Trapezoidal Velocity Profile Trajectory

Generate trajectories through multiple waypoints using trapezoidal velocity profiles

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Libraries:
Robotics System Toolbox / Utilities

Description

The Trapezoidal Velocity Profile Trajectory block generates a trajectory through a given set of waypoints that follow a trapezoidal velocity profile. The block outputs positions, velocities, and accelerations for a trajectory based on the given waypoints and velocity profile parameters.

Examples

Generate Trapezoidal Velocity Trajectory

Generate a trapezoidal velocity trajectory using the Trapezoidal Velocity block in Simulink^®.

• Open Live Script

Ports

Input

Time — Time point along trajectory

scalar | vector

Time point along trajectory, specified as a scalar or vector. In general, when specified as a scalar, this value is synced with simulation time and is used to specify the time point for sampling the trajectory. The block outputs a vector of the trajectory variables at that instant in time. If the time is specified as a vector, the block outputs a matrix with each column corresponding to each element of the vector.

Data Types: single | double

Waypoints — Waypoint positions along trajectory

n-by-p matrix

Positions of waypoints of the trajectory at given time points, specified as an n-by-p matrix, where n is the dimension of the trajectory and p is the number of waypoints.

Dependencies

To enable this input, set Waypoint source to External.

PeakVel — Peak velocity of the velocity profile

[1;2] (default) | scalar | n-element vector | n-by-(p – 1) matrix

Peak velocity of the profile segment, specified as a scalar, vector, or matrix. This peak velocity is the highest velocity achieved during the trapezoidal velocity profile.

A scalar value is applied to all elements of the trajectory and between all waypoints. An n-element vector is applied to each element of the trajectory between all waypoints. An n-by-(p – 1) matrix is applied to each element of the trajectory for each waypoint.

Dependencies

To enable this parameter, set Number of parameters to 1 or 2. Set Parameter 1 or Parameter 2 to Peak Velocity. Then, set Parameter source to External.

Data Types: single | double

Accel — Acceleration of the velocity profile

[2;2] (default) | scalar | n-element vector | n-by-(p – 1) matrix

Acceleration of the velocity profile, specified as a scalar, vector, or matrix. This acceleration defines the constant acceleration from zero velocity to the Peak velocity value.

A scalar value is applied to all elements of the trajectory and between all waypoints. An n-element vector is applied to each element of the trajectory between all waypoints. An n-by-(p – 1) matrix is applied to each element of the trajectory for each waypoint.

Dependencies

To enable this parameter, set Number of parameters to 1 or 2. Set Parameter 1 or Parameter 2 to Acceleration. Then, set Parameter source to External.

Data Types: single | double

EndTime — Duration of trajectory segment

[1;2] (default) | scalar | n-element vector | n-by-(p – 1) matrix

Duration of trajectory segment, specified as a scalar, vector, or matrix.

A scalar value is applied to all elements of the trajectory and between all waypoints. An n-element vector is applied to each element of the trajectory between all waypoints. An n-by-(p – 1) matrix is applied to each element of the trajectory for each waypoint.

Dependencies

To enable this parameter, set Number of parameters to 1 or 2. set Parameter 1 or Parameter 2 to End Time. Then, set Parameter source to External.

Data Types: single | double

AccelTime — Duration of acceleration phase of velocity profile

[1;1] (default) | scalar | n-element vector | n-by-(p – 1) matrix

Duration of acceleration phase of velocity profile, specified as a scalar, vector, or matrix.

A scalar value is applied to all elements of the trajectory and between all waypoints. An n-element vector is applied to each element of the trajectory between all waypoints. An n-by-(p – 1) matrix is applied to each element of the trajectory for each waypoint.

Dependencies

To enable this parameter, set Number of parameters to 1 or 2. set Parameter 1 or Parameter 2 to Acceleration Time. Then, set Parameter source to External.

Data Types: single | double

Output

q — Position of trajectory

scalar | vector | matrix

Position of the trajectory, specified as a scalar, vector, or matrix. If you specify a scalar for the Time input with an n-dimensional trajectory, the output is a vector with n elements. If you specify a vector of m elements for the Time input, the output is an n-by-m matrix.

Data Types: single | double

qd — Velocity of trajectory

scalar | vector | matrix

Velocity of the trajectory, specified as a scalar, vector, or matrix. If you specify a scalar for the Time input with an n-dimensional trajectory, the output is a vector with n elements. If you specify a vector of m elements for the Time input, the output is an n-by-m matrix.

Data Types: single | double

qdd — Acceleration of trajectory

scalar | vector | matrix

Acceleration of the trajectory, specified as a scalar, vector, or matrix. If you specify a scalar for the Time input with an n-dimensional trajectory, the output is a vector with n elements. If you specify a vector of m elements for the Time input, the output is an n-by-m matrix.

Data Types: single | double

Parameters

Waypoint source — Source for waypoints

Internal (default) | External

Specify External to specify the Waypoints and Time points parameters as block inputs instead of block parameters.

Waypoints — Waypoint positions along trajectory

n-by-p matrix

Positions of waypoints of the trajectory at given time points, specified as an n-by-p matrix, where n is the dimension of the trajectory and p is the number of waypoints.

