes a target state module configured to determine a target vehicle state having a target vehicle position in the road segment, the target vehicle position corresponding to one of the plurality of determined allowable vehicle positions. The system includes a trajectory generation module configured to determine a feasible trajectory on which the vehicle travels to the target vehicle position in response to the at least one vehicle constraint to schedule the vehicle trajectory.

The invention provides a situational awareness and planning system for a trajectory to perform complex autonomous maneuvers, such as overtaking on a freeway. The system is advantageous in that it is free from non-convex obstacle avoidance restrictions, it ensures the feasibility of the proposed trajectory and is realizable in real time. That is, the system is implementable in an electronic control unit (ECU) of the vehicle and operates within the processor clock time of the ECU.

The system may include an output configured to send a control signal to control the vehicle to follow the realizable trajectory.

The at least one road segment feature may include: a current trajectory of the vehicle; Road and / or lane boundaries; and / or driving regulations.

The at least one road segment feature may include at least one obstacle.

The at least one obstacle may include another vehicle, and the road segment data includes a speed, position, and / or orientation of the another vehicle.

The other vehicle may be in front of and on the same lane as the vehicle.

The at least one obstacle may include at least one pothole, a brake threshold and a blocked lane.

The permissible position module may be configured to define an artificial potential field that is greater than the set of achievable vehicle positions. The allowable position module may be configured to generate a net potential function describing the artificial potential field in response to the received road segment data. A potential value of the net potential function may vary over the artificial potential field.

The allowable vehicle positions may be determined as corresponding positions in the artificial potential field where the net potential function value is within a prescribed interval of potential values.

• eine Fahrspurgeschwindigkeitspotentialfunktion, die Informationen beinhaltet, die sich auf eine Geschwindigkeit beziehen, die jeder Fahrbahn der Straße zugeordnet ist;
• eine Straßenpotentialfunktion, die Informationen beinhaltet, die sich auf Straßenbegrenzungen beziehen;
• eine Fahrspurpotentialfunktion, die Informationen beinhaltet, die sich auf Begrenzungen und/oder eine Mitte jeder Fahrspur der Straße beziehen; und,
• eine weitere Fahrzeugpotentialfunktion, die Informationen zur Fahrzeugdynamik eines weiteren Fahrzeugs in dem Straßensegment beinhaltet.

The net potential function may include a contribution from one or more of the following elements:

• a lane speed potential function that includes information relating to a speed associated with each lane of the road;
• a road potential function that includes information related to road boundaries;
• a lane potential function that includes information related to boundaries and / or a center of each lane of the road; and,
• another vehicle potential function that includes information about the vehicle dynamics of another vehicle in the road segment.

The at least one vehicle restriction may include one or more current vehicle state variables.

The current vehicle state variables may include an actual vehicle position, a current vehicle direction angle, and an actual vehicle speed.

The at least one vehicle restriction may include one or more approved vehicle state variables.

The approved vehicle state variables may include an approved vehicle direction angle, an approved vehicle speed, and an authorized vehicle lateral position.

The at least one vehicle restriction may include one or more vehicle input restrictions.

The vehicle input limits may include an approved vehicle steering angle and an approved vehicle acceleration.

The at least one vehicle restriction includes one or more vehicle dynamics limitations.

The vehicle dynamics limitations may include one or more dimensions of the vehicle, a vehicle mass, a vehicle mass distribution, a type of terrain over which the vehicle is traveling, a vehicle tire type, and a vehicle tire pressure.

The achievable vehicle states may include an achievable vehicle speed, an achievable vehicle direction angle, an achievable longitudinal vehicle displacement, and an achievable vehicle lateral displacement.

The set of achievable vehicle states may be selected from a predetermined range of possible sets of achievable vehicle states. Each potential set of achievable vehicle conditions may have a different combination of values of one or more of the vehicle restrictions and / or the prescribed amount of time.

The set of achievable vehicle conditions may be determined at predefined intervals based on values of the at least one vehicle restriction received via the vehicle-to-vehicle communication.

The set of achievable vehicle states may be determined using a continuous time nonlinear kinematic bicycle model.

The target vehicle position may correspond to the allowable vehicle position farthest from a current vehicle position. The allowable vehicle position may correspond to one of the achievable vehicle positions in the set of achievable vehicle states.

The target state module may determine a target vehicle speed along the feasible trajectory.

The target vehicle speed may include a substantially uniform longitudinal velocity.

The target vehicle states may include a target vehicle speed and / or a target vehicle direction angle.

• ein Fahrzeugnavigationsteilsystem;
• einen Ultraschallsensor;
• einen Radarsensor;
• einen LiDAR-Sensor;
• einen Bildsensor; und,
• einen Fahrzeug-zu-Allem-Transceiver.

The at least one sensor or subsystem of the vehicle may include:

• a vehicle navigation subsystem;
• an ultrasonic sensor;
• a radar sensor;
• a LiDAR sensor;
• an image sensor; and,
• a vehicle-to-all transceiver.

The trajectory generation module may be configured to apply a model predictive control strategy to generate the viable trajectory.

According to another aspect of the invention, there is provided a method for a vehicle that is operable in an autonomous mode, the method being for planning a road trajectory of the vehicle. The method includes receiving road segment data from at least one sensor or subsystem of the vehicle, the road segment data indicating at least one feature of a road segment proximate the vehicle. The method includes determining a set of achievable vehicle conditions within a prescribed period of time as a function of at least one vehicle restriction, wherein each of the achievable vehicle conditions includes an achievable vehicle position. The method includes determining a plurality of allowable vehicle positions in the road segment in dependence from the received road segment data. The method includes determining a target vehicle state having a target vehicle position in the road segment, the target vehicle position corresponding to one of the determined allowable vehicle positions that are within the determined set of achievable vehicle positions. The method includes determining a feasible trajectory on which the vehicle travels to the target vehicle position in response to the at least one vehicle constraint to schedule the vehicle trajectory.

According to a further aspect of the invention, there is provided a vehicle comprising a system as described above.

