interpolate

Interpolate between states

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Syntax

interpStates = interpolate(space,state1,state2,ratio)

Description

interpStates = interpolate(space,state1,state2,ratio) interpolates states between the specified start state state1 and end state state2 based on the specified interpolation ratio ratio.

example

Examples

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Open Live Script

Create an SE(2) state space with default properties.

space = stateSpaceSE2
space = 
  stateSpaceSE2 with properties:

                 Name: 'SE2'
          StateBounds: [3×2 double]
    NumStateVariables: 3
             WeightXY: 1
          WeightTheta: 0.1000

Create a pair of states in 2-D space.

state1 = [2 10 -pi];
state2 = [0 -2.5 -pi/4];

Interpolate halfway between two states.

state = interpolate(space,state1,state2,0.5)
state = 1×3

    1.0000    3.7500   -1.9635

Interpolate multiple points with a fixed interval.

states = interpolate(space,state1,state2,0:0.02:1)
states = 51×3

    2.0000   10.0000   -3.1416
    1.9600    9.7500   -3.0945
    1.9200    9.5000   -3.0473
    1.8800    9.2500   -3.0002
    1.8400    9.0000   -2.9531
    1.8000    8.7500   -2.9060
    1.7600    8.5000   -2.8588
    1.7200    8.2500   -2.8117
    1.6800    8.0000   -2.7646
    1.6400    7.7500   -2.7175
    1.6000    7.5000   -2.6704
    1.5600    7.2500   -2.6232
    1.5200    7.0000   -2.5761
    1.4800    6.7500   -2.5290
    1.4400    6.5000   -2.4819
      ⋮
Open Live Script

Create an SE(3) state space with default properties.

space = stateSpaceSE3
space = 
  stateSpaceSE3 with properties:

                 Name: 'SE3'
          StateBounds: [7×2 double]
    NumStateVariables: 7
            WeightXYZ: 1
     WeightQuaternion: 0.1000

Create a pair of states in 3-D space.

state1 = [2 10 3 0.2 0 0 0.8];
state2 = [0 -2.5 4 0.7 0.3 0 0];

Interpolate halfway between two states.

state = interpolate(space,state1,state2,0.5)
state = 1×7

    1.0000    3.7500    3.5000    0.7428    0.2519         0    0.6203

Interpolate multiple points with a fixed interval.

states = interpolate(space,state1,state2,0:0.02:1)
states = 51×7

    2.0000   10.0000    3.0000    0.2425         0         0    0.9701
    1.9600    9.7500    3.0200    0.2663    0.0109         0    0.9638
    1.9200    9.5000    3.0400    0.2899    0.0217         0    0.9568
    1.8800    9.2500    3.0600    0.3133    0.0326         0    0.9491
    1.8400    9.0000    3.0800    0.3365    0.0434         0    0.9407
    1.8000    8.7500    3.1000    0.3594    0.0542         0    0.9316
    1.7600    8.5000    3.1200    0.3821    0.0650         0    0.9218
    1.7200    8.2500    3.1400    0.4045    0.0757         0    0.9114
    1.6800    8.0000    3.1600    0.4266    0.0864         0    0.9003
    1.6400    7.7500    3.1800    0.4484    0.0969         0    0.8886
    1.6000    7.5000    3.2000    0.4698    0.1075         0    0.8762
    1.5600    7.2500    3.2200    0.4909    0.1179         0    0.8632
    1.5200    7.0000    3.2400    0.5117    0.1283         0    0.8495
    1.4800    6.7500    3.2600    0.5321    0.1385         0    0.8353
    1.4400    6.5000    3.2800    0.5521    0.1487         0    0.8204
      ⋮

Input Arguments

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State space object, specified as a stateSpaceSE2, stateSpaceSE3, stateSpaceDubins, or stateSpaceReedsShepp object.

Start state for interpolation, specified as a three-element or seven-element vector of real values.

For the 2-D state space objects stateSpaceSE2, stateSpaceDubins, and stateSpaceReedsShepp, the state is a vector of form [x y theta], which defines the xy-position and orientation angle theta of a state in the state space.

For the 3-D state space object stateSpaceSE3, the state is a vector of form [x y z qw qx qy qz], which defines the xyz-position and quaternion orientation [qw qx qy qz] of a state in the state space.

Data Types: single | double

End state for interpolation, specified as a three-element or seven-element vector of real values.

For the 2-D state space objects stateSpaceSE2, stateSpaceDubins, and stateSpaceReedsShepp, the state is a vector of form [x y theta], which defines the xy-position and orientation angle theta of a state in the state space.

For the 3-D state space object stateSpaceSE3, the state is a vector of form [x y z qw qx qy qz], which defines the xyz-position and quaternion orientation [qw qx qy qz] of a state in the state space.

Data Types: single | double

Interpolation ratio, specified as a scalar in the range of [0, 1], or an n-element column vector of values in the range [0, 1]. n is the number of desired interpolation points.

Data Types: single | double

Output Arguments

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Interpolated states, returned as an n-by-3 or n-by-7 matrix of real values. n is the number of interpolation points specified by the ratio input argument.

For the 2-D state space objects stateSpaceSE2, stateSpaceDubins, and stateSpaceReedsShepp, each row is of form [x y theta], which defines the xy-position and orientation angle theta of the interpolated states.

For the 3-D state space object stateSpaceSE3, each row is of form [x y z qw qx qy qz], which defines the xyz-position and quaternion orientation [qw qx qy qz] of the interpolated states.

Data Types: single | double

Version History

Introduced in R2019b

See Also

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