Module `anise.rotation`¶

Classes¶

Class `DCM`¶

class DCM(
    np_rot_mat,
    from_id,
    to_id,
    np_rot_mat_dt=None
)

Defines a direction cosine matrix from one frame ID to another frame ID, optionally with its time derivative. It provides a number of run-time checks that prevent invalid rotations.

:type np_rot_mat: numpy.array :type from_id: int :type to_id: int :type np_rot_mat_dt: numpy.array, optional :rtype: DCM

Instance variables¶

Variable `from_id`¶

:rtype: int

Variable `rot_mat`¶

Return the position DCM (3x3 matrix) :rtype: numpy.ndarray

Variable `rot_mat_dt`¶

Return the time derivative of this DMC, if set. :rtype: numpy.ndarray

Variable `to_id`¶

:rtype: int

Methods¶

Method `angular_velocity_deg_s`¶

def angular_velocity_deg_s(
    self,
    /
)

Returns the angular velocity vector in deg/s if a rotation rate is defined. :rtype: np.array

Method `angular_velocity_rad_s`¶

def angular_velocity_rad_s(
    self,
    /
)

Returns the angular velocity vector in rad/s of this DCM is it has a defined rotation rate. :rtype: np.array

Method `from_align_and_clock`¶

def from_align_and_clock(
    primary_body_axis,
    primary_inertial_vec,
    secondary_body_axis,
    secondary_inertial_vec,
    from_id,
    to_id
)

Constructs a DCM using the "Align and Clock" (Two-Vector Targeting / TRIAD) method.

This defines a rotation based on two geometric constraints: 1. Align: The primary_body_axis is aligned exactly with the primary_inertial_vec. 2. Clock: The secondary_body_axis is aligned as closely as possible with the secondary_inertial_vec.

This constructs the rotation matrix \(R_{from \to to}\).

Arguments¶

primary_body_axis - The axis in the "from" frame to align (e.g. Sensor Boresight).
primary_inertial_vec - The target vector in the "to" frame (e.g. Vector to Earth).
secondary_body_axis - The axis in the "from" frame to clock (e.g. Solar Panel Normal).
secondary_inertial_vec - The target vector in the "to" frame (e.g. Vector to Sun).
from - The ID of the source frame.
to - The ID of the destination frame.

:type primary_body_axis: np.array :type primary_inertial_vec: np.array :type secondary_body_axis: np.array :type secondary_inertial_vec: np.array :type from_id: int :type to_id: int :rtype: DCM

Method `from_identity`¶

def from_identity(
    from_id,
    to_id
)

Builds an identity rotation.

:type from_id: int :type to_id: int :rtype: DCM

Method `from_r1`¶

def from_r1(
    angle_rad,
    from_id,
    to_id
)

Returns a rotation matrix for a rotation about the X axis.

Source: euler1 function from Baslisk

:type angle_rad: float :type from_id: int :type to_id: int :rtype: DCM

Method `from_r2`¶

def from_r2(
    angle_rad,
    from_id,
    to_id
)

Returns a rotation matrix for a rotation about the Y axis.

Source: euler2 function from Basilisk

:type angle_rad: float :type from_id: int :type to_id: int :rtype: DCM

Method `from_r3`¶

def from_r3(
    angle_rad,
    from_id,
    to_id
)

Returns a rotation matrix for a rotation about the Z axis.

Source: euler3 function from Basilisk

:type angle_rad: float :type from_id: int :type to_id: int :rtype: DCM

Method `get_state_dcm`¶

def get_state_dcm(
    self,
    /
)

Returns the 6x6 DCM to rotate a state. If the time derivative of this DCM is defined, this 6x6 accounts for the transport theorem. Warning: you MUST manually install numpy to call this function. :rtype: numpy.ndarray

Method `is_identity`¶

def is_identity(
    self,
    /
)

Returns whether this rotation is identity, checking first the frames and then the rotation matrix (but ignores its time derivative)

:rtype: bool

Method `is_valid`¶

def is_valid(
    self,
    /,
    unit_tol,
    det_tol
)

