# interpolate

## Syntax

## Description

interpolates along the length of a reference path, returning transition poses. For more
information, see Transition Poses.`poses`

= interpolate(`refPath`

)

`[`

also returns the motion directions of the vehicle at each pose, using inputs from any of the
preceding syntaxes.`poses`

,`directions`

] = interpolate(___)

## Examples

### Plan Path and Check Its Validity

Plan a vehicle path through a parking lot by using the optimal rapidly exploring random tree (RRT*) algorithm. Check that the path is valid, and then plot the transition poses along the path.

Load a costmap of a parking lot. Plot the costmap to see the parking lot and inflated areas for the vehicle to avoid.

```
data = load('parkingLotCostmap.mat');
costmap = data.parkingLotCostmap;
plot(costmap)
```

Define start and goal poses for the vehicle as [*x*,* y*,* Θ*] vectors. World units for the (*x*,*y*) locations are in meters. World units for the *Θ* orientation angles are in degrees.

```
startPose = [4, 4, 90]; % [meters, meters, degrees]
goalPose = [30, 13, 0];
```

Use a `pathPlannerRRT`

object to plan a path from the start pose to the goal pose.

planner = pathPlannerRRT(costmap); refPath = plan(planner,startPose,goalPose);

Check that the path is valid.

isPathValid = checkPathValidity(refPath,costmap)

`isPathValid = `*logical*
1

Interpolate the transition poses along the path.

transitionPoses = interpolate(refPath);

Plot the planned path and the transition poses on the costmap.

hold on plot(refPath,'DisplayName','Planned Path') scatter(transitionPoses(:,1),transitionPoses(:,2),[],'filled', ... 'DisplayName','Transition Poses') hold off

### Plan Path and Interpolate Along Path

Plan a vehicle path through a parking lot by using the rapidly exploring random tree (RRT*) algorithm. Interpolate the poses of the vehicle at points along the path.

Load a costmap of a parking lot. Plot the costmap to see the parking lot and inflated areas for the vehicle to avoid.

```
data = load('parkingLotCostmap.mat');
costmap = data.parkingLotCostmap;
plot(costmap)
```

Define start and goal poses for the vehicle as `[`

*x*,* y*,* Θ*`]`

vectors. World units for the (*x*,*y*) locations are in meters. World units for the *Θ* orientation angles are in degrees.

```
startPose = [4, 4, 90]; % [meters, meters, degrees]
goalPose = [30, 13, 0];
```

Use a `pathPlannerRRT`

object to plan a path from the start pose to the goal pose.

planner = pathPlannerRRT(costmap); refPath = plan(planner,startPose,goalPose);

Interpolate the vehicle poses every 1 meter along the entire path.

lengths = 0 : 1 : refPath.Length; poses = interpolate(refPath,lengths);

Plot the interpolated poses on the costmap.

plot(costmap) hold on scatter(poses(:,1),poses(:,2),'DisplayName','Interpolated Poses') hold off

## Input Arguments

`refPath`

— Planned vehicle path

`driving.Path`

object

Planned vehicle path, specified as a `driving.Path`

object.

`lengths`

— Points along length of path

real-valued vector

Points along the length of the path, specified as a real-valued vector. Values must
be in the range from 0 to the length of the path, as determined by the `Length`

property of `refPath`

. The
`interpolate`

function interpolates poses at these specified
points. `lengths`

is in world units, such as meters.

**Example: **`poses = interpolate(refPath,0:0.1:refPath.Length)`

interpolates poses every 0.1 meter along the entire length of the path.

## Output Arguments

`poses`

— Vehicle poses

*m*-by-3 matrix of [*x*, *y*,
*Θ*] vectors

Vehicle poses along the path, returned as an *m*-by-3 matrix of
[*x*, *y*, *Θ*] vectors.
*m* is the number of returned poses.

*x* and *y* specify the location of the vehicle in
world units, such as meters. *Θ* specifies the orientation angle of the
vehicle in degrees.

`poses`

always includes the transition poses, even if you
interpolate only at specified points along the path. If you do not specify the
`lengths`

input argument, then `poses`

includes
only the transition poses.

`directions`

— Motion directions

*m*-by-1 vector of 1s (forward motion) and –1s (reverse
motion)

Motion directions of vehicle poses, returned as an *m*-by-1 vector
of 1s (forward motion) and –1s (reverse motion). *m* is the number of
returned poses. Each element of `directions`

corresponds to a row of
`poses`

.

## More About

### Transition Poses

A path is composed of multiple segments that are combinations of
motions (for example, left turn, straight, and right turn). *Transition
poses* are vehicle poses corresponding to the end of one motion and the
beginning of another motion. They represent points along the path corresponding to a change
in the direction or orientation of the vehicle. The `interpolate`

function always returns transition poses, even if you interpolate only at specified points
along the path.

The path length between transition poses is given by the
`MotionLengths`

property of the path segments. For example, consider
the following path, which is a `driving.Path`

object composed of a single Dubins path segment. This segment consists of three motions, as
described by the `MotionLengths`

and `MotionTypes`

properties of the segment.

The `interpolate`

function interpolates the following transition
poses in this order:

The initial pose of the vehicle,

`StartPose`

.The pose after the vehicle turns left (

`"L"`

) for 4.39 meters at its maximum steering angle.The pose after the vehicle goes straight (

`"S"`

) for 6.32 meters.The pose after the vehicle turns right (

`"R"`

) for 4.39 meters at its maximum steering angle. This pose is also the goal pose, because it is the last pose of the entire path.

The plot shows these transition poses, which are [*x*,
*y*, *Θ*] vectors. *x* and
*y* specify the location of the vehicle in world units, such as meters.
*Θ* specifies the orientation angle of the vehicle in degrees.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

## Version History

**Introduced in R2018b**

## See Also

### Functions

### Objects

### Topics

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