Number of parameters — Number of velocity profile parameters

0 (default) | 1 | 2

Number of velocity profile parameters, specified as 0, 1, or 2. Increasing this value adds Parameter 1 and Parameter 2 for specifying parameters for the velocity profile.

Parameter 1 — Velocity profile parameter

Peak Velocity | Acceleration | End Time | Acceleration Time

Velocity profile parameter, specified as Peak Velocity, Acceleration, End Time, or Acceleration Time. Setting this parameter creates a parameter in the mask with this value as its name.

Dependencies

To enable this parameter, set Number of parameters to 1 or 2.

If Parameter Source is set to Internal, this parameter creates a parameter in the mask with this value as its name.

If Parameter Source is set to External, this parameter creates an input port based on this value.

Parameter 2 — Velocity profile parameter

Peak Velocity | Acceleration | End Time | Acceleration Time

Velocity profile parameter, specified as Peak Velocity, Acceleration, End Time, or Acceleration Time. Setting this parameter creates a parameter in the mask with this value as its name.

Dependencies

To enable this parameter, set Number of parameters to 2.

If Parameter Source is set to Internal, this parameter creates a parameter in the mask with this value as its name.

If Parameter Source is set to External, this parameter creates an input port based on this value.

Parameter source — Source for waypoints

Internal (default) | External

Specify External to specify the velocity profile parameters as block inputs instead of block parameters.

Dependencies

To enable this parameter, set Number of parameters to 1 or 2.

Peak velocity — Peak velocity of the velocity profile

[1;2] (default) | scalar | n-element vector | n-by-(p – 1) matrix

Peak velocity of the profile segment, specified as a scalar, vector, or matrix. This peak velocity is the highest velocity achieved during the trapezoidal velocity profile.

A scalar value is applied to all elements of the trajectory and between all waypoints. An n-element vector is applied to each element of the trajectory between all waypoints. An n-by-(p – 1) matrix is applied to each element of the trajectory for each waypoint.

Dependencies

To enable this parameter, set Number of parameters to 1 or 2. Then, set Parameter 1 or Parameter 2 to Peak Velocity.

Data Types: single | double

Acceleration — Acceleration of the velocity profile

[2;2] (default) | scalar | n-element vector | n-by-(p – 1) matrix

Acceleration of the velocity profile, specified as a scalar, vector, or matrix. This acceleration defines the constant acceleration from zero velocity to the Peak velocity value.

A scalar value is applied to all elements of the trajectory and between all waypoints. An n-element vector is applied to each element of the trajectory between all waypoints. An n-by-(p – 1) matrix is applied to each element of the trajectory for each waypoint.

Dependencies

To enable this parameter, set Number of parameters to 1 or 2. Then, set Parameter 1 or Parameter 2 to Acceleration.

Data Types: single | double

End time — Duration of trajectory segment

[1;2] (default) | scalar | n-element vector | n-by-(p – 1) matrix

Duration of trajectory segment, specified as a scalar, vector, or matrix.

A scalar value is applied to all elements of the trajectory and between all waypoints. An n-element vector is applied to each element of the trajectory between all waypoints. An n-by-(p – 1) matrix is applied to each element of the trajectory for each waypoint.

Dependencies

To enable this parameter, set Number of parameters to 1 or 2. Then, set Parameter 1 or Parameter 2 to End Time.

Data Types: single | double

Acceleration time — Duration of acceleration phase of velocity profile

[1;1] (default) | scalar | n-element vector | n-by-(p – 1) matrix

Duration of acceleration phase of velocity profile, specified as a scalar, vector, or matrix.

A scalar value is applied to all elements of the trajectory and between all waypoints. An n-element vector is applied to each element of the trajectory between all waypoints. An n-by-(p – 1) matrix is applied to each element of the trajectory for each waypoint.

Dependencies

To enable this parameter, set Number of parameters to 1 or 2. Then, set Parameter 1 or Parameter 2 to Acceleration Time.

Data Types: single | double

Simulate using — Type of simulation to run

Interpreted execution (default) | Code generation

• Interpreted execution — Simulate model using the MATLAB^® interpreter. This option shortens startup time but has a slower simulation speed than Code generation. In this mode, you can debug the source code of the block.

• Code generation — Simulate model using generated C code. The first time you run a simulation, Simulink generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time, but the speed of the subsequent simulations is comparable to Interpreted execution.

Tunable: No

Tips

For better performance, consider these options:

• Minimize the number of waypoint or parameter changes.

• Set the Waypoint source parameter to Internal.

• Set the Simulate using parameter to Code generation. For more information, see Interpreted Execution vs. Code Generation (Simulink).

References

[1] Lynch, Kevin M., and Frank C. Park. Modern Robotics: Mechanics, Planning and Control. Cambridge: Cambridge University Press, 2017.

[2] Spong, Mark W., Seth Hutchinson, and M. Vidyasagar. Robot Modeling and Control. John Wiley & Sons, 2006.

Extended Capabilities

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

Version History

Introduced in R2019a