trajectory

Create actor or vehicle trajectory in driving scenario

Syntax

trajectory(ac,waypoints)

trajectory(ac,waypoints,speed)

trajectory(ac,waypoints,speed,waittime)

trajectory(___,'Yaw',yaw)

Description

trajectory(ac,waypoints) creates a trajectory for an actor or vehicle, ac, from a set of waypoints.

Note

The trajectory function generates trajectories that have discontinuities in acceleration between waypoints, resulting in high amounts of jerk. To generate a smooth, jerk-limited trajectory, use the smoothTrajectory function instead.

trajectory(ac,waypoints,speed) also specifies the speed with which the actor or vehicle travels along the trajectory, in either forward or reverse motion.

trajectory(ac,waypoints,speed,waittime) specifies the wait time for an actor or vehicle in addition to the input arguments in the previous syntax. Use this syntax to generate stop-and-go driving scenarios by pausing an actor or vehicle actors at specific waypoints.

trajectory(___,'Yaw',yaw) specifies the yaw orientation angle of the actor or vehicle at each waypoint, in addition to any of the input argument combinations from preceding syntaxes.

Examples

Simulate Vehicle with Trajectory of Varying Speeds

Create a driving scenario and add a curved two-lane road to it.

scenario = drivingScenario('SampleTime',0.05);
roadcenters = [5 0; 30 10; 35 25];
lspec = lanespec(2);
road(scenario,roadcenters,'Lanes',lspec);

Add a vehicle to the scenario. Set a trajectory in which the vehicle drives around the curve at varying speeds.

v = vehicle(scenario,'ClassID',1);
waypoints = [6 2; 18 4; 25 7; 28 10; 31 15; 33 22];
speeds = [30 10 5 5 10 30];
trajectory(v,waypoints,speeds)

Plot the scenario and run the simulation. Observe how the vehicle slows down as it drives along the curve.

plot(scenario,'Waypoints','on','RoadCenters','on')
while advance(scenario)
    pause(0.1)
end

Generate Stop-and-Go Driving Scenario

Create a driving scenario consisting of two, two-lane roads that intersect at a right angle.

scenario = drivingScenario('StopTime',2.75);
roadCenters = [50 1 0; 2 0.9 0];
laneSpecification = lanespec(2,'Width',4);
road(scenario,roadCenters,'Lanes',laneSpecification);
roadCenters = [27 24 0; 27 -21 0];
road(scenario,roadCenters,'Lanes',laneSpecification);

Add an ego vehicle to the scenario. Specify the waypoints and the speed values for the vehicle at each waypoint. Set a wait time for the vehicle at the second waypoint. Generate a trajectory in which the ego vehicle travels through the specified waypoints at the specified speed.

egoVehicle = vehicle(scenario,'ClassID',1,'Position',[5 -1 0]);
waypoints = [5 -1 0; 16 -1 0; 40 -1 0];
speed = [30; 0; 30];
waittime = [0; 0.3; 0];
trajectory(egoVehicle,waypoints,speed,waittime);

Add a car to the scenario. Specify the waypoints and the speed values for the car at each waypoint. Set a wait time for the car at the second waypoint. Generate a trajectory in which the car travels through the specified waypoints at the specified speed.

car = vehicle(scenario,'ClassID',1,'Position',[48 4 0],'PlotColor',[0.494 0.184 0.556], 'Name','Car');
waypoints = [47 3 0; 38 3 0; 10 3 0];
speed = [30; 0; 30];
waittime = [0; 0.3; 0];
trajectory(car,waypoints,speed,waittime);

Add an ambulance to the scenario. Generate a trajectory in which the ambulance travels through the specified waypoints at a constant speed.

ambulance = vehicle(scenario,'ClassID',6,'Position',[25 22 0],'PlotColor',[0.466 0.674 0.188],'Name','Ambulance');
waypoints = [25 22 0; 25 13 0; 25 6 0; 26 2 0; 33 -1 0; 45 -1 0];
speed = 25;
trajectory(ambulance,waypoints,speed);

Create a custom figure window to plot the scenario.

fig = figure;
set(fig,'Position',[0,0,800,600]);
movegui(fig,'center');
hViewPnl = uipanel(fig,'Position',[0 0 1 1],'Title','Stop-and-Go Scenario');
hPlt = axes(hViewPnl);

Plot the scenario and run the simulation. The ego vehicle and the car pause for their specified wait times to avoid collision with the ambulance.

plot(scenario,'Waypoints','on','RoadCenters','on','Parent',hPlt)
while advance(scenario)
    pause(0.1)
end

Simulate Car Backing into Parking Space

Simulate a driving scenario in which a car drives in reverse to back into a parking space.

Create a driving scenario containing a parking lot.

scenario = drivingScenario;
vertices = [0 9; 18 9; 18 -9; 0 -9];
parkingLot(scenario,vertices,ParkingSpace=parkingSpace);

Create a car and define its trajectory. The car drives forward, stops, and then drives in reverse to back into the parking space. As the car enters the parking space, it has a yaw orientation angle that is 90 degrees counterclockwise from where it started.

car = vehicle(scenario,ClassID=1);
waypoints = [9 -5; 9 5; 6 -1.3; 2 -1.3];
speed = [3; 0; -2; 0];
yaw = [90 90 180 180];
smoothTrajectory(car,waypoints,speed,Yaw=yaw)

Plot the driving scenario and display the waypoints of the trajectory.

plot(scenario,Waypoints="on")
while advance(scenario)
    pause(0.001)
end

Define Trajectory of Pedestrian

Define the trajectory of a pedestrian who takes a sharp right turn at an intersection.

