# Trapezoidal Velocity Profile Trajectory

Generate trajectories through multiple waypoints using trapezoidal velocity profiles

**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

## 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.

*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.

*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.

*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.

*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.

*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 Simulation Modes (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**

## See Also

### Blocks

### Functions

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