Returns whether the rot_mat of this DCM is a valid rotation matrix. The criteria for validity are: -- The columns of the matrix are unit vectors, within a specified tolerance (unit_tol). -- The determinant of the matrix formed by unitizing the columns of the input matrix is 1, within a specified tolerance. This criterion ensures that the columns of the matrix are nearly orthogonal, and that they form a right-handed basis (det_tol). Source: SPICE's rotation.req

:type unit_tol: float :type det_tol: float :rtype: bool

Method `skew_symmetric`¶

def skew_symmetric(
    self,
    /
)

Returns the skew symmetric matrix if this DCM defines a rotation rate. :rtype: np.array

Method `to_quaternion`¶

def to_quaternion(
    self,
    /
)

:rtype: Quaternion

Method `transpose`¶

def transpose(
    self,
    /
)

Returns the transpose of this DCM

:rtype: DCM

Class `Quaternion`¶

class Quaternion(
    w,
    x,
    y,
    z,
    from_id,
    to_id
)

Represents the orientation of a rigid body or a coordinate frame transformation in three-dimensional space using Euler parameters.

Euler parameters, also known as unit quaternions, are a set of four parameters w, x, y, z. They are particularly useful because they avoid gimbal lock, are more compact than rotation matrices, and allow for smooth interpolation (SLERP).

Conventions¶

ANISE strictly adheres to the following conventions to ensure consistency with DCM and standard Guidance, Navigation, and Control (GNC) mathematics:

Hamiltonian Algebra: The quaternion multiplication follows the right-handed rule where \ i * j = k. This is the standard in robotics and computer graphics, but distinct from the "JPL/Shuster" convention (i * j = -k) sometimes found in legacy aerospace software.
Passive Rotation (Coordinate Transformation): A quaternion defined with from: A and to: B represents the transformation of coordinates from Frame A to Frame B.
The rotation of a vector v is computed as: v_B = q.conjugate() * v_A * q.
This matches the behavior of a Direction Cosine Matrix (DCM): v_B = [DCM_A->B] * v_A.
Operator Composition (Backward Chaining): Rotations are composed in "Operator Order", matching matrix multiplication rules.
To compute the rotation A -> C, you multiply B->C by A->B.
q_A_to_C = q_B_to_C * q_A_to_B
ANISE enforces strict frame checking: LHS.from must equal RHS.to.

Definitions¶

Euler parameters are defined in terms of the principal rotation vector. If a frame is rotated by an angle θ about a unit axis e = [e1, e2, e3]:

w = cos(θ / 2)
x = e1 * sin(θ / 2)
y = e2 * sin(θ / 2)
z = e3 * sin(θ / 2)

These parameters satisfy w^2 + x^2 + y^2 + z^2 = 1, which means they represent a rotation in SO(3) and can be used to interpolate rotations smoothly.

Applications¶

In the context of spacecraft mechanics, Euler parameters are often used because they provide a numerically stable way to represent the attitude of a spacecraft without the singularities that are present with Euler angles.

Usage¶

Importantly, ANISE prevents the composition of two Euler Parameters if the frames do not match.

:type w: float :type x: float :type y: float :type z: float :type from_id: int :type to_id: int

Instance variables¶

Variable `from_id`¶

:rtype: int

Variable `to_id`¶

:rtype: int

Variable `w`¶

:rtype: float

Variable `x`¶

:rtype: float

Variable `y`¶

:rtype: float

Variable `z`¶

:rtype: float

Methods¶

Method `about_x`¶

def about_x(
    angle_rad,
    from_id,
    to_id
)

Creates an Euler Parameter representing the short way rotation about the X (R1) axis

:type angle_rad: float :type from_id: int :type to_id: int :rtype: Quaternion

Method `about_y`¶

def about_y(
    angle_rad,
    from_id,
    to_id
)

Creates an Euler Parameter representing the short way rotation about the Y (R2) axis

:type angle_rad: float :type from_id: int :type to_id: int :rtype: Quaternion

Method `about_z`¶

def about_z(
    angle_rad,
    from_id,
    to_id
)

Creates an Euler Parameter representing the short way rotation about the Z (R3) axis

:type angle_rad: float :type from_id: int :type to_id: int :rtype: Quaternion

Method `as_vector`¶

def as_vector(
    self,
    /
)

Returns the data of this EP as a vector. :rtype: np.array

Method `b_matrix`¶

def b_matrix(
    self,
    /
)

Returns the 4x3 matrix which relates the body angular velocity vector w to the derivative of this Euler Parameter. dQ/dt = 1/2 [B(Q)] w

:rtype: np.array

Method `conjugate`¶

def conjugate(
    self,
    /
)

Compute the conjugate of the quaternion.