In yet another aspect of the invention, there is provided a non-transient computer-readable storage medium storing thereon instructions that, when executed by one or more processors, cause the one or more processors to perform the method described above.

It is expressly intended, within the scope of this application, that the various aspects, embodiments, examples and alternatives presented in the preceding paragraphs, in the claims and / or in the following description and drawings, and in particular, their individual features, be independent of each other or in any combination. This means that all embodiments and / or features of any embodiment can be combined in any manner and / or in any combination, provided that these features are not incompatible. The Applicant reserves the right to change any claim originally filed or to submit any new claim, including the right to alter any originally filed claim, to vary and / or rely on any feature of any other claim although it was previously unclaimed in this way.

list of figures

• 1 eine schematische Draufsicht eines (Prüf-) Fahrzeugs, das ein System gemäß einer Ausführungsform eines erfindungsgemäßen Aspekts beinhaltet, zusammen mit Teilsystemen und Sensoren, die Eingänge für das System bereitstellen, wobei das System zum Planen einer Trajektorie für das Prüffahrzeug dient, um ein Überholmanöver gegenüber einem Führungsfahrzeug durchführen;
• 2 das System von 1 detaillierter, insbesondere die Komponentenmodule des Systems;
• 3 eine schematische Draufsicht, die die sequentiellen Teilmanöver darstellt, die in dem Überholmanöver eingeschlossen sind, für das das System aus 1 eine Trajektorie plant;
• 4 eine schematische Draufsicht auf die Straßengeometrie, insbesondere den Koordinatenrahmen und -bereich für das Überholmanöver, für das das System aus 1 eine Trajektorie plant;
• 5 ein Flussdiagramm, das die Schritte eines Verfahrens zeigt, die von dem System aus 1 zum Planen der Trajektorie für das Überholmanöver unternommen werden;
• 6 eine schematische Draufsicht eines Teilabschnitts der Straße aus 4, die den Bereich aller Positionen zeigt, die das Prüffahrzeug innerhalb eines vorgeschriebenen Zeitraums von seiner aktuellen Position aus erreichen kann;
• 7a und 7b perspektivische Ansichten beziehungsweise Draufsichten eines Konturdiagramms, das ein Potentialfeld in der Nähe des Prüffahrzeugs darstellt, wie es durch das System aus 1 bestimmt wird;
• 8 Referenzzielpunkte auf der Straße für das Prüffahrzeug relativ zu dem Führungsfahrzeug zu mehreren Zeitschritten, wie durch das System aus 1 bestimmt; und,
• 9 geplante Trajektorien in Abhängigkeit von den tatsächlichen Trajektorien des Prüffahrzeugs während des Überholmanövers, wobei die geplanten Trajektorien durch das System aus 1 bestimmt werden.

One or more embodiments of the invention will now be described by way of example only with reference to the accompanying drawings; show here:

• 1 a schematic plan view of a (test) vehicle, which includes a system according to an embodiment of an aspect of the invention, together with subsystems and sensors that provide inputs for the system, the system is used to plan a trajectory for the test vehicle to an overtaking maneuver perform a leader vehicle;
• 2 the system of 1 in more detail, in particular the component modules of the system;
• 3 a schematic plan view illustrating the sequential partial maneuvers included in the overtaking maneuver for which the system 1 plans a trajectory;
• 4 a schematic plan view of the road geometry, in particular the coordinate frame and area for the overtaking maneuver, for which the system 1 plans a trajectory;
• 5 a flowchart showing the steps of a method, the from the system 1 to plan the trajectory for the overtaking maneuver;
• 6 a schematic plan view of a section of the road from 4 showing the range of all positions that the test vehicle can reach within a prescribed period of time from its current position;
• 7a and 7b perspective views and plan views, respectively, of a contour diagram illustrating a potential field in the vicinity of the test vehicle, as determined by the system 1 is determined;
• 8th Reference targets on the road for the test vehicle relative to the lead vehicle at multiple time intervals, as determined by the system 1 certainly; and,
• 9 planned trajectories depending on the actual trajectories of the test vehicle during the overtaking maneuver, the planned trajectories being determined by the system 1 be determined.

DETAILED DESCRIPTION

The present invention provides a system and method for a vehicle that can be operated in an autonomous mode. In particular, the invention provides a system and method for scheduling a trajectory of the vehicle to perform a complex maneuver. The embodiment described below is used in particular for performing an overtaking maneuver; however, the described system and method are equally suitable for planning trajectories for the vehicle to perform many different types of complex maneuvers. Other such complex maneuvers include the following: taking a highway exit, changing lanes, threading in a track with traffic and at the same time overtaking several vehicles.

The invention includes determining a set of so-called achievable states of the vehicle; that is, determining the set of possible positions and directional angles that the vehicle can achieve in a prescribed time from its current position. The invention also includes using received data relating to the road segment surrounding the vehicle to determine a set of so-called allowable positions for the vehicle, i. H. Positions of the vehicle to ensure that surrounding obstacles and road boundaries are avoided, with the allowable positions being within the set of reachable states. The set of allowable positions can be determined using potential functions. The invention then includes determining a target state of the vehicle, the target state including a target vehicle position corresponding to one of the allowable positions. The invention also includes generating a trajectory for the vehicle to be able to transition from its current state to the target state in a feasible manner. The realizable trajectory can be determined using a model predictive control strategy.

1 shows a vehicle 10 which can be operated in an autonomous mode. The vehicle 10 includes an autonomous or semi-autonomous system 12 which is configured to be a trajectory for the vehicle 10 to plan the vehicle 10 to control the planned trajectory.

If the vehicle 10 in autonomous mode, the system controls 12 automatically the movement of the vehicle 10 , z. B. steering and acceleration / deceleration. In the autonomous mode, the system can 12 Command signals to an electric power steering system (EPAS) of the vehicle 10 or in alternative arrangements, the system can 12 otherwise a steering mechanism of the vehicle 10 be assigned, so the system 12 Adjustments to the steering direction of the vehicle 10 can make. In the autonomous mode, the system can 12 a position of the vehicle 10 with respect to one or more features provided on a surface on which the vehicle is mounted 10 drives, for example, white lines on a road that designate, modify, manage, or otherwise control the boundary of a "trail."

