model

Tests.LieGroupTests.ModularRepresentations

Replaceable rotation representations produce equivalent SE(3) and SE_2(3) behavior

Public declarations

Explicit source declarations; dimensions, modifications and defaults are shown as written, without evaluation.

Role	Name	Type	Dimensions / attributes / default	Description
constant	`se3Tangent`	`Real`	`[6] = {0.4, -0.2, 0.3, 0.08, -0.04, 0.06}`
constant	`se23Tangent`	`Real`	`[9] = { 0.3, -0.1, 0.2, -0.05, 0.08, 0.12, 0.06, -0.03, 0.04}`

Members

Name	Kind	Description
SE3B232	package
SE23S123	package

Modelica declarations and implementation

Show parameters, interfaces and source

Parameters, inputs, outputs, defaults and equations from the source file.

model ModularRepresentations
  "Replaceable rotation representations produce equivalent SE(3) and SE_2(3) behavior"
  package SE3B232 = LieGroups.SE3.Generic(
    redeclare package Rotation = LieGroups.SO3.EulerSequences.B232);
  package SE23S123 = LieGroups.SE23.Generic(
    redeclare package Rotation = LieGroups.SO3.EulerSequences.S123);
  constant Real se3Tangent[6] = {0.4, -0.2, 0.3, 0.08, -0.04, 0.06};
  constant Real se23Tangent[9] = {
    0.3, -0.1, 0.2, -0.05, 0.08, 0.12, 0.06, -0.03, 0.04};
  LieGroups.SE3.WithQuaternion.Element se3Quaternion;
  LieGroups.SE3.WithMrp.Element se3Mrp;
  LieGroups.SE3.WithDcm.Element se3Dcm;
  LieGroups.SE3.WithEulerB321.Element se3Euler;
  SE3B232.Element se3B232;
  LieGroups.SE23.WithQuaternion.Element se23Quaternion;
  LieGroups.SE23.WithMrp.Element se23Mrp;
  LieGroups.SE23.WithDcm.Element se23Dcm;
  LieGroups.SE23.WithEulerB321.Element se23Euler;
  SE23S123.Element se23S123;
  LieGroups.SE23.WithQuaternion.Element mixedQuaternion;
  LieGroups.SE23.WithMrp.Element mixedMrp;
equation
  se3Quaternion = LieGroups.SE3.WithQuaternion.exp_map(se3Tangent);
  se3Mrp = LieGroups.SE3.WithMrp.exp_map(se3Tangent);
  se3Dcm = LieGroups.SE3.WithDcm.exp_map(se3Tangent);
  se3Euler = LieGroups.SE3.WithEulerB321.exp_map(se3Tangent);
  se3B232 = SE3B232.exp_map(se3Tangent);
  se23Quaternion = LieGroups.SE23.WithQuaternion.exp_map(se23Tangent);
  se23Mrp = LieGroups.SE23.WithMrp.exp_map(se23Tangent);
  se23Dcm = LieGroups.SE23.WithDcm.exp_map(se23Tangent);
  se23Euler = LieGroups.SE23.WithEulerB321.exp_map(se23Tangent);
  se23S123 = SE23S123.exp_map(se23Tangent);
  mixedQuaternion = LieGroups.SE23.WithQuaternion.exp_mixed(
    se23Quaternion, zeros(9), zeros(9), [0.0, 0.25; 0.0, 0.0]);
  mixedMrp = LieGroups.SE23.WithMrp.exp_mixed(
    se23Mrp, zeros(9), zeros(9), [0.0, 0.25; 0.0, 0.0]);

  assert(Tests.Assertions.maxAbsMatrix(
      LieGroups.SE3.WithQuaternion.to_Matrix(se3Quaternion)
        - LieGroups.SE3.WithMrp.to_Matrix(se3Mrp)) < 1.0e-8 and
         Tests.Assertions.maxAbsMatrix(
      LieGroups.SE3.WithQuaternion.to_Matrix(se3Quaternion)
        - LieGroups.SE3.WithDcm.to_Matrix(se3Dcm)) < 1.0e-8 and
         Tests.Assertions.maxAbsMatrix(
      LieGroups.SE3.WithQuaternion.to_Matrix(se3Quaternion)
        - LieGroups.SE3.WithEulerB321.to_Matrix(se3Euler)) < 1.0e-8 and
         Tests.Assertions.maxAbsMatrix(
      LieGroups.SE3.WithQuaternion.to_Matrix(se3Quaternion)
        - SE3B232.to_Matrix(se3B232)) < 1.0e-8,
    "Replaceable SE3 rotation representations disagreed");
  assert(Tests.Assertions.maxAbsVector(
      LieGroups.SE3.WithQuaternion.log_map(se3Quaternion) - se3Tangent) < 1.0e-8 and
         Tests.Assertions.maxAbsVector(
      LieGroups.SE3.WithMrp.log_map(se3Mrp) - se3Tangent) < 1.0e-8 and
         Tests.Assertions.maxAbsVector(
      LieGroups.SE3.WithDcm.log_map(se3Dcm) - se3Tangent) < 1.0e-8,
    "Replaceable SE3 exp/log representations disagreed");
  assert(Tests.Assertions.maxAbsMatrix(
      LieGroups.SE23.WithQuaternion.to_Matrix(se23Quaternion)
        - LieGroups.SE23.WithMrp.to_Matrix(se23Mrp)) < 1.0e-8 and
         Tests.Assertions.maxAbsMatrix(
      LieGroups.SE23.WithQuaternion.to_Matrix(se23Quaternion)
        - LieGroups.SE23.WithDcm.to_Matrix(se23Dcm)) < 1.0e-8 and
         Tests.Assertions.maxAbsMatrix(
      LieGroups.SE23.WithQuaternion.to_Matrix(se23Quaternion)
        - LieGroups.SE23.WithEulerB321.to_Matrix(se23Euler)) < 1.0e-8 and
         Tests.Assertions.maxAbsMatrix(
      LieGroups.SE23.WithQuaternion.to_Matrix(se23Quaternion)
        - SE23S123.to_Matrix(se23S123)) < 1.0e-8,
    "Replaceable SE_2(3) rotation representations disagreed");
  assert(Tests.Assertions.maxAbsMatrix(
      LieGroups.SE23.WithQuaternion.to_Matrix(mixedQuaternion)
        - LieGroups.SE23.WithMrp.to_Matrix(mixedMrp)) < 1.0e-8,
    "Replaceable SE_2(3) mixed exponential representations disagreed");
end ModularRepresentations;