Note¶

Because Euler Parameters are unit quaternions, the inverse and the conjugate are identical.

:rtype: Quaternion

Method `derivative`¶

def derivative(
    self,
    /,
    omega_rad_s
)

Returns the euler parameter derivative for this EP and the body angular velocity vector w dQ/dt = 1/2 [B(Q)] omega_rad_s

:type omega_rad_s: np.array :rtype: Quaternion

Method `is_zero`¶

def is_zero(
    self,
    /
)

Returns true if the quaternion represents a rotation of zero radians

:rtype: bool

Method `normalize`¶

def normalize(
    self,
    /
)

Normalize the quaternion.

:rtype: Quaternion

Method `prv`¶

def prv(
    self,
    /
)

Returns the principal rotation vector representation of this Euler Parameter :rtype: np.array

Method `scalar_norm`¶

def scalar_norm(
    self,
    /
)

Returns the norm of this Euler Parameter as a scalar.

:rtype: float

Method `short`¶

def short(
    self,
    /
)

Returns the short way rotation of this quaternion

:rtype: Quaternion

Method `to_dcm`¶

def to_dcm(
    self,
    /
)

Convert this quaterion to a DCM :rtype: DCM

Method `uvec_angle_rad`¶

def uvec_angle_rad(
    self,
    /
)

Returns the principal line of rotation (a unit vector) and the angle of rotation in radians

:rtype: tuple

Generated by pdoc 0.11.6 (https://pdoc3.github.io).

Module anise.rotation¶

Classes¶

Class DCM¶

Instance variables¶

Variable from_id¶

Variable rot_mat¶

Variable rot_mat_dt¶

Variable to_id¶

Methods¶

Method angular_velocity_deg_s¶

Method angular_velocity_rad_s¶

Method from_align_and_clock¶

Arguments¶

Method from_identity¶

Method from_r1¶

Method from_r2¶

Method from_r3¶

Method get_state_dcm¶

Method is_identity¶

Method is_valid¶

Method skew_symmetric¶

Method to_quaternion¶

Method transpose¶

Class Quaternion¶

Conventions¶

Definitions¶

Applications¶

Usage¶

Instance variables¶

Variable from_id¶

Variable to_id¶

Variable w¶

Variable x¶

Variable y¶

Variable z¶

Methods¶

Method about_x¶

Method about_y¶

Method about_z¶

Method as_vector¶

Method b_matrix¶

Method conjugate¶

Note¶

Method derivative¶

Method is_zero¶

Method normalize¶

Method prv¶

Method scalar_norm¶

Method short¶

Method to_dcm¶

Method uvec_angle_rad¶

Module `anise.rotation`¶

Class `DCM`¶

Variable `from_id`¶

Variable `rot_mat`¶

Variable `rot_mat_dt`¶

Variable `to_id`¶

Method `angular_velocity_deg_s`¶

Method `angular_velocity_rad_s`¶

Method `from_align_and_clock`¶

Method `from_identity`¶

Method `from_r1`¶

Method `from_r2`¶

Method `from_r3`¶

Method `get_state_dcm`¶

Method `is_identity`¶

Method `is_valid`¶

Method `skew_symmetric`¶

Method `to_quaternion`¶

Method `transpose`¶

Class `Quaternion`¶

Variable `from_id`¶

Variable `to_id`¶

Variable `w`¶

Variable `x`¶

Variable `y`¶

Variable `z`¶

Method `about_x`¶

Method `about_y`¶

Method `about_z`¶

Method `as_vector`¶

Method `b_matrix`¶

Method `conjugate`¶

Method `derivative`¶

Method `is_zero`¶

Method `normalize`¶

Method `prv`¶

Method `scalar_norm`¶

Method `short`¶

Method `to_dcm`¶

Method `uvec_angle_rad`¶