# 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
from adam.core.constants import Representations
from adam.core.rbd_algorithms import RBDAlgorithms
from adam.jax.jax_like import SpatialMath
from adam.model import Model
from adam.parametric.model import ParametricLink, URDFParametricModelFactory
[docs]
class KinDynComputationsParametric:
"""This is a small class that retrieves robot quantities using Jax for Floating Base systems.
This is parametric w.r.t the link length and densities.
"""
def __init__(
self,
urdfstring: str,
joints_name_list: list,
links_name_list: list,
root_link: str = None,
gravity: np.array = jnp.array([0, 0, -9.80665, 0, 0, 0]),
) -> None:
"""
Args:
urdfstring (str): either path or string of the urdf
joints_name_list (list): list of the actuated joints
links_name_list (list): list of parametric links
root_link (str, optional): Deprecated. The root link is automatically chosen as the link with no parent in the URDF. Defaults to None.
"""
[docs]
self.math = SpatialMath()
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self.links_name_list = links_name_list
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self.urdfstring = urdfstring
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self.joints_name_list = joints_name_list
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self.representation = Representations.MIXED_REPRESENTATION # Default
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,
)
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def set_frame_velocity_representation(
self, representation: Representations
) -> None:
"""Sets the representation of the velocity of the frames
Args:
representation (Representations): The representation of the velocity
"""
self.representation = representation
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def mass_matrix(
self,
base_transform: jnp.array,
joint_positions: jnp.array,
length_multiplier: jnp.array,
densities: jnp.array,
):
"""Returns the Mass Matrix functions computed the CRBA
Args:
base_transform (jnp.array): The homogenous transform from base to world frame
joint_positions (jnp.array): The joints position
length_multiplier (jnp.array): The length multiplier of the parametrized links
densities (jnp.array): The densities of the parametrized links
Returns:
M (jnp.array): Mass Matrix
"""
factory = URDFParametricModelFactory(
path=self.urdfstring,
math=self.math,
links_name_list=self.links_name_list,
length_multiplier=length_multiplier,
densities=densities,
)
model = Model.build(factory=factory, joints_name_list=self.joints_name_list)
self.rbdalgos = RBDAlgorithms(model=model, math=self.math)
self.rbdalgos.set_frame_velocity_representation(self.representation)
self.NDoF = self.rbdalgos.NDoF
[M, _] = self.rbdalgos.crba(base_transform, joint_positions)
return M.array
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def centroidal_momentum_matrix(
self,
base_transform: jnp.array,
joint_positions: jnp.array,
length_multiplier: jnp.array,
densities: jnp.array,
):
"""Returns the Centroidal Momentum Matrix functions computed the CRBA
Args:
base_transform (jnp.array): The homogenous transform from base to world frame
joint_positions (jnp.array): The joints position
length_multiplier (jnp.array): The length multiplier of the parametrized links
densities (jnp.array): The densities of the parametrized links
Returns:
Jcc (jnp.array): Centroidal Momentum matrix
"""
factory = URDFParametricModelFactory(
path=self.urdfstring,
math=self.math,
links_name_list=self.links_name_list,
length_multiplier=length_multiplier,
densities=densities,
)
model = Model.build(factory=factory, joints_name_list=self.joints_name_list)
self.rbdalgos = RBDAlgorithms(model=model, math=self.math)
self.rbdalgos.set_frame_velocity_representation(self.representation)
self.NDoF = self.rbdalgos.NDoF
[_, Jcm] = self.rbdalgos.crba(base_transform, joint_positions)
return Jcm.array
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def relative_jacobian(
self,
frame: str,
joint_positions: jnp.array,
length_multiplier: jnp.array,
densities: jnp.array,
):
"""Returns the Jacobian between the root link and a specified frame frames
Args:
frame (str): The tip of the chain
joint_positions (jnp.array): The joints position
length_multiplier (jnp.array): The length multiplier of the parametrized links
densities (jnp.array): The densities of the parametrized links
Returns:
J (jnp.array): The Jacobian between the root and the frame
"""
factory = URDFParametricModelFactory(
path=self.urdfstring,
math=self.math,
links_name_list=self.links_name_list,
length_multiplier=length_multiplier,
densities=densities,
)
model = Model.build(factory=factory, joints_name_list=self.joints_name_list)
self.rbdalgos = RBDAlgorithms(model=model, math=self.math)
self.rbdalgos.set_frame_velocity_representation(self.representation)
self.NDoF = self.rbdalgos.NDoF
return self.rbdalgos.relative_jacobian(frame, joint_positions).array
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def jacobian_dot(