If, in contrast, the vehicle 10 operated in a manual mode, a driver controls the movement of the vehicle 10 , In the manual mode owns the autonomous system 12 the control over the vehicle movement is not and is in a deactivated state.

The vehicle 10 includes a number of subsystems and sensors 14 that the autonomous system 12 Provide data so that it can plan a vehicle trajectory. The subsystems / sensors 14 include radar sensors 14a , acoustic sensors 14b , Cameras / Image Sensors 14c and LiDAR sensors 14d taking data from a road segment near the vehicle 10 receive. In particular, the received data may include information related to features of the road segment, including road and / or lane boundaries and stationary or moving obstacles. For example, stationary obstacles may be in the form of bumps or potholes, and movable obstacles may be in the form of other vehicles or pedestrians.

The subsystems / sensors 14 also include a navigation subsystem 14e for providing information regarding the surrounding road segment. In addition, the subsystems / sensors 14 one or more transceivers for communicating with other objects or vehicles in the vicinity of the vehicle 10 include. In general, this may be considered a vehicle-to-all (V2X) communications subsystem 14f and may include one or more of vehicle-to-vehicle (V2V) communication, vehicle-to-pedestrian (V2P) communication, vehicle-to-device (V2D) communication, and vehicle-to-vehicle (V2G) communication. Include communication.

2 shows the system 12 detail. In particular, the system includes 12 a component for planning a trajectory 16 and a trajectory tracking and vehicle actuation component 18 , The component for planning a trajectory 16 again contains a module for reachable states 20 , a module for an allowed position or a perceptual module 22 , a goal state module 24 and a generation module 26 for a trajectory, and their operation will be described in detail below. The system 12 has a receiver 28 which is to receive data from subsystems and sensors 14 for use in determining a trajectory for the vehicle 10 is configured. The generated vehicle trajectory is used by the component to schedule a trajectory 16 is spent and can control the operation of the vehicle 10 used to track the planned trajectory. An edition 29 from the trajectory tracking and vehicle actuation component 18 shows current vehicle conditions after actuation based on sensor measurements and Estimate current vehicle conditions, and this output becomes the module for planning a trajectory 16 and the trajectory tracking and the vehicle actuation module 18 after actuation of the vehicle 10 traced back in a loop.

As mentioned above, in the present embodiment, the system plans a trajectory for the vehicle 10 used as test vehicle (SV) 10 is designated to perform an overtaking maneuver on a preceding vehicle, which is referred to as a leading vehicle (LV). 3 shows the sequence of sub-maneuvers included in the overtaking maneuver. In the described embodiment, the SV drive 10 and the LV 30 along a dual carriageway or highway 32 , In particular, the highway includes 32 a "slow track" 34 and a "fast track" 36 indicated by dashed line markings 38 are separated and a limit 40 . 42 on each side of the highway 32 have, and the SV 10 and the LV 30 drive on the slow lane 34 , with the SV 10 behind the LV 30 , The overtaking maneuver shown involves three consecutive sub-maneuvers, namely: (i) lane change 44 ; (ii) tracking 46 ; and (iii) track threading 48 , 3 also provides a reasonable minimum distance 50 to whom the SV 10 behind the LV 30 should remain before an overtaking maneuver is initiated, as well as a reasonable minimum distance 52 the SV 10 before the LV 30 should be left before a threading is completed to complete an overtaking maneuver. In addition, shows 3 a suitable minimum lateral distance 54 , the side-by-side vehicles (for example, during a lane keeping maneuver) in the fast and slow lanes 34 . 36 should be maintained. The system 12 plans a trajectory for the SV 10 to the LV 30 to overtake while the LV 30 is avoided and within the road boundary 40 . 42 and while also maintaining the appropriate minimum distances to be maintained between vehicles.

4 shows the road geometry, in particular the coordinate frame and the coordinate range for the overtaking maneuver that the SV 10 in the embodiment described herein. In addition to a coordinate inertia cross (I-frame) 60 three more coordinate frames are used, namely a vehicle frame (V-frame) 62 , an obstacle frame (O-frame) 64 and a road frame (R-frame) 66 , The V-frame is in the center of gravity of the SV 10 and follows the roll-pitch-yaw (RPY) convention. Similarly, the O Framework in the main focus of the LV 30 and follows the RPY convention, while the R Frame at the projection of the origin of the V-frame on the innermost (rightmost) edge 42 the street 32 with the x- Axis is located in the direction of travel. A generic point on the road is referred to as w = (X, Y), wr = (Xr, Yr), wv = (Xv, Yv) or where = (Xo, Yo) I - R - V - or O-frame is expressed. δ _w is the width of the track 34 , The shaded area 68 denotes a rectangle that extends along the R-frame 66 with vertices V = (V1, V2, V3, V4), and its use will be described in detail below.

Regarding 5 now becomes a procedure 70 described that the system 12 to plan a trajectory for SV 10 to perform an overtaking maneuver at the LV 30 performs. In particular, the method uses a frame of realizable field-like functions and a model predictive control (MPC) to perform an overtaking maneuver on a highway. In summary, the frame contains an artificial potential field (APF) or a module 22 for a permissible position, a destination generation block or a destination state module 24 and the trajectory generation block or module 26 , The APF is used to control the surrounding area of the SV 10 map. Unlike typical approaches with a potential field where the location of an obstacle is used to identify areas that should not be entered, the method described combines the location, orientation, and relative speed of an obstacle to map a valid area around the SV 10 to create. At each sampling time, the target state module identifies 24 the most desirable point of the road, with the dynamics of SV 10 is compatible and calculates the reference state setpoint (eg, velocity, lateral position, and heading angle) to be tracked. To achieve this goal, the target state module combines 24 the permissible areas or points in the potential field with the vehicle dynamics capability of the SV 10 by the achievable rate of SV 10 is absorbed by its current state. The generation module 26 for a trajectory uses an MPC strategy to generate realizable trajectories and the SV 10 to guide to the required reference (target) status. The MPC approach provides stability in the closed loop while ensuring the long-term viability of the optimization problem required by any model predictive problem formulation. Therefore lies in the described system 12 the burden of obstacle avoidance at the module 22 for the perception or permissible position, and the burden of the realizable trajectory lies with the MPC or the generation module 26 for a trajectory.