Create a driving scenario. Add road segments that define an intersection.

scenario = drivingScenario;
roadCenters = [0 10; 0 -10];
road(scenario,roadCenters);
road(scenario,flip(roadCenters,2));

Add a pedestrian actor to the scenario.

pedestrian = actor(scenario, ...
    'ClassID',4, ...
    'Length',0.24, ...
    'Width',0.45, ...
    'Height',1.7, ...
    'Position',[-9 0 0], ...
    'RCSPattern',[-8 -8; -8 -8], ...
    'Mesh', driving.scenario.pedestrianMesh, ...
    'Name','Pedestrian');

Define the trajectory of the pedestrian. The pedestrian approaches the intersection, pauses briefly, and then takes a sharp right turn at the intersection. To define the sharp right turn, specify two waypoints at the intersection that are close together. For these waypoints, specify the yaw orientation angle of the second waypoint at a 90-degree angle from the first waypoint.

waypoints = [-9 0; -0.25 0; 0 -0.25; 0 -9];
speed = [1.5; 0; 0.5; 1.5];
yaw =  [0; 0; -90; -90];
waittime = [0; 0.2; 0; 0];
trajectory(pedestrian,waypoints,speed,waittime,'Yaw', yaw);

Plot the driving scenario and display the waypoints of the pedestrian.

plot(scenario,'Waypoints','on')
while advance(scenario)
    pause(0.001)
end

Input Arguments

ac — Actor

Actor object | Vehicle object

Actor belonging to a drivingScenario object, specified as an Actor or Vehicle object. To create these objects, use the actor and vehicle functions, respectively.

waypoints — Trajectory waypoints

real-valued N-by-2 matrix | real-valued N-by-3 matrix

Trajectory waypoints, specified as a real-valued N-by-2 or N-by-3 matrix, where N is the number of waypoints.

• If waypoints is an N-by-2 matrix, then each matrix row represents the (x, y) coordinates of a waypoint. The z-coordinate of each waypoint is zero.

• If waypoints is an N-by-3 matrix, then each matrix row represents the (x, y, z) coordinates of a waypoint.

Waypoints are in the world coordinate system. Units are in meters.

Example: [1 0 0; 2 7 7; 3 8 8]

Data Types: single | double

speed — Actor speed

30.0 | real-valued scalar | N-element real-valued vector

Actor speed at each waypoint in waypoints, specified as a real-valued scalar or N-element real-valued vector. N is the number of waypoints.

• When speed is a scalar, the speed is constant throughout the actor motion.

• When speed is a vector, the vector values specify the speed at each waypoint. For forward motion, specify positive speed values. For reverse motion, specify negative speed values. To change motion directions, separate the positive speeds and negative speeds by a waypoint with 0 speed.

Speeds are interpolated between waypoints. speed can be zero at any waypoint but cannot be zero at two consecutive waypoints. Units are in meters per second.

Example: [10 8 9] specifies speeds of 10 m/s, 8 m/s, and 9 m/s.

Example: [10 0 -10] specifies a speed of 10 m/s in forward motion, followed by a pause, followed by a speed of 10 m/s in reverse.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

waittime — Pause time for actor

0 (default) | N-element vector of nonnegative values

Pause time for the actor, specified as an N-element vector of nonnegative values. N is the number of waypoints. When you specify a pause time for the actor at a particular waypoint, you must set the corresponding speed value to 0. You can set the waitime to 0 at any waypoint, but you cannot set waittime at two consecutive waypoints to non-zero values. Units are in seconds.

Data Types: single | double

yaw — Yaw orientation angle of actor

N-element real-valued vector

Yaw orientation angle of the actor at each waypoint, specified as an N-element real-valued vector, where N is the number of waypoints. Units are in degrees and angles are positive in the counterclockwise direction.

If you do not specify yaw, then the yaw at each waypoint is NaN, meaning that the yaw has no constraints.

Example: [0 90] specifies an actor at a 0-degree angle at the first waypoint and a 90-degree angle at the second waypoint.

Example: [0 NaN] specifies an actor at a 0-degree angle at the first waypoint. The actor has no constraints on its yaw at the second waypoint.

Data Types: single | double

Algorithms

The trajectory function creates a trajectory for an actor to follow in a scenario. A trajectory consists of the path followed by an object and its speed along the path. You specify the path using N two-dimensional or three-dimensional waypoints. Each of the N – 1 segments between waypoints defines a curve whose curvature varies linearly with distance along the segment. The function fits a piecewise clothoid curve to the (x, y) coordinates of the waypoints by matching the curvature on both sides of the waypoint. For a nonclosed curve, the curvature at the first and last waypoint is zero. If the first and last waypoints coincide, then the curvatures before and after the endpoints are matched. The z-coordinates of the trajectory are interpolated using a shape-preserving piecewise cubic curve.

The generated trajectory results in a piecewise constant-acceleration profile for each segment between waypoints. These segments have acceleration discontinuities between them. To avoid discontinuities in acceleration, use the smoothTrajectory function to generate trajectories instead.

Version History

Introduced in R2018a