self,
frame: str,
base_transform: jnp.array,
joint_positions: jnp.array,
base_velocity: jnp.array,
joint_velocities: jnp.array,
length_multiplier: jnp.array,
densities: jnp.array,
) -> jnp.array:
"""Returns the Jacobian derivative relative to the specified frame
Args:
frame (str): The frame to which the jacobian will be computed
base_transform (jnp.array): The homogenous transform from base to world frame
joint_positions (jnp.array): The joints position
base_velocity (jnp.array): The base velocity
joint_velocities (jnp.array): The joint velocities
length_multiplier (jnp.array): The length multiplier of the parametrized links
densities (jnp.array): The densities of the parametrized links
Returns:
Jdot (jnp.array): The Jacobian derivative relative to the frame
"""
factory = URDFParametricModelFactory(
path=self.urdfstring,
math=self.math,
links_name_list=self.links_name_list,
length_multiplier=length_multiplier,
densities=densities,
)
model = Model.build(factory=factory, joints_name_list=self.joints_name_list)
self.rbdalgos = RBDAlgorithms(model=model, math=self.math)
self.rbdalgos.set_frame_velocity_representation(self.representation)
self.NDoF = self.rbdalgos.NDoF
return self.rbdalgos.jacobian_dot(
frame, base_transform, joint_positions, base_velocity, joint_velocities
).array
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def forward_kinematics(
self,
frame: str,
base_transform: jnp.array,
joint_positions: jnp.array,
length_multiplier: jnp.array,
densities: jnp.array,
):
"""Computes the forward kinematics relative to the specified frame
Args:
frame (str): The frame to which the fk will be computed
base_transform (jnp.array): The homogenous transform from base to world frame
joint_positions (jnp.array): The joints position
length_multiplier (jnp.array): The length multiplier of the parametrized links
densities (jnp.array): The densities of the parametrized links
Returns:
T_fk (jnp.array): The fk represented as Homogenous transformation matrix
"""
factory = URDFParametricModelFactory(
path=self.urdfstring,
math=self.math,
links_name_list=self.links_name_list,
length_multiplier=length_multiplier,
densities=densities,
)
model = Model.build(factory=factory, joints_name_list=self.joints_name_list)
self.rbdalgos = RBDAlgorithms(model=model, math=self.math)
self.rbdalgos.set_frame_velocity_representation(self.representation)
self.NDoF = self.rbdalgos.NDoF
return self.rbdalgos.forward_kinematics(
frame, base_transform, joint_positions
).array
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def forward_kinematics_fun(
self, frame, length_multiplier: jnp.array, densities: jnp.array
):
return lambda T, joint_positions: self.forward_kinematics(
frame, T, joint_positions
)
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def jacobian(
self,
frame: str,
base_transform,
joint_positions,
length_multiplier: jnp.array,
densities: jnp.array,
):
"""Returns the Jacobian relative to the specified frame
Args
frame (str): The frame to which the jacobian will be computed
base_transform (jnp.array): The homogenous transform from base to world frame
s (jnp.array): The joints position
length_multiplier (jnp.array): The length multiplier of the parametrized links
densities (jnp.array): The densities of the parametrized links
Returns:
J_tot (jnp.array): The Jacobian relative to the frame
"""
factory = URDFParametricModelFactory(
path=self.urdfstring,
math=self.math,
links_name_list=self.links_name_list,
length_multiplier=length_multiplier,
densities=densities,
)
model = Model.build(factory=factory, joints_name_list=self.joints_name_list)
self.rbdalgos = RBDAlgorithms(model=model, math=self.math)
self.rbdalgos.set_frame_velocity_representation(self.representation)
self.NDoF = self.rbdalgos.NDoF
return self.rbdalgos.jacobian(frame, base_transform, joint_positions).array
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def bias_force(
self,
base_transform: jnp.array,
joint_positions: jnp.array,
base_velocity: jnp.array,
s_dot: jnp.array,
length_multiplier: jnp.array,
densities: jnp.array,
) -> jnp.array:
"""Returns the bias force of the floating-base dynamics ejoint_positionsuation,
using a reduced RNEA (no acceleration and external forces)
Args:
base_transform (jnp.array): The homogenous transform from base to world frame
joint_positions (jnp.array): The joints position
base_velocity (jnp.array): The base velocity
s_dot (jnp.array): The joints velocity
length_multiplier (jnp.array): The length multiplier of the parametrized links
densities (jnp.array): The densities of the parametrized links
Returns:
h (jnp.array): the bias force
"""
factory = URDFParametricModelFactory(
path=self.urdfstring,
math=self.math,
links_name_list=self.links_name_list,
length_multiplier=length_multiplier,
densities=densities,
)
model = Model.build(factory=factory, joints_name_list=self.joints_name_list)
self.rbdalgos = RBDAlgorithms(model=model, math=self.math)
self.rbdalgos.set_frame_velocity_representation(self.representation)
