Timed Elastic Band

Plan path to avoid obstacles and generate time-optimal trajectories

Since R2025a

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  • Timed Elastic Band Block

Libraries:
Navigation Toolbox / Control Algorithms

Description

The Timed Elastic Band (TEB) block computes a feasible path that avoids obstacles while guiding the vehicle towards a specified reference path. The reference path is typically computed using a global path planner like plannerRRTStar.

The local path planner smooths the path while optimizing travel time, and maintains a safe distance from obstacles known or unknown to the global planner.

Examples

New
Avoid Obstacles Using TEB Local Planner in Simulink

Avoid Obstacles Using TEB Local Planner in Simulink

Perform path following using TEB local planner in Simulink.

Ports

Input

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Current pose of the robot, specified as a three-element vector of the form [x y theta]. x and y specify the robot position in meters. theta specifies the robot orientation in radians.

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

Current velocity of the robot, specified as a two-element vector of the form [v w]. v specifies the linear velocity of the robot in meters per second. w specifies the angular velocity of the robot in radians per second.

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

Local map information, specified as a bus. The bus comprises these fields:

  • Resolution - Grid resolution, specified as a scalar in cells per meter representing the number and size of grid locations.

  • GridLocationInWorld - [x,y] world coordinates of the bottom-left corner of the grid, specified as a 1-by-2 vector.

  • OccMat - Occupancy grid values, specified as an h-by-w matrix. h and w are defined by the two elements of the GridSize property of the occupancy grid object.

  • GridSize - Number of rows and columns in grid, specified as a 1-by-2 real-valued vector representing the number of rows and columns, in that order.

  • GridOriginInLocal - Location of the bottom-left corner of the grid in local coordinates, specified as a two-element vector, [xLocal yLocal].

Data Types: bus

Reference path to follow, specified as an N-by-3 matrix.

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

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.

Dependencies

To enable this input port, select the Specify max velocity using input port checkbox in the Trajectory tab.

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

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 to NaN, the value of maximum reverse velocity is same as that of the maximum linear velocity. Units is in meters per second.

Dependencies

To enable this input port, select the Specify max reverse velocity using input port checkbox in the Trajectory tab.

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

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.

Dependencies

To enable this input port, select the Specify max acceleration using input port checkbox in the Trajectory tab.

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

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.

Dependencies

To enable this input port, select the Specify min turning radius using input port checkbox in the Trajectory tab.

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

Weight for time, specified as a positive scalar. To lower the travel time, increase this weight value.

Dependencies

To enable this input port, select the Specify time weight using input port parameter in the Optimization tab .

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

Cost function weight for smooth motion, specified as a positive scalar. To obtain a smoother path, increase this weight value.

Dependencies

To enable this input port, select the Specify smoothness weight using input port parameter in the Optimization tab .

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

Cost function weight for maintaining a safe distance from obstacles, specified as a positive scalar.

Dependencies

To enable this input port, select the Specify obstacle weight using input port parameter in the Optimization tab.

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

Safe distance between the robot and the obstacles, specified as a positive scalar, in meters.

Dependencies

To enable this input port, select the Specify obstacle safety margin using input port parameter in the Main tab.

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

Number of iterations to optimize the trajectory, specified as a positive integer.

Dependencies

To enable this input port, select the Specify number of iterations using input port checkbox in the Optimization tab.

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

Lookahead time, specified as a positive scalar in seconds.

Dependencies

To enable this input port, select the Specify lookahead time using input port checkbox in the Main tab.

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

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.

Dependencies

To enable this input port, select the Specify goal tolerance using input portcheckbox in the Main tab.

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

Reference delta time, specified as a positive scalar in seconds. It specifies the travel time between consecutive poses.

Dependencies

To enable this input port, select the Specify reference delta time using input port checkbox in the Trajectory tab.

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

Output

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Velocity commands, returned as an N-by-2 matrix. The first column is the linear velocity in meters per second, and the second column is the angular velocity in radians per second.

Data Types: double

Timestamps corresponding to velocity commands, returned as an N-element column vector.

Data Types: double

Optimized path, returned as an N-by-3 matrix. Each row is of the form [x y theta], which defines the xy-position and orientation angle theta at a point in the path.

Data Types: double

Extra information, returned as a bus. The bus comprises these fields:

FieldDescription
LastFeasibleIdx

Index specifying an element in the optimized path and timestamp outputs until which the trajectory is feasible. Beyond this index, the value of ExitFlag will be greater than zero. This implies one or more scenarios corresponding to ExitFlag > 0 has occurred.

DistanceFromStartPose

Distance of each pose in optPath from the first pose in optPath. The value of curState is always the first pose in optPath.

HasReachedGoal

Indicates whether the robot has successfully reached the last pose in the ReferencePath within a tolerance, and returns as true if successful. Otherwise, this value returns false.