In step 72 determines the module for reachable states 20 a set of achievable vehicle conditions within a prescribed Period. That is, the reachable state module 20 determines a set of all viable vehicle states that the SV 10 within the prescribed period. Each achievable vehicle state in the set includes an achievable vehicle speed, an achievable vehicle direction angle, an achievable longitudinal vehicle displacement, and an achievable vehicle lateral displacement.

The achievable rate is determined depending on at least one vehicle restriction. In particular, the vehicle limitations include one or more current vehicle state variables, such as a current vehicle position, a current vehicle direction angle, and an actual vehicle speed. The vehicle limitations also include approved state variables, such as an approved vehicle direction angle, an approved vehicle speed, and an authorized vehicle lateral position. Additionally, the vehicle limitations include vehicle input restrictions such as an approved vehicle steering angle and an approved vehicle acceleration. Further, the vehicle limitations include one or more vehicle dynamics limitations, such as dimensions of the vehicle, vehicle mass, vehicle mass distribution, a type of terrain over which the vehicle is traveling, a vehicle tire type, and a vehicle tire pressure. 6 sets the V-frame area 74 of positions that the SV 10 in the case where the SV 10 with a constant speed of 33.33 m / s for a prescribed time of 1.6 s with authorized steering inputs. In particular shows 6 a convex approach of the achievable set. It should be noted that the exact achievable set is a non-convex set that is difficult to compute and plot, and accordingly, a convex approximation is used instead.

The set of achievable vehicle states may be selected from a predetermined one of potential sets of achievable vehicle states, each potential set of achievable vehicle states having a different combination of values of one or more of the vehicle limitations and / or the prescribed time period. In such a case, the set of achievable states is calculated off-line and stored in an on-board memory of the vehicle 10 saved. Alternatively, the set of achievable vehicle conditions may be determined at predefined intervals based on values of the vehicle restrictions and updated at regular intervals via the vehicle-to-all communication.

$$y=h\left(x,u\right)$$

Mathematically, for a system with states x, inputs u and outputs y subject to system dynamics described by the following: $$\dot{x}=f\left(x.u\right)$$

$$y=H\left(x.u\right)$$

wobei u(-) ∈ u die Eingabe für das obige System in dem Zeitbereich t = [0, t_*] darstellt.Where, if f and h are the state and output functions (linear or non-linear), then the achievable set is that denoted by ℜ (t _* ; x ₀ ) for a system defined by the above state and output equations , defines the collection of all states that can be reached in a prescribed time, if the initial state is by applying permitted inputs, ie $$R\left(t_{*};x_0\right)={\displaystyle \underset{u(\cdot ).t\in \left[0t_{*}\right]}{\cup }x\left(t_{*};x_0.u(\cdot )\right)}$$

where u (-) ∈ u represents the input for the above system in the time domain t = [0, t _* ].

In step 76 receives the system 12 and in particular the component for planning a trajectory 16 Road segment data from the sensors and subsystems 14 , The received road segment data shows at least one feature of a road segment in the vicinity of the SV 10 on. The road segment data includes data related to obstacles in the road segment. In this case, one of the obstacles is another vehicle, namely the LV 30 , The road segment data includes the current speed, relative position and orientation of the LV 30 , At highway speed, an overtaking maneuver may be about 50 meters behind the LV 30 be initiated and about 50 m before the LV 30 end up. Therefore, the SV 10 Have an accurate situation awareness (via the received road segment data) about the surrounding obstacles in the road segment to plan trajectories that avoid the obstacles.

The road segment data may also include data indicative of non-moving objects such as potholes, thresholds, and blocked lanes. As mentioned above, the road segment data also includes data representing the road boundaries 40 . 42 and the lane boundary 38 Show. Further, the road segment data includes data indicative of driving regulations, such as a speed limit of the road 32 and which lanes can be used to make an overtaking maneuver. additionally The road segment data includes a current vehicle state or a current vehicle trajectory.

In step 78 determines the module 24 for a permissible position, a plurality of permissible vehicle positions in the road segment 68 , This determination is made as a function of the received road segment data. The plurality of allowable vehicle positions are within the particular set of achievable vehicle positions. In the described embodiment, a APF used to determine the allowable rate. In particular, that will APF used to the surrounding area, especially the area 68 of the SV 10 map. With the APF becomes a map of the allowed areas around the SV 10 created. The APF is greater than the set of achievable vehicle positions 74 ,

A potential-field-like perception can be designed in such a way that it leads to the desired driver behavior. The environment (the road segment) is described by the use of a potential field in which some road elements (eg, road borders, road markings, other road users) are considered to design a potential function to include driving regulations and the SV 10 through the permissible road areas.

A net potential function U _r is generated by combining some potential functions, where the design of each potential function is to include one or more driving rules. In particular, it is a road potential function U _street designed to the SV 10 from the road borders / limits 40 . 42 and is a lane potential function U _track designed for tracking, and is a track speed potential function U _Geschw designed so that the SV 10 the innermost (slowest) track 34 if more than one track is available. In addition, a motor vehicle potential function U _{motor vehicle} designed so that the SV 10 either a suitable distance to the LV 30 or if the other lane 36 is available, changes to a faster track. The net potential function U _r is created by superimposing these single potential functions to create a perception map that can be used to overtake in a human-like manner. The structure of the individual potential functions will be explained below.