self.NDoF = self.rbdalgos.NDoF
return self.rbdalgos.rnea(
base_transform, joint_positions, base_velocity, s_dot, self.g
).array.squeeze()
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def coriolis_term(
self,
base_transform: jnp.array,
joint_positions: jnp.array,
base_velocity: jnp.array,
s_dot: jnp.array,
length_multiplier: jnp.array,
densities: jnp.array,
) -> jnp.array:
"""Returns the coriolis term of the floating-base dynamics ejoint_positionsuation,
using a reduced RNEA (no acceleration and external forces)
Args:
base_transform (jnp.array): The homogenous transform from base to world frame
joint_positions (jnp.array): The joints position
base_velocity (jnp.array): The base velocity
s_dot (jnp.array): The joints velocity
length_multiplier (jnp.array): The length multiplier of the parametrized links
densities (jnp.array): The densities of the parametrized links
Returns:
C (jnp.array): the Coriolis term
"""
factory = URDFParametricModelFactory(
path=self.urdfstring,
math=self.math,
links_name_list=self.links_name_list,
length_multiplier=length_multiplier,
densities=densities,
)
model = Model.build(factory=factory, joints_name_list=self.joints_name_list)
self.rbdalgos = RBDAlgorithms(model=model, math=self.math)
self.rbdalgos.set_frame_velocity_representation(self.representation)
self.NDoF = self.rbdalgos.NDoF
return self.rbdalgos.rnea(
base_transform,
joint_positions,
base_velocity.reshape(6, 1),
s_dot,
np.zeros(6),
).array.squeeze()
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def gravity_term(
self,
base_transform: jnp.array,
joint_positions: jnp.array,
length_multiplier: jnp.array,
densities: jnp.array,
) -> jnp.array:
"""Returns the gravity term of the floating-base dynamics ejoint_positionsuation,
using a reduced RNEA (no acceleration and external forces)
Args:
base_transform (jnp.array): The homogenous transform from base to world frame
joint_positions (jnp.array): The joints position
length_multiplier (jnp.array): The length multiplier of the parametrized links
densities (jnp.array): The densities of the parametrized links
Returns:
G (jnp.array): the gravity term
"""
factory = URDFParametricModelFactory(
path=self.urdfstring,
math=self.math,
links_name_list=self.links_name_list,
length_multiplier=length_multiplier,
densities=densities,
)
model = Model.build(factory=factory, joints_name_list=self.joints_name_list)
self.rbdalgos = RBDAlgorithms(model=model, math=self.math)
self.rbdalgos.set_frame_velocity_representation(self.representation)
self.NDoF = self.rbdalgos.NDoF
return self.rbdalgos.rnea(
base_transform,
joint_positions,
np.zeros(6).reshape(6, 1),
np.zeros(self.NDoF),
self.g,
).array.squeeze()
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def CoM_position(
self,
base_transform: jnp.array,
joint_positions: jnp.array,
length_multiplier: jnp.array,
densities: jnp.array,
) -> jnp.array:
"""Returns the CoM position
Args:
base_transform (jnp.array): The homogenous transform from base to world frame
joint_positions (jnp.array): The joints position
length_multiplier (jnp.array): The length multiplier of the parametrized links
densities (jnp.array): The densities of the parametrized links
Returns:
com (jnp.array): The CoM position
"""
factory = URDFParametricModelFactory(
path=self.urdfstring,
math=self.math,
links_name_list=self.links_name_list,
length_multiplier=length_multiplier,
densities=densities,
)
model = Model.build(factory=factory, joints_name_list=self.joints_name_list)
self.rbdalgos = RBDAlgorithms(model=model, math=self.math)
self.rbdalgos.set_frame_velocity_representation(self.representation)
self.NDoF = self.rbdalgos.NDoF
return self.rbdalgos.CoM_position(
base_transform, joint_positions
).array.squeeze()
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def get_total_mass(
self, length_multiplier: jnp.array, densities: jnp.array
) -> float:
"""Returns the total mass of the robot
Args:
length_multiplier (jnp.array): The length multiplier of the parametrized links
densities (jnp.array): The densities of the parametrized links
Returns:
mass: The total mass
"""
factory = URDFParametricModelFactory(
path=self.urdfstring,
math=self.math,
links_name_list=self.links_name_list,
length_multiplier=length_multiplier,
densities=densities,
)
model = Model.build(factory=factory, joints_name_list=self.joints_name_list)
self.rbdalgos = RBDAlgorithms(model=model, math=self.math)
self.rbdalgos.set_frame_velocity_representation(self.representation)
self.NDoF = self.rbdalgos.NDoF
return self.rbdalgos.get_total_mass()
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def get_original_densities(self) -> list[float]:
"""Returns the original densities of the parametric links
Returns:
densities: The original densities of the parametric links
"""
densities = []
model = self.rbdalgos.model
for name in self.links_name_list:
link = model.links[name]
assert isinstance(link, ParametricLink)
densities.append(link.original_density)
return densities