distance
Distance between two states
Description
Examples
Calculate Distance Between Two States in SE3
Create an SE(3) state space.
space = stateSpaceSE3
space = stateSpaceSE3 with properties: Name: 'SE3' StateBounds: [7x2 double] NumStateVariables: 7 WeightXYZ: 1 WeightQuaternion: 0.1000
Calculate distance between two states.
dist = distance(space,[2 10 3 0.2 0 0 0.8],[0 -2.5 4 0.7 0.3 0 0])
dist = 12.7269
Calculate Euclidean distance between two states.
space.WeightQuaternion = 0; distEuc = distance(space,[2 10 3 0.2 0 0 0.8; 4 5 2 1 2 4 2],[62 5 33 0.2 0 0 0.8; 9 9 3 3 1 3.1 7])
distEuc = 2×1
67.2681
6.4807
Input Arguments
space
— State space object
stateSpaceSE2
object | stateSpaceSE3
object | stateSpaceDubins
object | stateSpaceReedsShepp
object
State space object, specified as a stateSpaceSE2
,
stateSpaceSE3
,
stateSpaceDubins
, or stateSpaceReedsShepp
object.
states1
— Initial states for distance calculation
n-by-3 matrix of real values | n-by-7 matrix of real values
Initial states for distance calculation, specified as an n-by-3 or n-by-7 matrix of real values. n is the number of specified states.
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 a state in the state space.
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 a state in the state space.
The function supports following combinations for distance calculation:
n-to-n — n number of states in
states1
and n number of states instates2
.For example,
distance(space,rand(10,7),rand(10,7))
1-to-n — 1 state in
states1
and n number of states instates2
.For example,
distance(space,rand(1,7),rand(10,7))
n-to-1 — n number of states in
states1
and 1 state instates2
.For example,
distance(space,rand(10,7),rand(1,7))
Data Types: single
| double
states2
— Final states for distance calculation
n-by-3 matrix of real values | n-by-7 matrix of real values
Final states for distance calculation, specified as an n-by-3 or n-by-7 matrix of real values. n is the number of specified states.
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 a state in the state space.
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 a state in the state space.
The function supports following combinations for distance calculation:
n-to-n — n number of states in
states1
and n number of states instates2
.For example,
distance(space,rand(10,7),rand(10,7))
1-to-n — 1 state in
states1
and n number of states instates2
.For example,
distance(space,rand(1,7),rand(10,7))
n-to-1 — n number of states in
states1
and 1 state instates2
.For example,
distance(space,rand(10,7),rand(1,7))
Data Types: single
| double
Output Arguments
dist
— Distance between states
n-element column vector
Distance between states, returned as an n-element column vector. n is the number of specified states.
The function supports following combinations for distance calculation:
Data Types: single
| double
Version History
Introduced in R2019b
See Also
stateSpaceSE2
| stateSpaceSE3
| stateSpaceDubins
| stateSpaceReedsShepp
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