Track potential function

wobei ω ein Verstärkungsfaktor ist, v_Spur,i die Nenngeschwindigkeit der i^ten Spur ist und U_Geschw,i das Potential ist, das durch die Spurgeschwindigkeit der i^ten Spur verursacht wird.Different tracks on a road are assigned an implicit speed, ie the speed decreases from the innermost track 34 to the extreme lane 36 progressively too. A higher speed can indicate a higher risk, so every track 34 . 36 the street 32 a certain potential is assigned to describe their assigned risk level. In the present embodiment, this is described by the following function: $$U_{\text{Speed}\text{.}i}\left(w_{\text{r}}\right)=\gamma \left(v_{\text{track}.i}\left(w_{\text{r}}\right)-v_{\text{track}\mathrm{,1}}\left(w_{\text{r}}\right)\right)$$

in which ω is an amplification factor, v _{lane, i} the rated speed of the i ^th track is and U _{Geschw, i} the potential is that caused by the track speed of the i ^th track.

Street potential function

wobei ω ein Skalierungsfaktor ist, J_b die y-Koordinate einer der Straßenkanten 40, 42 ist.The road potential is designed so that the boundaries 40 . 42 have the highest (infinite) potential and the middle of the road has the lowest potential. In the present embodiment, this is described by the following function: $${\text{U}}_{\text{Street}.i}\left(w_{\text{r}}\right)=\frac{\omega }{2}{\left(\frac{1}{J_{\text{r}}-J_{\text{b}}}\right)}^2$$

where ω is a scaling factor, J _b the y-coordinate of one of the road edges 40 . 42 is.

Track potential function

wobei *_Fahrbahn die Amplitude des Spurteilerpotentials bereitstellt, J₁,_i die y-Koordinate der i^ten Fahrspurteilung ist und σ ein Skalierungsfaktor ist.A track potential function creates a virtual barrier between the tracks 34 . 36 to the SV 10 to steer in the direction of the lane center. In the present embodiment, this is described by the Gaussian function to achieve the desired behavior: $$U_{\text{track}.i}\left(w_{\text{r}}\right)={*}_{\text{roadway}}\text{exp}\left(\frac{-{\left(J_{\text{r}}-J_{\text{l}.i}\right)}^2}{2{\sigma }^2}\right)$$

where * _lane provides the amplitude of the tracker potential, J ₁ , _i the y- Coordinate of the i ^th driving judgment is and σ is a scaling factor.

Automobile potential function

wobei α ein Yukawa-Skalierungsfaktor ist, A_{Kraftfahrzeug} die Yukawa-Amplitude ist und K_d der euklidische Abstand zur nächsten Koordinate des mit B_lv bezeichneten Hindernisses ist, angegeben als $$K_{\text{d}}=\underset{b_0\in B_{\text{lv}}}{{\displaystyle \text{min}}}\Vert b_0-w_{\text{r}}\Vert .$$

The LV 30 is referred to as a rectangular area with virtual triangular wedges, also referred to as buffer areas, at the front and back of the LV 30 attached modeled. The place, ie the x and y coordinate, the vertex of the triangle behind the LV 30 is based on the speed of the LV 30 and the interval time h _t calculated. while B _lv is called the set of coordinates that the LV 30 and containing the two triangular wedges, the Yukawa function to describe the potential due to the LV 30 and the triangular wedges used as follows: $$U_{\text{motor vehicle}}\left(w_{\text{r}}\right)={*}_{\text{motor vehicle}}\left(\frac{e^{-\alpha K_{\text{d}}}}{K_{\text{d}}}\right)$$

where α is a Yukawa scaling factor, A _{motor vehicle} the Yukawa amplitude is and K _d the Euclidean distance to the next coordinate of the B _lv designated obstacle is indicated as $$K_{\text{d}}=\underset{b_{}}{{\displaystyle \text{<figure-callout id="0" label="min b" filenames="DE102019201124A1\_0037.png,DE102019201124A1\_0038.png" state="{{state}}">min </figure-callout>}}}\Vert b_0-w_{\text{r}}\Vert ,$$

wobei gilt: $$U_{\text{Spur}}={\displaystyle \sum _{i=1}^{N_{\text{Spuren}}}{U}_{\text{Spur},i}}$$

und $$U_{\text{Geschw}}={\displaystyle \sum _{i=1}^{N_{\text{Spuren}}}{U}_{\text{Geschw},i}}$$

These individual potentials are superimposed to form a total perception map or net potential function of the area that the SV 10 surrounds, and is indicated by $$U_{\text{r}}\left(w_{\text{r}}\right)=U_{\text{Speed}}+U_{\text{Street}}+U_{\text{track}}+U_{\text{motor vehicle}}$$

where: $$U_{\text{track}}={\displaystyle \underset{i=1}{\overset{N_{\text{traces}}}{\Sigma }}{U}_{\text{track}.i}}$$

and $$U_{\text{Speed}}={\displaystyle \underset{i=1}{\overset{N_{\text{traces}}}{\Sigma }}{U}_{\text{Speed}.i}}$$

In practice, the net potential field in the V-frame is examined to facilitate trajectory planning, and so does the above function U _r ( w _r ) are converted (linearly) into the V-frame to give a net potential function $$U_{\text{V}}\left(w_{\text{V}}\right)\triangleq U_{\text{r}}\left(T_{\text{r}}^{\text{v}}\left(w_{\text{V}}\right)\right),$$

By assigning a threshold limit U _whole , the permissible areas or positions of the road are the SV 10 surrounded, expressed as: $$G_{\text{v}}=\left\{w_{\text{v}}\in T_{\text{v}}^{\text{r}}\left(B_{\text{lv}}\right):U_{\text{V}}\left(w_{\text{V}}\right)\le U_{\text{all}}\right\},$$

This provides a range of allowed ranges and the SV 10 must plan trajectories that hold it within this sentence to reduce the risk.

The sentence g _v does not take into account the driving dynamics of the SV 10 , and thus some areas of the road with an allowable potential may not be achievable in practice. The method of selecting reference points in the set of allowable ranges associated with SV dynamics 10 are compatible, is described below.

7 shows an exemplary simulation that is derived from the module 22 is executed for permissible positions. In particular shows 7 (a) a three-dimensional view of the total potential function in the R-frame, and the local minima in the middle of each track to guide the SV 10 can go along with one through the LV 30 generated trapezoidal field are seen. 7 (b) shows the level curves for the same time in the R-frame. The LV 30 is with buffer areas 31 , ie triangular appendices, shown in which the potential field rises rapidly to prevent the SV 10 during different phases of an overtaking maneuver too close to the LV 30 comes.

