package
LieGroups.SE2
Special Euclidean Group SE(2) — 2D rigid body motions
Group element: X = {px, py, theta} (translation-first ordering).
Lie algebra element: xi = {vx, vy, omega} (translation-first ordering).
Uses the translation-first convention from AAE 590 PS02-04.
Members
| Name | Kind | Description |
|---|---|---|
| product | function | SE(2) group product: (t1,R1) * (t2,R2) = (R1*t2+t1, R1*R2) |
| inverse | function | SE(2) inverse: (t,R)^{-1} = (-R^T*t, -theta) |
| exp_map | function | Exponential map: se(2) -> SE(2) |
| log_map | function | Logarithmic map: SE(2) -> se(2) |
| to_Matrix | function | Convert SE(2) element to 3x3 homogeneous matrix |
| adjoint | function | Adjoint Ad_X for SE(2), translation-first ordering |
| small_adjoint | function | Small adjoint ad_xi for se(2), translation-first ordering |
| wedge | function | Wedge map: se(2) vector -> 3x3 matrix (xi^wedge) |
| vee | function | Vee map: 3x3 se(2) matrix -> vector (M^vee) |
Modelica declarations and implementation
Show parameters, interfaces and source
Parameters, inputs, outputs, defaults and equations from the source file.
package SE2 "Special Euclidean Group SE(2) — 2D rigid body motions"
annotation(Documentation(info="<html>
<p>Group element: X = {px, py, theta} (translation-first ordering).</p>
<p>Lie algebra element: xi = {vx, vy, omega} (translation-first ordering).</p>
<p>Uses the translation-first convention from AAE 590 PS02-04.</p>
</html>"));
end SE2;