diff --git a/src/adam/casadi/computations.py b/src/adam/casadi/computations.py
index ff67fda2..1d7c2e9d 100644
--- a/src/adam/casadi/computations.py
+++ b/src/adam/casadi/computations.py
@@ -1,5 +1,7 @@
 # Copyright (C) Istituto Italiano di Tecnologia (IIT). All rights reserved.
 
+import warnings
+
 import casadi as cs
 import numpy as np
 
@@ -34,8 +36,10 @@ def __init__(
         self.g = gravity
         self.f_opts = f_opts
         if root_link is not None:
-            raise DeprecationWarning(
-                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF"
+            warnings.warn(
+                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF",
+                DeprecationWarning,
+                stacklevel=2,
             )
 
     def set_frame_velocity_representation(
@@ -294,7 +298,7 @@ def jacobian_dot(
             frame (str): The frame to which the jacobian will be computed
             base_transform (cs.SX): The homogenous transform from base to world frame
             joint_positions (cs.SX): The joints position
-            base_velocity (cs.SX): The base velocity in mixed representation
+            base_velocity (cs.SX): The base velocity
             joint_velocities (cs.SX): The joint velocities
 
         Returns:
@@ -369,7 +373,7 @@ def bias_force(
         Args:
             base_transform (cs.SX): The homogenous transform from base to world frame
             joint_positions (cs.SX): The joints position
-            base_velocity (cs.SX): The base velocity in mixed representation
+            base_velocity (cs.SX): The base velocity
             joint_velocities (cs.SX): The joints velocity
 
         Returns:
@@ -402,7 +406,7 @@ def coriolis_term(
         Args:
             base_transform (cs.SX): The homogenous transform from base to world frame
             joint_positions (cs.SX): The joints position
-            base_velocity (cs.SX): The base velocity in mixed representation
+            base_velocity (cs.SX): The base velocity
             joint_velocities (cs.SX): The joints velocity
 
         Returns:
diff --git a/src/adam/core/rbd_algorithms.py b/src/adam/core/rbd_algorithms.py
index 4c67d980..de2f744d 100644
--- a/src/adam/core/rbd_algorithms.py
+++ b/src/adam/core/rbd_algorithms.py
@@ -8,9 +8,7 @@
 
 
 class RBDAlgorithms:
-    """This is a small class that implements Rigid body algorithms retrieving robot quantities represented
-    in mixed representation, for Floating Base systems - as humanoid robots.
-    """
+    """This is a small class that implements Rigid body algorithms retrieving robot quantities, for Floating Base systems - as humanoid robots."""
 
     def __init__(self, model: Model, math: SpatialMath) -> None:
         """
@@ -248,7 +246,7 @@ def jacobian_dot(
             frame (str): The frame to which the jacobian will be computed
             base_transform (npt.ArrayLike): The homogenous transform from base to world frame
             joint_positions (npt.ArrayLike): The joints position
-            base_velocity (npt.ArrayLike): The base velocity in mixed representation
+            base_velocity (npt.ArrayLike): The base velocity
             joint_velocities (npt.ArrayLike): The joints velocity
 
         Returns:
@@ -370,7 +368,7 @@ def rnea(
             frame (str): The frame to which the jacobian will be computed
             base_transform (T): The homogenous transform from base to world frame
             joint_positions (T): The joints position
-            base_velocity (T): The base velocity in mixed representation
+            base_velocity (T): The base velocity
             joint_velocities (T): The joints velocity
             g (T): The 6D gravity acceleration
 
diff --git a/src/adam/jax/computations.py b/src/adam/jax/computations.py
index 82d3611f..7578ba17 100644
--- a/src/adam/jax/computations.py
+++ b/src/adam/jax/computations.py
@@ -1,5 +1,7 @@
 # Copyright (C) Istituto Italiano di Tecnologia (IIT). All rights reserved.
 
+import warnings
+
 import jax.numpy as jnp
 import numpy as np
 
@@ -32,8 +34,10 @@ def __init__(
         self.NDoF = self.rbdalgos.NDoF
         self.g = gravity
         if root_link is not None:
-            raise DeprecationWarning(
-                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF"
+            warnings.warn(
+                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF",
+                DeprecationWarning,
+                stacklevel=2,
             )
 
     def set_frame_velocity_representation(
diff --git a/src/adam/numpy/computations.py b/src/adam/numpy/computations.py
index 9ddd2d26..249a891d 100644
--- a/src/adam/numpy/computations.py
+++ b/src/adam/numpy/computations.py
@@ -1,5 +1,6 @@
 # Copyright (C) Istituto Italiano di Tecnologia (IIT). All rights reserved.
 