Returning to 5 determines the target state module 24 in step 80 a target vehicle state with a target vehicle position in the road segment 68 , The target vehicle position corresponds to one of the several determined ones in step 78 calculated permissible vehicle positions. For example, in the described embodiment, the target vehicle position is the allowable vehicle position furthest from the vehicle 10 is removed. The target vehicle state also includes a target vehicle speed and a target vehicle direction angle.

wobei u ≐ (α_x, δ_f) ∈ U die Steueraktion ist, a_x die Längsbeschleunigung ist und δ_f der vordere Lenkwinkel ist. Die Systemmatrizen A_c und B_c sind durch Folgendes gegeben: $$A_c=\left[\begin{array}{cccc}0& 0& 0& 1\\ 0& 0& v_{\text{Ziel}}& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right],$$

$$B_c=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 0& v_{\text{Ziel}}/L_{\text{wb}}\\ 0& 0\end{array}\right],$$

wobei L_wb der Radstand des SV 10 ist.The dynamics of the SV 10 in the I-frame while driving on the road 32 at a desired speed v _goal are shown with a linear kinematic bicycle model. By designating the vehicle states of interest as x ≐ [X, Y, ψ, v _x ] ^T , where ψ is the direction angle, v _x the longitudinal velocity, X, Y is the longitudinal and transverse displacement of the SV 10 are, the dynamics of the SV 10 described by the following $$\dot{x}=A_{c}x+B_{c}u$$

where u ≐ (α _x , δ _f ) ∈ U is the control action, a _x the longitudinal acceleration is and δ _f the front steering angle is. The system matrices A _c and B _c are given by the following: $$A_c=\left[\begin{array}{cccc}0& 0& 0& 1\\ 0& 0& {\mathrm{<figure-callout\; id="0"\; label="v\; aim"\; filenames="DE102019201124A1\_0037.png,DE102019201124A1\_0038.png"\; state="\{\{state\}\}">v\; </figure-callout>}}_{\text{aim}}& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right].$$

$$B_c=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 0& v_{\text{aim}}/{\mathrm{<figure-callout\; id="0"\; label="L\; wb"\; filenames="DE102019201124A1\_0037.png,DE102019201124A1\_0038.png"\; state="\{\{state\}\}">L\; </figure-callout>}}_{\text{wb}}\\ 0& 0\end{array}\right].$$

in which L _wb the wheelbase of the SV 10 is.

wobei im Allgemeinen für einen Satz Γ ⊂ ℝ^na+nb der Projektionsbetrieb als Proj_a(Γ) = {α ∈ ℝ^na: ∃b ∈ ℝ^nb, (a, b) ∈ Γ} definiert ist.In ideal highway driving situations, the dynamics of the system can be described by ẋ = [v _x 0,0,0] ^T , and maneuvers (eg, lane change, threading, etc.) can be considered transitions from one set of states to another set of States are considered. In such ideal scenarios, there is the task of SV 10 to adapt its trajectory to avoid obstacles while ensuring that the vehicle speed is the desired longitudinal speed v _goal does not exceed. Starting from an initial position w ₀ = (X ₀ , J ₀ ) and driving at v _goal using allowed control actions from the set {(a _x , δ _f ): a _x ≤ 0, (a _X , δ _f ) ∈ U _v }, the set ℜ of the states that can be reached without exceeding the desired velocity v _goal in the time interval t _{* of} the system can be determined using the equation given above for ℜ (t _* ; x ₀ ). Thus, the set of achievable lateral and longitudinal coordinates is SV 10 in the V-frame $$R_{\text{V}}=T_{\text{V}}^I\left({\text{proj}}_{\text{w}}\left(R\right)\right).$$

wherein in general for a set Γ ⊂ ℝ ^{na + nb} of the projection operating as _a Proj (Γ) = {α ∈ ℝ ^na: ∃b ∈ ℝ ^nb, (a, b) ∈ Γ} is defined.

und ℜ_v sind die zulässigen Gebiete oder Regionen, die das SV 10 umgeben, die in Bezug auf den Fahrzeugzustand und die Fahrzeugdynamik erreichbar sind, folgende $$R_{\text{V},\text{ganz}}\triangleq G_{\text{v}}\cap R_{\text{V}}.$$

Then using the equations given above for $G_{\text{v}}$

and ℜ _v are the permitted areas or regions that the SV 10 surrounded, which are achievable with respect to the vehicle condition and the vehicle dynamics, following $$R_{\text{V}.\text{all}}\triangleq G_{\text{v}}\cap R_{\text{V}},$$

The reference target coordinates w _v = (X _v , Ĵ _v ) are selected from ℜ _{v, all} the way to the SV 10 in the time interval t _* to maximize distance, ie $${\widehat{w}}_v=\underset{w_{\text{v}}\in R_{\text{V}.\text{all}}}{{\displaystyle \text{argmax}}}\Vert w_{\text{v}}-w_{\text{v0}}\Vert ,$$

It may as well be for the SV 10 be advantageous, the longitudinal distance of X _v0 to traverse X _v at a uniform longitudinal speed so that the target speed is selected as the following. $${\widehat{v}}_x=\frac{\Vert {\widehat{X}}_v*X_{\text{v0}}\Vert }{t_{*}},$$

Further, assuming that the SV 10 in the described embodiment, driving on a straight road ψ = 0, the target direction angle of the SV remains 10 Further, ψ = 0. Thus, x = [X _v, Ŷ _v , ψ, v _x ] is obtained by stacking the reference targets for each state of the target state vector for the system.

