Sample 2D rotations when given axis of rotation

Author: LemonPi

src/pytorch_kinematics/transforms/perturbation.py

@@ -1,8 +1,9 @@
 import torch
-from pytorch_kinematics.transforms.rotation_conversions import axis_angle_to_matrix
+from pytorch_kinematics.transforms.rotation_conversions import axis_and_angle_to_matrix_33
 
 
-def sample_perturbations(T, num_perturbations, radian_sigma, translation_sigma):
+def sample_perturbations(T, num_perturbations, radian_sigma, translation_sigma, axis_of_rotation=None,
+                         translation_perpendicular_to_axis_of_rotation=True):
     """
     Sample perturbations around the given transform. The translation and rotation are sampled independently from
     0 mean gaussians. The angular perturbations' directions are uniformly sampled from the unit sphere while its
@@ -11,18 +12,33 @@ def sample_perturbations(T, num_perturbations, radian_sigma, translation_sigma):
     :param num_perturbations: number of perturbations to sample
     :param radian_sigma: standard deviation of the gaussian angular perturbation in radians
     :param translation_sigma: standard deviation of the gaussian translation perturbation in meters / T units
+    :param axis_of_rotation: if not None, the axis of rotation to sample the perturbations around
+    :param translation_perpendicular_to_axis_of_rotation: if True and the axis_of_rotation is not None, the translation
+    perturbations will be perpendicular to the axis of rotation
     :return: perturbed transforms; may not include the original transform
     """
     dtype = T.dtype
     device = T.device
     perturbed = torch.eye(4, dtype=dtype, device=device).repeat(num_perturbations, 1, 1)
 
-    delta_R = torch.randn((num_perturbations, 3), dtype=dtype, device=device) * radian_sigma
-    delta_R = axis_angle_to_matrix(delta_R)
+    delta_t = torch.randn((num_perturbations, 3), dtype=dtype, device=device) * translation_sigma
+    # consider sampling from the Bingham distribution
+    theta = torch.randn(num_perturbations, dtype=dtype, device=device) * radian_sigma
+    if axis_of_rotation is not None:
+        axis_angle = axis_of_rotation
+        # sample translation perturbation perpendicular to the axis of rotation
+        # remove the component of delta_t along the axis_of_rotation
+        if translation_perpendicular_to_axis_of_rotation:
+            delta_t -= (delta_t * axis_of_rotation).sum(dim=1, keepdim=True) * axis_of_rotation
+    else:
+        axis_angle = torch.randn((num_perturbations, 3), dtype=dtype, device=device)
+        # normalize to unit length
+        axis_angle = axis_angle / axis_angle.norm(dim=1, keepdim=True)
+
+    delta_R = axis_and_angle_to_matrix_33(axis_angle, theta)
     perturbed[:, :3, :3] = delta_R @ T[..., :3, :3]
     perturbed[:, :3, 3] = T[..., :3, 3]
 
-    delta_t = torch.randn((num_perturbations, 3), dtype=dtype, device=device) * translation_sigma
     perturbed[:, :3, 3] += delta_t
 
     return perturbed