TrajectoryCost

Cost of optimized trajectory for cost functions in the Timed Elastic Band algorithm.

ExitFlag

Scalar value indicating the exit condition of the Timed Elastic Band function.

  • 0 — Indicates that the Timed Elastic Band function returned feasible velocity commands and trajectory.

  • 1 — Indicates that the trajectory output returned by the Timed Elastic Band function is collision free only until the index value specified using LastFeasibleIdx.

  • 2 — Indicates that the poses corresponding to indices after the LastFeasibleIdx violates the obstacle safety margin constraint of the TEB controller by more than 10%.

  • 3 — Indicates that the turning radius of the vehicle while moving from a pose at LastFeasibleIdx to a subsequent pose violates the minimum turning radius constraint by more than 10%.

  • 4 — Indicates that one or more time stamps returned by the Timed Elastic Band function are older than the previous time stamp.

  • 5 — Indicates that the robot will not reach the reference path within a specified look-ahead time even if it travels at a maximum linear velocity from its current position.

Data Types: bus

Parameters

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To edit block parameters interactively, use the Property Inspector. From the Simulink® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Main Tab

Specify sample time of the controller in seconds. This block only supports discrete sample time.

Select this check box to add an input port for specifying the Lookahead time (s) parameter.

Specify lookahead time as a positive scalar. Units in seconds. The controller generates velocity commands and optimizes the trajectory until the controller reaches the lookahead time. A higher lookahead 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 lookahead time reduces the available time to react to new, unknown obstacles, but enables the controller to run at a faster rate.

Dependencies

To enable this parameter, clear the Specify lookahead time using input port checkbox.

Select this checkbox to add an input port for specifying the Goal tolerance ([m m rad]) parameter.

Specify the tolerance around goal pose 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.

Dependencies

To enable this parameter, clear the Specify goal tolerance using input port checkbox.

Specify the shape of the robot as Rectangle or Point.

Specify the size of the robot as a two-element positive vector of the form [length width], in meters.

Transformation matrix, specified as an se2 object defining an SE(2) transformation matrix or three-element row vector representing the origin of the robot. The vector is of the form [x, y, theta]. When you specify the origin as [x, y, theta], the Timed Elastic Band block computes the associated SE(2) transformation matrix and stores it in the FixedTransform field.

The default origin is at the center of the rear end of the robot. You can use this parameter to specify a new origin for the robot relative to the default origin.

This parameter is valid only if the robot is of rectangular shape.

Select this checkbox to add an input port for specifying the Obstacle safety margin (m) parameter.

Safe distance between the robot and the obstacles, specified as a positive scalar, in meters.

Dependencies

To enable this parameter, clear the Specify obstacle safety margin using input port checkbox.

Trajectory Tab

Select this checkbox to add an input port for specifying the Maximum velocity ([m/s rad/s]) parameter.

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.

Dependencies

To enable this parameter, clear the Specify max velocity using input port checkbox.

Select this checkbox to add an input port for specifying the Maximum reverse velocity (m/s) parameter.

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 to NaN, the value of maximum reverse velocity is same as that of the maximum linear velocity. Units is in meters per second.

Dependencies

To enable this parameter, clear the Specify max reverse velocity using input port checkbox.

Select this checkbox to add an input port for specifying the Maximum acceleration ([m/s^2 rad/s^2]) parameter.

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.

Dependencies

To enable this parameter, clear the Specify max acceleration using input port checkbox.

Select this checkbox to add an input port for specifying the Minimum turning radius (m) parameter.

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.

Dependencies

To enable this parameter, clear the Specify min turning radius using input port checkbox.

Select this checkbox to add an input port for specifying the Reference delta time (s) parameter.

Reference delta time, specified as a positive scalar in seconds. It specifies the travel time between consecutive poses. This parameter affects the addition and deletion of poses for the optimized trajectory. Increase the value of this parameter to have fewer poses and reduce it to have more poses in the output path.

Dependencies

To enable this parameter, clear the Specify reference delta time using input port checkbox.

Optimization Tab

Select this checkbox to add an input port for specifying the Number of iterations parameter.

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.

Dependencies

To enable this parameter, clear the Specify number of iterations using input port checkbox.

Select this checkbox to add an input port for specifying the Time weight parameter.

Cost function weight for time, specified as a positive scalar. To lower the travel time, increase this weight value.

Dependencies

To enable this parameter, clear the Specify time weight using input port checkbox.

Select this checkbox to add an input port for specifying the Smoothness weight parameter.

Cost function weight for smooth motion, specified as a positive scalar. To obtain a smoother path, increase this weight value.

Dependencies

To enable this parameter, clear the Specify smoothness weight using input port checkbox.

Select this checkbox to add an input port for specifying the Obstacle weight parameter.

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.

Dependencies

To enable this parameter, clear the Specify obstacle weight using input port checkbox.

Extended Capabilities

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C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2025a

See Also

Objects

Blocks