package

LieGroups.SE23.Quat

SE_2(3) with quaternion rotation parameterization

Group element: X = {px,py,pz, vx,vy,vz, qw,qx,qy,qz} (10 params).

Lie algebra: xi = {vb_x,vb_y,vb_z, ab_x,ab_y,ab_z, omega_x,omega_y,omega_z} (9 params).

Ordering: position, velocity, rotation (group); velocity, acceleration, rotation (algebra).

Members

Name	Kind	Description
product	function	SE_2(3) group product
inverse	function	SE_2(3) inverse
exp_map	function	Exponential map: se_2(3) -> SE_2(3)
log_map	function	Logarithmic map: SE_2(3) -> se_2(3)
exp_mixed	function	Mixed exponential for SE_2(3) INS propagation
to_Matrix	function	Convert SE_2(3) element to 5x5 matrix
adjoint	function	Adjoint Ad_X for SE_2(3)
small_adjoint	function	Small adjoint ad_xi for se_2(3)
wedge	function	se_2(3) tangent to homogeneous algebra matrix
vee	function	Homogeneous se_2(3) matrix to tangent
left_jacobian	function	Forward left Jacobian J_l of SE_2(3) (9x9)
left_jacobian_inv	function	Inverse left Jacobian of SE_2(3)
right_jacobian	function	Right Jacobian of SE_2(3)
right_jacobian_inv	function	Inverse right Jacobian of SE_2(3)
mixed_increment_coefficients	function	Rotation coefficients C1, C2, C3 of the mixed exponential increment block
mixed_increment_coefficient_derivatives	function	Derivatives of the mixed exponential increment coefficients by theta squared
mixed_increment_matrix	function	Increment block N of the closed-form mixed exponential
mixed_increment_matrix_jacobian	function	Derivative of the mixed exponential increment block by its algebra element
product_left_factor_jacobian	function	Right-trivialized derivative of product with respect to its left factor
product_right_factor_jacobian	function	Right-trivialized derivative of product with respect to its right factor
inverse_jacobian	function	Right-trivialized derivative of inverse with respect to its element
exp_mixed_state_jacobian	function	Right-trivialized derivative of exp_mixed with respect to its initial state
exp_mixed_left_increment_jacobian	function	Right-trivialized derivative of exp_mixed with respect to its left increment
exp_mixed_right_increment_jacobian	function	Right-trivialized derivative of exp_mixed with respect to its right increment

Modelica declarations and implementation

Show parameters, interfaces and source

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

package Quat "SE_2(3) with quaternion rotation parameterization"
  annotation(Documentation(info="<html>
    <p>Group element: X = {px,py,pz, vx,vy,vz, qw,qx,qy,qz} (10 params).</p>
    <p>Lie algebra: xi = {vb_x,vb_y,vb_z, ab_x,ab_y,ab_z, omega_x,omega_y,omega_z} (9 params).</p>
    <p>Ordering: position, velocity, rotation (group); velocity, acceleration, rotation (algebra).</p>
  </html>"));
end Quat;