Since the area B _lv , (the set of coordinates that the LV 30 and the two triangular wedges into which the SV 10 should not occur), ie the impermissible area containing the LV 30 surrounds itself at a velocity v _{lx -v x} in the R-frame 66 moves, the allowable achievable range and reference targets change accordingly with each step. An example simulation of the reference targets generated by the target state module 24 Running for some time steps is in 8th in the I-frame 60 shown, with the reference goals along with the position of SV 10 (indicated by a square) as crosses and the LV 30 (indicated by a rhombus) are shown. In particular shows 8th that the target references provided by the SV 10 to overtake the LV 30 were selected. In particular, the SV moves 10 behind the LV 30 and then the center of the fast track becomes the lowest potential area and is compatible with the test vehicle dynamics; thus allowing the SV 10 moved to this lane to the LV 30 to overtake. After the SV 10 sufficiently in front of the LV 30 has moved, the middle of the slow track again becomes the area of the lowest potential and is also from the SV 10 reachable. Therefore, the SV 10 at a distance sufficiently in front of the LV 30 thread into the slow lane to complete the overtaking maneuver.

Back on 5 Referring to FIG 82 the generation module 26 for a trajectory configured to be a viable trajectory for the SV 10 determined to travel to the target vehicle position in response to one or more of the vehicle limitations described above. In particular, the target states x generated at each time step using the above approach result in piecewise references. For example, if it is determined that a lane change is required, Ŷ _{v will change} from the middle of one lane to the other. In the described embodiment, an MPC method is used to schedule the trajectory to the SV 10 from its current state to an allowed destination state in an approved manner, ie, taking into account vehicle dynamics, state constraints, and input constraints. The advantage of the described MPC strategy is the ability to steer the state of a restricted system towards any desired value (ie, the desired target state) regardless of whether or not it belongs to the terminal set. The procedure guarantees the asymptotic convergence of the system state to any approved persistent target state. If the persistent state is not allowed, the control strategy steers the system to the nearest admitted steady state.

wobei x_r = [Y, ψ, v_x]^T der Systemzustand ist, u = [a_x, δ_f]^T die Eingabe ist und die Systemmatrizen folgende sind: $$A_{\text{rc}}=\left[\begin{array}{ccc}0& v_{\text{Ziel}}& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$$

und $$B_{\text{rc}}=\left[\begin{array}{cc}0& 0\\ 0& v_{\text{Ziel}}/L_{\text{wb}}\\ 1& 0\end{array}\right].$$

In the present embodiment, the dynamics of the state (X) depends only on v _x , and thus it is possible to further simplify the system for generating a trajectory in order to reduce the computation time. In particular, the reduced order system is the following $${\dot{x}}_{\text{r}}=A_{\text{rc}}{x}_{\text{r}}+B_{\text{rc}}u.$$

where x _r = [Y, ψ, v _x ] ^{T is} the system state, u = [a _x , δ _f ] ^{T is} the input and the system matrices are: $$A_{\text{rc}}=\left[\begin{array}{ccc}0& {\mathrm{<figure-callout\; id="0"\; label="v\; aim"\; filenames="DE102019201124A1\_0037.png,DE102019201124A1\_0038.png"\; state="\{\{state\}\}">v\; </figure-callout>}}_{\text{aim}}& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$$

and $$B_{\text{rc}}=\left[\begin{array}{cc}0& 0\\ 0& v_{\text{aim}}/L_{\text{wb}}\\ 1& 0\end{array}\right],$$

This reduced-order system absorbs the relevant dynamics of the system and is suitable for planning permissible and realizable trajectories. In addition, the reduced system is in a stable state while the SV 10 on straight highways without hindrance as ẋ _r (t) = [0,0,0] ^T drives. Further, the reference vector (s) calculated above correspond to a steady state condition for the reduced order system expressed as x _{r, ss} = [Ŷ, ψ, v _x ] ^T.

$$y_{\text{r}}\left(k\right)=C{x}_{\text{r}}\left(k\right)+Du\left(k\right)$$

wobei die Matrizen A, B, C, D konstant sind, das Paar (A, B) stabilisierbar ist, und das System harten Beschränkungen unterliegt, die als Folgendes ausgedrückt sind: $$z=\left(x_{\text{r}},u_{\text{r}}\right)\in Z=\left\{z\in {ℝ}^{n_x+n_u}:A_{z}z\le b_z\right\}$$

wobei A_z ∈ ℝ^nz×(nx+nu) und b_z ∈ ℝ^nz, wobei n_z die Anzahl der Beschränkungen ist, sodass

ein nicht leeres kompaktes konvexes Polyhedron ist, das den Ursprung seines Inneren enthält. In der beschriebenen Ausführungsform wird der obige Satz von harten Beschränkungen aus Zuständen und Eingaben erhalten, die die folgenden Ungleichungen erfüllen: $$x_{\text{r},\text{min}}\le x_{\text{r}}\le x_{\text{r},\text{max}}$$

$$u_{\text{min}}\le u\le u_{\text{max}}$$

By discretizing the reduced-order system with a sampling time T _s , the following discrete time system is obtained: $$x_{\text{r}}\left(k+1\right)=A{x}_{\text{r}}\left(k\right)+Bu\left(k\right)$$

$$y_{\text{r}}\left(k\right)=C{x}_{\text{r}}\left(k\right)+Du\left(k\right)$$

wherein the matrices A, B, C, D are constant, the pair (A, B) is stabilizable, and the system is subject to hard constraints expressed as: $$z=\left(x_{\text{r}}.u_{\text{r}}\right)\in Z=\left\{z\in {ℝ}^{n_x+n_u}:A_{z}z\le b_z\right\}$$

where A _z ∈ ℝ ^{nz × (nx + nu)} and b _z ∈ ℝ ^nz , where n _{z is} the number of constraints _such that

is a non-empty compact convex polyhedron containing the origin of its interior. In the described embodiment, the above set of hard constraints are obtained from states and inputs that satisfy the following inequalities: $$x_{\text{r}.\text{min}}\le x_{\text{r}}\le x_{\text{r}.\text{Max}}$$

$$u_{\text{min}}\le u\le u_{\text{Max}}$$

für t ∈ [k T_s, (k + N) · T_s], mit N als dem Vorhersagehorizont berechnet, indem die optimale Lösung u* auf das oben angegebene dynamische System angewendet wird.At every single time k, the system is solved by setting the target state as x _s = x _{r, ss} and the initial state as x _s (0) = x _r (k T _s ). Then the reference trajectory ${\left[Y*.\psi *.v_{\text{x}}^{*}\right]}^T$

for t ∈ [k T _s , (k + N) * T _s ], with N as the prediction horizon calculated by applying the optimal solution u * to the above dynamic system.