+import warnings
 
 import numpy as np
 
@@ -32,8 +33,10 @@ def __init__(
         self.NDoF = model.NDoF
         self.g = gravity
         if root_link is not None:
-            raise DeprecationWarning(
-                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF"
+            warnings.warn(
+                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF",
+                DeprecationWarning,
+                stacklevel=2,
             )
 
     def set_frame_velocity_representation(
diff --git a/src/adam/parametric/casadi/computations_parametric.py b/src/adam/parametric/casadi/computations_parametric.py
index 4149662d..6fc8cd3b 100644
--- a/src/adam/parametric/casadi/computations_parametric.py
+++ b/src/adam/parametric/casadi/computations_parametric.py
@@ -1,5 +1,7 @@
 # Copyright (C) Istituto Italiano di Tecnologia (IIT). All rights reserved.
 
+import warnings
+
 import casadi as cs
 import numpy as np
 
@@ -49,8 +51,10 @@ def __init__(
         self.g = gravity
         self.f_opts = f_opts
         if root_link is not None:
-            raise DeprecationWarning(
-                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF"
+            warnings.warn(
+                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF",
+                DeprecationWarning,
+                stacklevel=2,
             )
 
     def set_frame_velocity_representation(
diff --git a/src/adam/parametric/jax/computations_parametric.py b/src/adam/parametric/jax/computations_parametric.py
index 7920006a..2fa061de 100644
--- a/src/adam/parametric/jax/computations_parametric.py
+++ b/src/adam/parametric/jax/computations_parametric.py
@@ -1,5 +1,7 @@
 # Copyright (C) Istituto Italiano di Tecnologia (IIT). All rights reserved.
 
+import warnings
+
 import jax.numpy as jnp
 import numpy as np
 from jax import grad, jit, vmap
@@ -38,8 +40,10 @@ def __init__(
         self.joints_name_list = joints_name_list
         self.representation = Representations.MIXED_REPRESENTATION  # Default
         if root_link is not None:
-            raise DeprecationWarning(
-                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF"
+            warnings.warn(
+                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF",
+                DeprecationWarning,
+                stacklevel=2,
             )
 
     def set_frame_velocity_representation(
diff --git a/src/adam/parametric/numpy/computations_parametric.py b/src/adam/parametric/numpy/computations_parametric.py
index f7030376..bcea1e32 100644
--- a/src/adam/parametric/numpy/computations_parametric.py
+++ b/src/adam/parametric/numpy/computations_parametric.py
@@ -1,5 +1,7 @@
 # Copyright (C) Istituto Italiano di Tecnologia (IIT). All rights reserved.
 
+import warnings
+
 import numpy as np
 
 from adam.core.constants import Representations
@@ -36,8 +38,10 @@ def __init__(
         self.joints_name_list = joints_name_list
         self.representation = Representations.MIXED_REPRESENTATION  # Default
         if root_link is not None:
-            raise DeprecationWarning(
-                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF"
+            warnings.warn(
+                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF",
+                DeprecationWarning,
+                stacklevel=2,
             )
 
     def set_frame_velocity_representation(
diff --git a/src/adam/parametric/pytorch/computations_parametric.py b/src/adam/parametric/pytorch/computations_parametric.py
index 63568d45..a185ee02 100644
--- a/src/adam/parametric/pytorch/computations_parametric.py
+++ b/src/adam/parametric/pytorch/computations_parametric.py
@@ -1,5 +1,7 @@
 # Copyright (C) Istituto Italiano di Tecnologia (IIT). All rights reserved.
 
+import warnings
+
 import numpy as np
 import torch
 
@@ -39,8 +41,10 @@ def __init__(
         self.urdfstring = urdfstring
         self.representation = Representations.MIXED_REPRESENTATION  # Default
         if root_link is not None:
-            raise DeprecationWarning(
-                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF"
+            warnings.warn(
+                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF",
+                DeprecationWarning,
+                stacklevel=2,
             )
 
     def set_frame_velocity_representation(
diff --git a/src/adam/pytorch/computation_batch.py b/src/adam/pytorch/computation_batch.py
index b5e96a10..6ea59fdc 100644
--- a/src/adam/pytorch/computation_batch.py
+++ b/src/adam/pytorch/computation_batch.py
@@ -2,6 +2,8 @@
 # This software may be modified and distributed under the terms of the
 # GNU Lesser General Public License v2.1 or any later version.
 
