graphslam.pose.base_pose module

A base class for poses.

class graphslam.pose.base_pose.BasePose

Bases: ndarray

A base class for poses.

copy()

Return a copy of the pose.

Returns:

A copy of the pose

Return type:

BasePose

equals(other, tol=1e-06)

Check whether two poses are equal.

Parameters:

• other (BasePose) – The pose to which we are comparing

• tol (float) – The tolerance

Returns:

Whether the two poses are equal

Return type:

bool

classmethod identity()

Return the identity pose.

Returns:

The identity pose

Return type:

BasePose

property inverse

Return the pose’s inverse.

Returns:

The pose’s inverse

Return type:

BasePose

jacobian_boxplus()

Compute the Jacobian of \(p_1 \boxplus \Delta \mathbf{x}\) w.r.t. \(\Delta \mathbf{x}\) evaluated at \(\Delta \mathbf{x} = \mathbf{0}\).

Let

# The dimensionality of :math:`\Delta \mathbf{x}`, which should be the same as
# the compact dimensionality of `self`
n_dx = self.COMPACT_DIMENSIONALITY

# The dimensionality of :math:`p_1 \boxplus \Delta \mathbf{x}`, which should be
# the same as the dimensionality of `self`
n_boxplus = len(self.to_array())

Then the shape of the Jacobian will be n_boxplus x n_dx.

Returns:

The Jacobian of \(p_1 \boxplus \Delta \mathbf{x}\) w.r.t. \(\Delta \mathbf{x}\) evaluated at \(\Delta \mathbf{x} = \mathbf{0}\)

Return type:

np.ndarray

jacobian_inverse()

Compute the Jacobian of \(p^{-1}\).

Let

# The dimensionality of `self`
n_self = len(self.to_array())

Then the shape of the Jacobian will be n_self x n_self.

Returns:

The Jacobian of \(p^{-1}\)

Return type:

np.ndarray

jacobian_self_ominus_other_wrt_other(other)

Compute the Jacobian of \(p_1 \ominus p_2\) w.r.t. \(p_2\).

Let

# The dimensionality of `other`
n_other = len(other.to_array())

# The dimensionality of `self - other`
n_ominus = len((self - other).to_array())

Then the shape of the Jacobian will be n_ominus x n_other.

Parameters:

other (BasePose) – The pose that is being subtracted from self

Returns:

The Jacobian of \(p_1 \ominus p_2\) w.r.t. \(p_2\).

Return type:

np.ndarray

jacobian_self_ominus_other_wrt_other_compact(other)

Compute the Jacobian of \(p_1 \ominus p_2\) w.r.t. \(p_2\).

Let

# The dimensionality of `other`
n_other = len(other.to_array())

# The compact dimensionality of `self - other`
n_compact = (self - other).COMPACT_DIMENSIONALITY

Then the shape of the Jacobian will be n_compact x n_other.

Parameters:

other (BasePose) – The pose that is being subtracted from self

Returns:

The Jacobian of \(p_1 \ominus p_2\) w.r.t. \(p_2\).

Return type:

np.ndarray

jacobian_self_ominus_other_wrt_self(other)

Compute the Jacobian of \(p_1 \ominus p_2\) w.r.t. \(p_1\).

Let

# The dimensionality of `self`
n_self = len(self.to_array())

# The dimensionality of `self - other`
n_ominus = len((self - other).to_array())

Then the shape of the Jacobian will be n_ominus x n_self.

Parameters:

other (BasePose) – The pose that is being subtracted from self

Returns:

The Jacobian of \(p_1 \ominus p_2\) w.r.t. \(p_1\).

Return type:

np.ndarray

jacobian_self_ominus_other_wrt_self_compact(other)

Compute the Jacobian of \(p_1 \ominus p_2\) w.r.t. \(p_1\).

Let

# The dimensionality of `self`
n_self = len(self.to_array())

# The compact dimensionality of `self - other`
n_compact = (self - other).COMPACT_DIMENSIONALITY

Then the shape of the Jacobian will be n_compact x n_self.