The dynamic in 8th generated reference points are used directly to generate trajectories. 9 represents planned trajectories and the actual path of SV 10 who is in the reference frame of the LV 30 is shown, in an exemplary simulation, by the generation module 26 for a trajectory is performed. In particular shows 9 in that the overtaking maneuver is about 50 m behind the LV 30 whereby the boundaries expected from a typical highway maneuver for given vehicle speeds and given forward time are maintained. In addition, the planned trajectories are from the generation module 26 stable for a trajectory or the MPC module and show no deviant behavior. Assuming perfect trajectory tracking, it is shown that the actual trajectory that the SV 10 follows a smooth path from the middle of the slow track to the middle of the fast track follows. The trajectories planned by the new MPC are permanently realizable, providing the autonomous driving functionality with an additional safety net.

Numerous modifications can be made to the above examples without departing from the scope of the present invention as defined in the appended claims.

Although a continuous time nonlinear kinematic bicycle model is used in the embodiment described above, higher order vehicle models may also be used to calculate the set of achievable states.

Although the system 12 and the procedure 70 have been described above with reference to a highway overtaking maneuver, they are equally applicable to other types of relatively complex maneuvers that a vehicle can perform.

Although the system 12 has been described above as generating trajectories while traveling at a nearly constant speed, so that the vehicle 10 is not accelerated or decelerated during the lane change part maneuver, realizable trajectories for a varying longitudinal velocity are generated in various embodiments.

Claims (15)

A system for a vehicle that is operable in an autonomous mode, the system for scheduling a trajectory of the vehicle, the system including: a receiver configured to receive road segment data from at least one subsystem of the vehicle, the road segment data indicating at least one feature of a road segment proximate to the vehicle; an achievable state module configured to determine a set of achievable vehicle states within a prescribed period of time in response to at least one vehicle restriction, each of the achievable vehicle states including an achievable vehicle position; an allowable position module configured to determine a plurality of allowable vehicle positions in the road segment based on the received road segment data, wherein the plurality of allowable vehicle positions are within the determined set of accessible vehicle positions; a target state module configured to determine a target vehicle state having a target vehicle position in the road segment, the target vehicle position corresponding to one of the plurality of determined allowable vehicle positions; and, a trajectory generation module configured to determine a viable trajectory on which the vehicle travels to the target vehicle position in response to the at least one vehicle constraint to schedule the vehicle trajectory. System after Claim 1 wherein the system includes a vehicle actuation module configured to transmit a control signal to control the vehicle to follow the realizable trajectory. System after Claim 1 or 2 wherein the at least one road segment feature comprises: a current trajectory of the vehicle; Road and / or lane boundaries; and / or, driving instructions. The system of claim 1, wherein the at least one road segment feature comprises at least one obstacle, optionally wherein the at least one obstacle includes another vehicle and the road segment data includes at least one speed, position and / or orientation of the another vehicle. The system of any preceding claim, wherein the allowed position module is configured to: Defining an artificial potential field greater than the set of achievable vehicle positions; and, Generating a net potential function describing the artificial potential field as a function of the received road segment data, wherein a potential value of the net potential function varies over the artificial potential field. System after Claim 5 wherein the net potential function includes a contribution from one or more of the following: a lane speed potential function that includes information relating to a speed associated with each lane of the road; a road potential function that includes information related to road boundaries; a lane potential function that includes information related to boundaries and / or a center of each lane of the road; and, another vehicle potential function that includes information about vehicle dynamics of another vehicle on the road. The system of claim 1, wherein the at least one vehicle restriction includes one or more current vehicle state variables, optionally wherein the current vehicle state variables include a current vehicle position, a current vehicle direction angle, and an actual vehicle speed. The system of claim 1, wherein the at least one vehicle restriction includes one or more approved vehicle state variables, optionally wherein the permitted vehicle state variables include an approved vehicle direction angle, an approved vehicle speed, and an authorized vehicle lateral position. The system of claim 1, wherein the at least one vehicle restriction includes one or more vehicle input limits, optionally wherein the vehicle input constraints include an approved vehicle steering angle, an approved vehicle acceleration, and / or one or more vehicle dynamics limitations. A system according to any one of the preceding claims, wherein the achievable vehicle conditions include an achievable vehicle speed, an achievable vehicle direction angle, an achievable longitudinal vehicle displacement, and an achievable vehicle lateral displacement. The system of claim 1, wherein the target vehicle position corresponds to the allowable vehicle position furthest from a current vehicle position, the allowable vehicle position corresponding to one of the achievable vehicle positions in the set of achievable vehicle states. The system of any one of the preceding claims, wherein the at least one subsystem of the vehicle includes at least one of: a vehicle navigation subsystem; an ultrasonic sensor; a radar sensor; a LiDAR sensor; an image sensor; and, a vehicle-to-all transceiver. The system of any one of the preceding claims, wherein the trajectory generation module is configured to apply a model predictive control strategy to generate the viable trajectory. A method for a vehicle that is operable in an autonomous mode, the method being for scheduling a trajectory of the vehicle, the method including: Receiving road segment data from at least one subsystem of the vehicle, the road segment data indicating at least one feature of a road segment proximate to the vehicle; Determining a set of achievable vehicle conditions within a prescribed period of time in response to at least one vehicle restriction, each of the achievable vehicle conditions including an achievable vehicle position; Determining a plurality of allowable vehicle positions in the road segment in response to the received road segment data; Determining a target vehicle state with a target vehicle position in the road segment, the target vehicle position corresponding to one of the determined allowable vehicle positions that are within the determined set of achievable vehicle positions; and, Determining a feasible trajectory on which the vehicle travels to the target vehicle position in response to the at least one vehicle constraint to schedule the vehicle trajectory. Vehicle having a system according to one of the Claims 1 to 13 includes.

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