+import warnings
+
 import jax
 import jax.numpy as jnp
 import numpy as np
@@ -23,14 +25,14 @@ def __init__(
         self,
         urdfstring: str,
         joints_name_list: list = None,
-        root_link: str = "root_link",
+        root_link: str = None,
         gravity: np.array = jnp.array([0, 0, -9.80665, 0, 0, 0]),
     ) -> None:
         """
         Args:
             urdfstring (str): path of the urdf
             joints_name_list (list): list of the actuated joints
-            root_link (str, optional): the first link. Defaults to 'root_link'.
+            root_link (str, optional): Deprecated. The root link is automatically chosen as the link with no parent in the URDF. Defaults to None.
         """
         math = SpatialMath()
         factory = URDFModelFactory(path=urdfstring, math=math)
@@ -39,6 +41,12 @@ def __init__(
         self.NDoF = self.rbdalgos.NDoF
         self.g = gravity
         self.funcs = {}
+        if root_link is not None:
+            warnings.warn(
+                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF",
+                DeprecationWarning,
+                stacklevel=2,
+            )
 
     def set_frame_velocity_representation(
         self, representation: Representations
diff --git a/src/adam/pytorch/computations.py b/src/adam/pytorch/computations.py
index 3fc70805..54fb02d2 100644
--- a/src/adam/pytorch/computations.py
+++ b/src/adam/pytorch/computations.py
@@ -1,6 +1,8 @@
 # Copyright (C) Istituto Italiano di Tecnologia (IIT). All rights reserved.
 
 
+import warnings
+
 import numpy as np
 import torch
 
@@ -35,8 +37,10 @@ def __init__(
         self.NDoF = self.rbdalgos.NDoF
         self.g = gravity
         if root_link is not None:
-            raise DeprecationWarning(
-                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF"
+            warnings.warn(
+                "The root_link argument is not used. The root link is automatically chosen as the link with no parent in the URDF",
+                DeprecationWarning,
+                stacklevel=2,
             )
 
     def set_frame_velocity_representation(
@@ -50,7 +54,7 @@ def set_frame_velocity_representation(
         self.rbdalgos.set_frame_velocity_representation(representation)
 
     def mass_matrix(
-        self, base_transform: torch.Tensor, joint_position: torch.Tensor
+        self, base_transform: torch.Tensor, joint_positions: torch.Tensor
     ) -> torch.Tensor:
         """Returns the Mass Matrix functions computed the CRBA
 
@@ -61,11 +65,11 @@ def mass_matrix(
         Returns:
             M (torch.tensor): Mass Matrix
         """
-        [M, _] = self.rbdalgos.crba(base_transform, joint_position)
+        [M, _] = self.rbdalgos.crba(base_transform, joint_positions)
         return M.array
 
     def centroidal_momentum_matrix(
-        self, base_transform: torch.Tensor, joint_position: torch.Tensor
+        self, base_transform: torch.Tensor, joint_positions: torch.Tensor
     ) -> torch.Tensor:
         """Returns the Centroidal Momentum Matrix functions computed the CRBA
 
@@ -76,11 +80,11 @@ def centroidal_momentum_matrix(
         Returns:
             Jcc (torch.tensor): Centroidal Momentum matrix
         """
-        [_, Jcm] = self.rbdalgos.crba(base_transform, joint_position)
+        [_, Jcm] = self.rbdalgos.crba(base_transform, joint_positions)
         return Jcm.array
 
     def forward_kinematics(
-        self, frame, base_transform: torch.Tensor, joint_position: torch.Tensor
+        self, frame, base_transform: torch.Tensor, joint_positions: torch.Tensor
     ) -> torch.Tensor:
         """Computes the forward kinematics relative to the specified frame
 
@@ -96,7 +100,7 @@ def forward_kinematics(
             self.rbdalgos.forward_kinematics(
                 frame,
                 base_transform,
-                joint_position,
+                joint_positions,
             )
         ).array
 
@@ -177,7 +181,7 @@ def bias_force(
         base_velocity: torch.Tensor,
         joint_velocities: torch.Tensor,
     ) -> torch.Tensor:
-        """Returns the bias force of the floating-base dynamics ejoint_positionsuation,
+        """Returns the bias force of the floating-base dynamics equation,
         using a reduced RNEA (no acceleration and external forces)
 
         Args:
@@ -204,7 +208,7 @@ def coriolis_term(
         base_velocity: torch.Tensor,
         joint_velocities: torch.Tensor,
     ) -> torch.Tensor:
-        """Returns the coriolis term of the floating-base dynamics ejoint_positionsuation,
+        """Returns the coriolis term of the floating-base dynamics equation,
         using a reduced RNEA (no acceleration and external forces)
 
         Args:
@@ -228,7 +232,7 @@ def coriolis_term(
     def gravity_term(
         self, base_transform: torch.Tensor, joint_positions: torch.Tensor
     ) -> torch.Tensor:
-        """Returns the gravity term of the floating-base dynamics ejoint_positionsuation,
+        """Returns the gravity term of the floating-base dynamics equation,
         using a reduced RNEA (no acceleration and external forces)
 
         Args: