Avoid unseen obstacles with time-optimal trajectories
controllerTEB object creates a controller (local planner)
using the Timed Elastic Band (TEB) algorithm. The controller enables a robot to follow a
reference path typically generated by a global planner, such as RRT or Hybrid A*.
Additionally, the planner avoids obstacles and smooths the path while optimizing travel time,
and maintains a safe distance from obstacles known or unknown to the global planner. The
object also computes velocity commands and an optimal trajectory using the current pose of the
robot and its current linear and angular velocities.
creates a TEB controller object,
controller = controllerTEB(
controller, that computes the linear
and angular velocity commands for a differential-drive robot to follow the reference path
refpath and travel for 5 seconds in an obstacle-free environment.
refpath input sets the value of the ReferencePath
attempts to avoid obstacles in the specified occupancy map
controller = controllerTEB(
controller assumes the space outside the map boundary is free. The
map input sets the value of the Map
specifies properties using one or more name-value arguments in addition to any combination
of input arguments from the previous syntaxes.
controller = controllerTEB(___,
ReferencePath — Reference path to follow
N-by-2 matrix | N-by-3 matrix |
navPath object with SE(2) state space
Reference path to follow, specified as an N-by-2 matrix,
N-by-3 matrix, or
with an SE(2) state space. When specified as a matrix, each row represents a pose on the
path. Use the LookAheadTime
property to select a part of the
ReferencePath for which to
optimize the trajectory and generate velocity commands.
If you specify the reference path as an N-by-2 matrix, then the
object computes the orientation using the
headingFromXY function and appends it as the third column.
Map — Occupancy map representing environment
binaryOccupancyMap() (default) |
binaryOccupancyMap object |
Occupancy map representing the environment, specified as a
binaryOccupancyMap object or
occupancyMap object containing the obstacles in the vicinity of the robot.
When optimizing the trajectory, the controller considers the space outside the boundary
of the map to be free. Larger maps can lead to slower performance.
CostWeights — Weights for cost function optimization
struct("Time",10,"Smoothness",1000,"Obstacle",50) (default) | structure
Weights for cost function optimization, specified as a structure. The fields of the structure are:
Cost function weight for time, specified as a positive scalar. To lower the travel time, increase this weight value.
Cost function weight for smooth motion, specified as a positive scalar. To obtain a smoother path, increase this weight value.
Cost function weight for maintaining a safe distance from obstacles, specified as a positive scalar. To prioritize maintaining a safe distance from obstacles, increase this weight value.
RobotInformation — Robot geometry information for collision checking
0.67],"Shape","Rectangle") (default) | structure
Robot geometry information for collision checking, specified as a structure. The fields of the structure are:
Size of the robot, specified as a two-element positive vector of the form [length width], in meters.
Shape of the robot, specified as
When you set
MinTurningRadius — Minimum turning radius for vehicle on optimized path
0 (default) | nonnegative scalar
Minimum turning radius for the vehicle on the optimized path, specified as a nonnegative scalar. This value corresponds to the radius of the turning circle at the maximum steering angle of the vehicle. Units are in meters.
Decrease this value to allow sharp turns and in place rotations. Increase this value to limit sharp turns. When you increase the value, the vehicle will make more forward and reverse motions to turn in a restricted space.
ObstacleSafetyMargin — Safe distance between robot and obstacles
0.5 (default) | positive scalar
Safe distance between the robot and the obstacles, specified as a positive scalar, in meters. Note that this is a soft constraint that the planner may ignore.
NumIteration — Number of iterations to optimize trajectory
2 (default) | positive integer
Number of iterations to optimize the trajectory, specified as a positive integer. This value is the number of times interpolation occurs and the controller calls the solver for trajectory optimization.
MaxVelocity — Maximum limits of linear and angular velocity
[0.8 1.6] (default) | two-element positive vector
Maximum limits of linear and angular velocity for velocity commands, specified as a two-element positive vector. The first element is the linear velocity limit, in meters per second, and the second element is the angular velocity limit, in radians per second.
MaxReverseVelocity — Maximum velocity for reverse motion
NaN (default) | positive scalar
Maximum velocity of the vehicle while moving in reverse direction, specified as a
positive scalar. The default value is
NaN. When the property is set
NaN, the value of maximum reverse velocity is same as that of the
maximum linear velocity.
MaxAcceleration — Maximum limits of linear and angular acceleration
[2.4 4.8] (default) | two-element positive vector
Maximum limits of linear and angular acceleration for velocity commands, specified as a two-element positive vector. The first element is the linear acceleration limit, in meters per second squared, and the second element is the angular acceleration limit, in radians per second squared.
ReferenceDeltaTime — Reference travel time between consecutive poses
0.3 (default) | positive scalar
Reference travel time between consecutive poses, specified as a positive scalar in seconds. This property affects the addition and deletion of poses for the optimized trajectory. Increase the value of this property to have fewer poses and reduce it to have more poses in the output path.
LookAheadTime — Look-ahead time
5 (default) | positive scalar
Look-ahead time, specified as a positive scalar in seconds. The controller generates velocity commands and optimizes the trajectory until the controller reaches the look-ahead time. A higher look-ahead time generates velocity commands further into the future. This enables the robot to react earlier to unseen obstacles, but increases the controller execution time. Conversely, a shorter look-ahead time reduces the available time to react to new, unknown obstacles, but enables the controller to run at a faster rate.
This property impacts the number of velocity commands, timestamps, and poses in the path.
GoalTolerance — Tolerance around goal pose
0.1 0.1 0.1] (default) | three-element vector
Tolerance around the goal pose, specified as a three-element vector of the form [x y θ]. x and y denote the position of the robot in x and y directions, respectively. Units are in meters. θ is the heading angle of the robot in radians. This goal tolerance value specifies the limit for determining whether the robot has reached the goal pose.
Compute Velocity Commands and Optimal Trajectory for Differential-Drive Robot Using Timed Elastic Band Algorithm
Set Up Parking Lot Environment
occupancyMap object from a parking lot map and set the map resolution to 3 cells per meter.
load parkingMap.mat; resolution = 3; map = occupancyMap(map,resolution);
Visualize the map. The map contains the floor plan of a parking lot with some parking slots already occupied.
show(map) title("Parking Lot Map") hold on
Set Up and Run Global Planner
validator = validatorOccupancyMap(stateSpaceSE2,Map=map); validator.ValidationDistance = 0.1;
Create an RRT* path planner. Increase the maximum connection distance.
rrtstar = plannerRRTStar(validator.StateSpace,validator); rrtstar.MaxConnectionDistance = 0.2;
Set the start and goal states.
start = [2 9 0]; goal = [27 18 -pi/2];
Plan a path with default settings.
rng(42,"twister") % Set random number generator seed for repeatable result. route = plan(rrtstar,start,goal); refpath = route.States;
RRT* uses a random orientation, which can cause unnecessary turns.
headingToNextPose = headingFromXY(refpath(:,1:2));
Align the orientation to the path, except for at the start and goal states.
refpath(2:end-1,3) = headingToNextPose(2:end-1);
Visualize the path.
plot(refpath(:,1),refpath(:,2),"r-",LineWidth=2) hold off
Set Up and Run Local Planner
Create a local
occupancyMap object with a width and height of 15 meters and the same resolution as the global map.
localmap = occupancyMap(15,15,map.Resolution);
controllerTEB object by using the reference path generated by the global planner and the local map.
teb = controllerTEB(refpath,localmap);
Specify the properties of the
teb.LookAheadTime = 10; % sec teb.ObstacleSafetyMargin = 0.4; % meters % To generate time-optimal trajectories, specify a larger weight value, % like 100, for the cost function, Time. To follow the reference path % closely, keep the weight to a smaller value like 1e-3. teb.CostWeights.Time = 100;
Create a deep clone of the
teb2 = clone(teb);
curpose = refpath(1,:); curvel = [0 0]; simtime = 0; % Reducing timestep can lead to more accurate path tracking. timestep = 0.1; itr = 0; goalReached = false;
Compute velocity commands and optimal trajectory.
while ~goalReached && simtime < 200 % Update map to keep robot in the center of the map. Also update the % map with new information from the global map or sensor measurements. moveMapBy = curpose(1:2) - localmap.XLocalLimits(end)/2; localmap.move(moveMapBy,FillValue=0.5) syncWith(localmap,map) if mod(itr,10) == 0 % every 1 sec % Generate new vel commands with teb [velcmds,tstamps,curpath,info] = step(teb,curpose,curvel); goalReached = info.HasReachedGoal; feasibleDriveDuration = tstamps(info.LastFeasibleIdx); % If robot is far from goal and only less than third of trajectory % is feasible, then an option is to re-plan the path to follow to % reach the goal. if info.ExitFlag == 1 && ... feasibleDriveDuration < (teb.LookAheadTime/3) route = plan(rrtstar,curpose,[27 18 -pi/2]); refpath = route.States; headingToNextPose = headingFromXY(refpath(:,1:2)); refpath(2:end-1,3) = headingToNextPose(2:end-1); teb.ReferencePath = refpath; end timestamps = tstamps + simtime; % Show the updated information input to or output % from controllerTEB clf show(localmap) hold on plot(refpath(:,1),refpath(:,2),".-",Color="#EDB120", ... DisplayName="Reference Path") quiver(curpath(:,1),curpath(:,2), ... cos(curpath(:,3)),sin(curpath(:,3)), ... 0.2,Color="#A2142F",DisplayName="Current Path") quiver(curpose(:,1),curpose(:,2), ... cos(curpose(:,3)),sin(curpose(:,3)), ... 0.5,"o",MarkerSize=20,ShowArrowHead="off", ... Color="#0072BD",DisplayName="Start Pose") end simtime = simtime+timestep; % Compute the instantaneous velocity to be sent to the robot from the % series of timestamped commands generated by controllerTEB velcmd = velocityCommand(velcmds,timestamps,simtime); % Very basic robot model, should be replaced by simulator. statedot = [velcmd(1)*cos(curpose(3)) ... velcmd(1)*sin(curpose(3)) ... velcmd(2)]; curpose = curpose + statedot*timestep; if exist("hndl","var") delete(hndl) end hndl = quiver(curpose(:,1),curpose(:,2), ... cos(curpose(:,3)),sin(curpose(:,3)), ... 0.5,"o",MarkerSize=20,ShowArrowHead="off", ... Color="#D95319",DisplayName="Current Robot Pose"); itr = itr + 1; drawnow end legend
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Version HistoryIntroduced in R2023a
R2023b: Specify minimum turning radius, maximum reverse velocity, and goal tolerance
You can now specify
Minimum turning radius for a vehicle on the optimized path by using the
Maximum velocity for reverse motion by using the
The limit for determining whether the robot has reached the goal pose by using the