Parameters:

other (BasePose) – The pose that is being subtracted from self

Returns:

The Jacobian of \(p_1 \ominus p_2\) w.r.t. \(p_1\).

Return type:

np.ndarray

jacobian_self_oplus_other_wrt_other(other)

Compute the Jacobian of \(p_1 \oplus p_2\) w.r.t. \(p_2\).

Let

# The dimensionality of `other`
n_other = len(other.to_array())

# The dimensionality of `self + other`
n_oplus = len((self + other).to_array())

Then the shape of the Jacobian will be n_oplus x n_other.

Parameters:

other (BasePose) – The pose that is being added to self

Returns:

The Jacobian of \(p_1 \oplus p_2\) w.r.t. \(p_2\).

Return type:

np.ndarray

jacobian_self_oplus_other_wrt_other_compact(other)

Compute the Jacobian of \(p_1 \oplus p_2\) w.r.t. \(p_2\).

Let

# The dimensionality of `other`
n_other = len(other.to_array())

# The compact dimensionality of `self + other`
n_compact = (self + other).COMPACT_DIMENSIONALITY

Then the shape of the Jacobian will be n_compact x n_other.

Parameters:

other (BasePose) – The pose that is being added to self

Returns:

The Jacobian of \(p_1 \oplus p_2\) w.r.t. \(p_2\).

Return type:

np.ndarray

jacobian_self_oplus_other_wrt_self(other)

Compute the Jacobian of \(p_1 \oplus p_2\) w.r.t. \(p_1\).

Let

# The dimensionality of `self`
n_self = len(self.to_array())

# The dimensionality of `self + other`
n_oplus = len((self + other).to_array())

Then the shape of the Jacobian will be n_oplus x n_self.

Parameters:

other (BasePose) – The pose that is being added to self

Returns:

The Jacobian of \(p_1 \oplus p_2\) w.r.t. \(p_1\).

Return type:

np.ndarray

jacobian_self_oplus_other_wrt_self_compact(other)

Compute the Jacobian of \(p_1 \oplus p_2\) w.r.t. \(p_1\).

Let

# The dimensionality of `self`
n_self = len(self.to_array())

# The compact dimensionality of `self + other`
n_compact = (self + other).COMPACT_DIMENSIONALITY

Then the shape of the Jacobian will be n_compact x n_self.

Parameters:

other (BasePose) – The pose that is being added to self

Returns:

The Jacobian of \(p_1 \oplus p_2\) w.r.t. \(p_1\).

Return type:

np.ndarray

jacobian_self_oplus_point_wrt_point(point)

Compute the Jacobian of \(p_1 \oplus p_2\) w.r.t. \(p_2\), where \(p_2\) is a point.

Let

# The dimensionality of `point`
n_point = len(point.to_array())

# The dimensionality of `self + point`
n_oplus = len((self + point).to_array())

Then the shape of the Jacobian will be n_oplus x n_point.

Parameters:

point (BasePose) – The point that is being added to self

Returns:

The Jacobian of \(p_1 \oplus p_2\) w.r.t. \(p_2\).

Return type:

np.ndarray

jacobian_self_oplus_point_wrt_self(point)

Compute the Jacobian of \(p_1 \oplus p_2\) w.r.t. \(p_1\), where \(p_2\) is a point.

Let

# The dimensionality of `self`
n_self = len(self.to_array())

# The dimensionality of `self + point`
n_oplus = len((self + point).to_array())

Then the shape of the Jacobian will be n_oplus x n_self.

Parameters:

point (BasePose) – The point that is being added to self

Returns:

The Jacobian of \(p_1 \oplus p_2\) w.r.t. \(p_1\).

Return type:

np.ndarray

property orientation

Return the pose’s orientation.

Returns:

The pose’s orientation

Return type:

float, np.ndarray

property position

Return the pose’s position.

Returns:

The pose’s position

Return type:

np.ndarray

to_array()

Return the pose as a numpy array.

Returns:

The pose as a numpy array

Return type:

np.ndarray

to_compact()

Return the pose as a compact numpy array.

Returns:

The pose as a compact numpy array

Return type:

np.ndarray