Fixes the implementation of `quat_inv()` (#2797)

# Description

Corrects `quat_inv()` in utils/math.py: the inverse is now computed as:

`quat_conjugate(q) / q.pow(2).sum(dim=-1, keepdim=True).clamp(min=eps)`

ensuring correct results for **non-unit** quaternions.  

Fixes #1263 (see discussion for details). Also updated `CHANGELOG.rst`
and corrected a few minor typos within.

## Type of change

<!-- As you go through the list, delete the ones that are not
applicable. -->

- Bug fix (non-breaking change which fixes an issue)
- This change requires a documentation update

## Checklist

- [x] I have run the [`pre-commit` checks](https://pre-commit.com/) with
`./isaaclab.sh --format`
- [x] I have made corresponding changes to the documentation
- [x] My changes generate no new warnings
- [ ] I have added tests that prove my fix is effective or that my
feature works
- [x] I have updated the changelog and the corresponding version in the
extension's `config/extension.toml` file
- [x] I have added my name to the `CONTRIBUTORS.md` or my name already
exists there

---------
Co-authored-by: Kelly Guo <kellyg@nvidia.com>

source/isaaclab/config/extension.toml

 [package]
 
 # Note: Semantic Versioning is used: https://semver.org/
-version = "0.40.10"
+version = "0.40.11"
 
 # Description
 title = "Isaac Lab framework for Robot Learning"

source/isaaclab/docs/CHANGELOG.rst

 Changelog
 ---------
 
+0.40.11 (2025-06-27)
+~~~~~~~~~~~~~~~~~~~~
+
+Added
+^^^^^
+
+* Added unit test for :func:`~isaaclab.utils.math.quat_inv`.
+
+Fixed
+^^^^^
+
+* Fixed the implementation mistake in :func:`~isaaclab.utils.math.quat_inv`.
+
+
 0.40.10 (2025-06-25)
 ~~~~~~~~~~~~~~~~~~~~
 
 Fixed
 ^^^^^
 
-* Fixed :meth:`omni.isaac.lab.utils.dict.update_class_from_dict` preventing setting flat Iterables with different lengths.
+* Fixed :func:`~isaaclab.utils.dict.update_class_from_dict` preventing setting flat Iterables with different lengths.
 
 
 0.40.9 (2025-06-25)
@@ -17,7 +31,7 @@ Added
 ^^^^^
 
 * Added ``sample_bias_per_component`` flag to :class:`~isaaclab.utils.noise.noise_model.NoiseModelWithAdditiveBias` to enable independent per-component bias
- sampling, which is now the default behavior. If set to False, the previous behavior of sharing the same bias value across all components is retained.
+  sampling, which is now the default behavior. If set to False, the previous behavior of sharing the same bias value across all components is retained.
 
 
 0.40.8 (2025-06-18)
@@ -27,8 +41,8 @@ Fixed
 ^^^^^
 
 * Fixed data inconsistency between read_body, read_link, read_com when write_body, write_com, write_joint performed, in
- :class:`~isaaclab.assets.Articulation`, :class:`~isaaclab.assets.RigidObject`, and
- :class:`~isaaclab.assets.RigidObjectCollection`
+  :class:`~isaaclab.assets.Articulation`, :class:`~isaaclab.assets.RigidObject`, and
+  :class:`~isaaclab.assets.RigidObjectCollection`
 * added pytest that check against these data consistencies
 
 
@@ -38,7 +52,7 @@ Fixed
 Added
 ^^^^^
 
-* :class:`NoiseModel` support for manager-based workflows.
+* :class:`~isaaclab.utils.noise.NoiseModel` support for manager-based workflows.
 
 Changed
 ^^^^^^^

source/isaaclab/isaaclab/utils/math.py

@@ -254,16 +254,17 @@ def quat_conjugate(q: torch.Tensor) -> torch.Tensor:
 
 
 @torch.jit.script
-def quat_inv(q: torch.Tensor) -> torch.Tensor:
-    """Compute the inverse of a quaternion.
+def quat_inv(q: torch.Tensor, eps: float = 1e-9) -> torch.Tensor:
+    """Computes the inverse of a quaternion.
 
     Args:
         q: The quaternion orientation in (w, x, y, z). Shape is (N, 4).
+        eps: A small value to avoid division by zero. Defaults to 1e-9.
 
     Returns:
         The inverse quaternion in (w, x, y, z). Shape is (N, 4).
     """
-    return normalize(quat_conjugate(q))
+    return quat_conjugate(q) / q.pow(2).sum(dim=-1, keepdim=True).clamp(min=eps)
 
 
 @torch.jit.script

source/isaaclab/test/utils/test_math.py

@@ -593,6 +593,35 @@ def test_quat_apply_inverse(device):
     torch.testing.assert_close(scipy_result.to(device=device), apply_result, atol=2e-4, rtol=2e-4)
 
 
+@pytest.mark.parametrize("device", ["cpu", "cuda:0"])
+def test_quat_inv(device):
+    """Test for quat_inv method.
+
+    For random unit and non-unit quaternions q, the Hamilton products
+    q ⊗ q⁻¹ and q⁻¹ ⊗ q must both equal the identity quaternion (1,0,0,0)
+    within numerical precision.
+    """
+    num = 2048
+
+    # -------- non-unit sample (average ‖q‖ ≈ 10) --------
+    q_nonunit = torch.randn(num, 4, device=device) * 5.0
+
+    # -------- unit sample (‖q‖ = 1) --------
+    q_unit = torch.randn(num, 4, device=device)
+    q_unit = q_unit / q_unit.norm(dim=-1, keepdim=True)
+
+    identity = torch.tensor([1.0, 0.0, 0.0, 0.0], device=device)
+
+    for q in (q_nonunit, q_unit):
+        q_inv = math_utils.quat_inv(q)
+
+        id_batch = identity.expand_as(q)
+
+        # left and right products must both be identity
+        torch.testing.assert_close(math_utils.quat_mul(q, q_inv), id_batch, atol=1e-4, rtol=1e-4)
+        torch.testing.assert_close(math_utils.quat_mul(q_inv, q), id_batch, atol=1e-4, rtol=1e-4)
+
+
 def test_quat_apply_benchmarks():
     """Test for quat_apply and quat_apply_inverse methods compared to old methods using torch.bmm and torch.einsum.
     The new implementation uses :meth:`torch.einsum` instead of `torch.bmm` which allows