pypose.se3

pypose.se3 = functools.partial(<class 'pypose.lietensor.lietensor.LieTensor'>, ltype=<pypose.lietensor.lietensor.se3Type object>)

Alias of se3 type LieTensor.

Parameters:

data (Tensor, or list, or ‘int…’) –

A Tensor object, or constructing a Tensor object from list, which defines tensor data (see below), or from ‘int…’, which defines tensor shape.

The shape of Tensor object must be (*, 6), where * is empty, one, or more batched dimensions (the lshape of this LieTensor), otherwise error will be raised.

Internally, se3 LieTensors are stored by concatenating the “velocity” vector with the axis-angle representation of the rotation:

\[\mathrm{data}[*, :] = [\tau_x, \tau_y, \tau_z, \delta_x, \delta_y, \delta_z], \]

where \(\begin{pmatrix} \tau_x & \tau_y & \tau_z \end{pmatrix}^T = \mathbf{J}^{-1} \begin{pmatrix} t_x & t_y & t_z \end{pmatrix}^T\) is the product between the left Jacobian inverse (of SO3’s logarithm map) and the translation vector, and \(\begin{pmatrix} \delta_x & \delta_y & \delta_z \end{pmatrix}^T\) is the axis-angle vector as in pypose.so3. More details go to pypose.Log() with SE3_type input.

Examples

>>> pp.se3(torch.randn(2, 6))
se3Type LieTensor:
tensor([[-0.8710, -1.4994, -0.2843,  1.0185, -0.3932, -0.4839],
        [-0.4750, -0.4804, -0.7083, -1.8141, -1.4409, -0.3125]])
>>> pp.se3([0, 0, 0, 0, 0, 1])
se3Type LieTensor:
tensor([0., 0., 0., 0., 0., 1.])

If data is tensor-like, the last dimension should correspond to the 6 elements of the above embedding.

Note

It is not advised to construct se3 Tensors by specifying storage sizes with ‘int…’, which does not initialize data.

Consider using pypose.randn_se3 or pypose.identity_se3 instead.

See pypose.Exp, pypose.Inv for implementations of relevant operations.