diff --git a/nipype/algorithms/confounds.py b/nipype/algorithms/confounds.py
index 8f7e31061b..c6378fe8a3 100644
--- a/nipype/algorithms/confounds.py
+++ b/nipype/algorithms/confounds.py
@@ -269,6 +269,16 @@ class FramewiseDisplacementInputSpec(BaseInterfaceInputSpec):
         desc="Source of movement parameters",
         mandatory=True,
     )
+    metric = traits.Enum(
+        "L1",
+        "riemannian",
+        usedefault=True,
+        mandatory=True,
+        desc="Distance metric to apply: "
+        "L1 = Manhattan distance (original definition); "
+        "riemannian = Riemannian distance on the "
+        "Special Euclidean group in 3D (geodesic)",
+    )
     radius = traits.Float(
         50,
         usedefault=True,
@@ -342,9 +352,38 @@ def _run_interface(self, runtime):
             arr=mpars,
             source=self.inputs.parameter_source,
         )
-        diff = mpars[:-1, :6] - mpars[1:, :6]
-        diff[:, 3:6] *= self.inputs.radius
-        fd_res = np.abs(diff).sum(axis=1)
+
+        if self.inputs.metric == "L1":
+            diff = mpars[:-1, :6] - mpars[1:, :6]
+            diff[:, 3:6] *= self.inputs.radius
+            fd_res = np.abs(diff).sum(axis=1)
+
+        elif self.inputs.metric == "riemannian":
+            from geomstats.invariant_metric import InvariantMetric
+            from geomstats.special_euclidean_group import SpecialEuclideanGroup
+
+            SE3_GROUP = SpecialEuclideanGroup(n=3)
+            SO3_GROUP = SE3_GROUP.rotations
+            DIM_TRANSLATIONS = SE3_GROUP.translations.dimension
+            DIM_ROTATIONS = SE3_GROUP.rotations.dimension
+
+            so3pars = mpars[:, DIM_TRANSLATIONS:]
+            so3pars = SO3_GROUP.rotation_vector_from_tait_bryan_angles(
+                so3pars, extrinsic_or_intrinsic="extrinsic", order="zyx"
+            )
+
+            se3pars = np.hstack([so3pars, mpars[:, :DIM_TRANSLATIONS]])
+
+            diag_rotations = self.inputs.radius * np.ones(DIM_ROTATIONS)
+            diag_translations = np.ones(DIM_TRANSLATIONS)
+            diag = np.concatenate([diag_rotations, diag_translations])
+            inner_product = np.diag(diag)
+            metric = InvariantMetric(
+                group=SE3_GROUP,
+                inner_product_mat_at_identity=inner_product,
+                left_or_right="left",
+            )
+            fd_res = metric.dist(se3pars[:-1], se3pars[1:])
 
         self._results = {
             "out_file": op.abspath(self.inputs.out_file),
diff --git a/nipype/algorithms/tests/test_auto_FramewiseDisplacement.py b/nipype/algorithms/tests/test_auto_FramewiseDisplacement.py
index 1bc46fba64..82f9ee7143 100644
--- a/nipype/algorithms/tests/test_auto_FramewiseDisplacement.py
+++ b/nipype/algorithms/tests/test_auto_FramewiseDisplacement.py
@@ -7,6 +7,7 @@ def test_FramewiseDisplacement_inputs():
         figdpi=dict(usedefault=True,),
         figsize=dict(usedefault=True,),
         in_file=dict(extensions=None, mandatory=True,),
+        metric=dict(mandatory=True, usedefault=True,),
         normalize=dict(usedefault=True,),
         out_figure=dict(extensions=None, usedefault=True,),
         out_file=dict(extensions=None, usedefault=True,),
diff --git a/nipype/algorithms/tests/test_confounds.py b/nipype/algorithms/tests/test_confounds.py
index 29f18c9221..f242cb241a 100644
--- a/nipype/algorithms/tests/test_confounds.py
+++ b/nipype/algorithms/tests/test_confounds.py
@@ -15,14 +15,48 @@
 except ImportError:
     pass
 
+nogeomstats = True
+try:
+    import geomstats
+
+    nogeomstats = False
+except ImportError:
+    pass
+
 
 def test_fd(tmpdir):
     tempdir = tmpdir.strpath
     ground_truth = np.loadtxt(example_data("fsl_motion_outliers_fd.txt"))
+
+    fdisplacement = FramewiseDisplacement(
+        in_file=example_data("fsl_mcflirt_movpar.txt"),
+        out_file=tempdir + "/fd.txt",
+        parameter_source="FSL",
+    )
+    res = fdisplacement.run()
+
+    with open(res.outputs.out_file) as all_lines:
+        for line in all_lines:
+            assert "FramewiseDisplacement" in line
+            break
+
+    assert np.allclose(
+        ground_truth, np.loadtxt(res.outputs.out_file, skiprows=1), atol=0.16
+    )
+    assert np.abs(ground_truth.mean() - res.outputs.fd_average) < 1e-2
+
+
+@pytest.mark.skipif(nogeomstats, reason="geomstats is not installed")
+def test_fd_riemannian(tmpdir):
+    tempdir = tmpdir.strpath
+    # TODO(nina): Adapt ground_truth w. SPM Euler angles convention
+    ground_truth = np.loadtxt(example_data("fsl_motion_outliers_fd.txt"))
+
     fdisplacement = FramewiseDisplacement(
         in_file=example_data("fsl_mcflirt_movpar.txt"),
         out_file=tempdir + "/fd.txt",
         parameter_source="FSL",
+        metric="riemannian",
     )
     res = fdisplacement.run()
 
diff --git a/nipype/info.py b/nipype/info.py
index 7a2e4ae70e..5d3730f146 100644
--- a/nipype/info.py
+++ b/nipype/info.py
@@ -178,7 +178,7 @@ def get_nipype_gitversion():
         "sphinxcontrib-napoleon",
     ],
     "duecredit": ["duecredit"],
-    "nipy": ["nitime", "nilearn<0.5.0", "dipy", "nipy", "matplotlib"],
+    "nipy": ["nitime", "nilearn<0.5.0", "dipy", "nipy", "matplotlib", "geomstats>=1.1.0"],
     "profiler": ["psutil>=5.0"],
     "pybids": ["pybids>=0.7.0"],
     "specs": ["black"],