# Pure Pursuit

Linear and angular velocity control commands

Since R2019b

Libraries:
Robotics System Toolbox / Mobile Robot Algorithms

## Description

The Pure Pursuit block computes linear and angular velocity commands for following a path using a set of waypoints and the current pose of a differential drive vehicle. The block takes updated poses to update velocity commands for the vehicle to follow a path along a desired set of waypoints. Use the Max angular velocity and Desired linear velocity parameters to update the velocities based on the performance of the vehicle.

The look-ahead distance port and parameter compute a look-ahead point on the path, which is an instantaneous local goal for the vehicle. The angular velocity command is computed based on this point. Changing the look-ahead distance has a significant impact on the performance of the algorithm. A higher look-ahead distance results in a smoother trajectory for the vehicle, but can cause the vehicle to cut corners along the path. Too low of a look-ahead distance can result in oscillations in tracking the path, causing unstable behavior. For more information on the pure pursuit algorithm, see Pure Pursuit Controller.

## Ports

### Input

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Current vehicle pose, specified as an `[x y theta]` vector, which corresponds to the x-y position and orientation angle, theta. Positive angles are measured counterclockwise from the positive x-axis.

Waypoints, specified as an n-by-2 array of `[x y]` pairs, where n is the number of waypoints. You can generate the waypoints using path planners like `mobileRobotPRM` or specify them as an array in Simulink®.

Desired linear velocity, specified as a scalar in meters per second. The controller assumes that the vehicle drives at a constant linear velocity and that the computed angular velocity is independent of the linear velocity.

#### Dependencies

To enable this port, select the Specify desired linear velocity from input port parameter.

Look-ahead distance, specified as a scalar in meters per second. The look-ahead distance changes the response of the controller. A vehicle with a higher look-ahead distance produces smooth paths but takes larger turns at corners. A vehicle with a smaller look-ahead distance follows the path closely and takes sharp turns, but oscillate along the path. For more information on the effects of look-ahead distance, see Pure Pursuit Controller.

#### Dependencies

To enable this port, select the Specify lookahead distance from input port parameter.

### Output

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Linear velocity, returned as a scalar in meters per second.

Data Types: `double`

Angular velocity, returned as a scalar in radians per second.

Data Types: `double`

Target direction for the vehicle, returned as a scalar in radians. The forward direction of the vehicle is considered zero radians, with positive angles measured counterclockwise. This output can be used as the input to the TargetDir port for the Vector Field Histogram (Navigation Toolbox) block.

#### Dependencies

To enable this port, select the Show Target Direction output port parameter.

## Parameters

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Select this parameter to enable input of desired linear velocities at the Desired Linear Velocity input port.

Clear this parameter to specify desired linear velocity using the Desired linear velocity (m/s) parameter

Desired linear velocity, specified as a scalar in meters per second. The controller assumes that the vehicle drives at a constant linear velocity and that the computed angular velocity is independent of the linear velocity.

#### Dependencies

To enable this parameter, clear the Specify desired linear velocity from input port parameter.

Maximum angular velocity, specified as a scalar in radians per second. The controller saturates the absolute angular velocity output at the given value.

Select this parameter to enable input of look-ahead distances at the Lookahead Distance input port.

Clear this parameter to specify desired linear velocity using the Lookahead distance (m) parameter

Look-ahead distance, specified as a scalar in meters. The look-ahead distance changes the response of the controller. A vehicle with a higher look-ahead distance produces smooth paths but takes larger turns at corners. A vehicle with a smaller look-ahead distance follows the path closely and takes sharp turns, but oscillate along the path. For more information on the effects of look-ahead distance, see Pure Pursuit Controller.

#### Dependencies

To enable this parameter, clear the Specify lookahead distance from input port parameter.

Select this parameter to enable the Target Direction output port. This port gives the target direction as an angle in radians from the forward position, with positive angles measured counterclockwise.

• `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

## Version History

Introduced in R2019b

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