# Copyright (C) Istituto Italiano di Tecnologia (IIT). All rights reserved.
import warnings
import casadi as cs
import numpy as np
from adam.casadi.casadi_like import SpatialMath
from adam.core import RBDAlgorithms
from adam.core.constants import Representations
from adam.model import Model, URDFModelFactory
[docs]
class KinDynComputations:
"""Class that retrieves robot quantities using CasADi for Floating Base systems."""
def __init__(
self,
urdfstring: str,
joints_name_list: list = None,
root_link: str = None,
gravity: np.array = np.array([0.0, 0.0, -9.80665, 0.0, 0.0, 0.0]),
f_opts: dict = dict(jit=False, jit_options=dict(flags="-Ofast"), cse=True),
) -> None:
"""
Args:
urdfstring (str): either path or string of the urdf
joints_name_list (list): list of the actuated joints
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)
model = Model.build(factory=factory, joints_name_list=joints_name_list)
[docs]
self.rbdalgos = RBDAlgorithms(model=model, math=math)
[docs]
self.NDoF = self.rbdalgos.NDoF
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,
)
[docs]
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.rbdalgos.set_frame_velocity_representation(representation)
[docs]
def mass_matrix_fun(self) -> cs.Function:
"""Returns the Mass Matrix functions computed the CRBA
Returns:
M (casADi function): Mass Matrix
"""
base_transform = cs.SX.sym("H", 4, 4)
joint_positions = cs.SX.sym("s", self.NDoF)
M, _ = self.rbdalgos.crba(base_transform, joint_positions)
return cs.Function(
"M", [base_transform, joint_positions], [M.array], self.f_opts
)
[docs]
def centroidal_momentum_matrix_fun(self) -> cs.Function:
"""Returns the Centroidal Momentum Matrix functions computed the CRBA
Returns:
Jcc (casADi function): Centroidal Momentum matrix
"""
base_transform = cs.SX.sym("H", 4, 4)
joint_positions = cs.SX.sym("s", self.NDoF)
_, Jcm = self.rbdalgos.crba(base_transform, joint_positions)
return cs.Function(
"Jcm", [base_transform, joint_positions], [Jcm.array], self.f_opts
)
[docs]
def forward_kinematics_fun(self, frame: str) -> cs.Function:
"""Computes the forward kinematics relative to the specified frame
Args:
frame (str): The frame to which the fk will be computed
Returns:
H (casADi function): The fk represented as Homogenous transformation matrix
"""
joint_positions = cs.SX.sym("s", self.NDoF)
base_transform = cs.SX.sym("H", 4, 4)
H = self.rbdalgos.forward_kinematics(frame, base_transform, joint_positions)
return cs.Function(
"H", [base_transform, joint_positions], [H.array], self.f_opts
)
[docs]
def jacobian_fun(self, frame: str) -> cs.Function:
"""Returns the Jacobian relative to the specified frame
Args:
frame (str): The frame to which the jacobian will be computed
Returns:
J_tot (casADi function): The Jacobian relative to the frame
"""
joint_positions = cs.SX.sym("s", self.NDoF)
base_transform = cs.SX.sym("H", 4, 4)
J_tot = self.rbdalgos.jacobian(frame, base_transform, joint_positions)
return cs.Function(
"J_tot", [base_transform, joint_positions], [J_tot.array], self.f_opts
)
[docs]
def relative_jacobian_fun(self, frame: str) -> cs.Function:
"""Returns the Jacobian between the root link and a specified frame frames
Args:
frame (str): The tip of the chain
Returns:
J (casADi function): The Jacobian between the root and the frame
"""
joint_positions = cs.SX.sym("s", self.NDoF)
J = self.rbdalgos.relative_jacobian(frame, joint_positions)
return cs.Function("J", [joint_positions], [J.array], self.f_opts)
[docs]
def jacobian_dot_fun(self, frame: str) -> cs.Function:
"""Returns the Jacobian derivative relative to the specified frame
Args:
frame (str): The frame to which the jacobian will be computed
Returns:
J_dot (casADi function): The Jacobian derivative relative to the frame
"""
base_transform = cs.SX.sym("H", 4, 4)
joint_positions = cs.SX.sym("s", self.NDoF)
base_velocity = cs.SX.sym("v_b", 6)
joint_velocities = cs.SX.sym("s_dot", self.NDoF)
J_dot = self.rbdalgos.jacobian_dot(
frame, base_transform, joint_positions, base_velocity, joint_velocities
)
return cs.Function(
"J_dot",
[base_transform, joint_positions, base_velocity, joint_velocities],
[J_dot.array],
self.f_opts,
)
[docs]
def CoM_position_fun(self) -> cs.Function:
"""Returns the CoM position
Returns:
CoM (casADi function): The CoM position
"""
joint_positions = cs.SX.sym("s", self.NDoF)
base_transform = cs.SX.sym("H", 4, 4)
com_pos = self.rbdalgos.CoM_position(base_transform, joint_positions)
return cs.Function(
"CoM_pos", [base_transform, joint_positions], [com_pos.array], self.f_opts
)
[docs]
def CoM_jacobian_fun(self) -> cs.Function:
"""Returns the CoM Jacobian
Returns:
J_com (casADi function): The CoM Jacobian
"""
joint_positions = cs.SX.sym("s", self.NDoF)
base_transform = cs.SX.sym("H", 4, 4)
J_com = self.rbdalgos.CoM_jacobian(base_transform, joint_positions)
return cs.Function(
"J_com", [base_transform, joint_positions], [J_com.array], self.f_opts
)
[docs]
def bias_force_fun(self) -> cs.Function:
"""Returns the bias force of the floating-base dynamics equation,
using a reduced RNEA (no acceleration and external forces)
Returns:
h (casADi function): the bias force
"""
base_transform = cs.SX.sym("H", 4, 4)
joint_positions = cs.SX.sym("s", self.NDoF)
base_velocity = cs.SX.sym("v_b", 6)
joint_velocities = cs.SX.sym("s_dot", self.NDoF)
h = self.rbdalgos.rnea(
base_transform, joint_positions, base_velocity, joint_velocities, self.g
)
return cs.Function(
"h",
[base_transform, joint_positions, base_velocity, joint_velocities],
[h.array],
self.f_opts,
)
[docs]
def coriolis_term_fun(self) -> cs.Function:
"""Returns the coriolis term of the floating-base dynamics equation,
using a reduced RNEA (no acceleration and external forces)
Returns:
C (casADi function): the Coriolis term
"""
base_transform = cs.SX.sym("H", 4, 4)
joint_positions = cs.SX.sym("s", self.NDoF)
base_velocity = cs.SX.sym("v_b", 6)
joint_velocities = cs.SX.sym("s_dot", self.NDoF)
# set in the bias force computation the gravity term to zero
C = self.rbdalgos.rnea(
base_transform,
joint_positions,
base_velocity,
joint_velocities,
np.zeros(6),
)
return cs.Function(
"C",
[base_transform, joint_positions, base_velocity, joint_velocities],
[C.array],
self.f_opts,
)
[docs]
def gravity_term_fun(self) -> cs.Function:
"""Returns the gravity term of the floating-base dynamics equation,
using a reduced RNEA (no acceleration and external forces)
Returns:
G (casADi function): the gravity term
"""
base_transform = cs.SX.sym("H", 4, 4)
joint_positions = cs.SX.sym("s", self.NDoF)
# set in the bias force computation the velocity to zero
G = self.rbdalgos.rnea(
base_transform, joint_positions, np.zeros(6), np.zeros(self.NDoF), self.g
)
return cs.Function(
"G", [base_transform, joint_positions], [G.array], self.f_opts
)
[docs]
def get_total_mass(self) -> float:
"""Returns the total mass of the robot
Returns:
mass: The total mass
"""
return self.rbdalgos.get_total_mass()
[docs]
def mass_matrix(self, base_transform: cs.SX, joint_positions: cs.SX):
"""Returns the Mass Matrix functions computed the CRBA
Args:
base_transform (cs.SX): The homogenous transform from base to world frame
joint_positions (cs.SX): The joints position
Returns:
M (cs.SX): Mass Matrix
"""
if isinstance(base_transform, cs.MX) and isinstance(joint_positions, cs.MX):
raise ValueError(
"You are using casadi MX. Please use the function KinDynComputations.mass_matrix_fun()"
)
M, _ = self.rbdalgos.crba(base_transform, joint_positions)
return M.array
[docs]
def centroidal_momentum_matrix(self, base_transform: cs.SX, joint_positions: cs.SX):
"""Returns the Centroidal Momentum Matrix functions computed the CRBA
Args:
base_transform (cs.SX): The homogenous transform from base to world frame
joint_positions (cs.SX): The joints position
Returns:
Jcc (cs.SX): Centroidal Momentum matrix
"""
if isinstance(base_transform, cs.MX) and isinstance(joint_positions, cs.MX):
raise ValueError(
"You are using casadi MX. Please use the function KinDynComputations.centroidal_momentum_matrix_fun()"
)
_, Jcm = self.rbdalgos.crba(base_transform, joint_positions)
return Jcm.array
[docs]
def relative_jacobian(self, frame: str, joint_positions: cs.SX):
"""Returns the Jacobian between the root link and a specified frame frames
Args:
frame (str): The tip of the chain
joint_positions (cs.SX): The joints position
Returns:
J (cs.SX): The Jacobian between the root and the frame
"""
if isinstance(joint_positions, cs.MX):
raise ValueError(
"You are using casadi MX. Please use the function KinDynComputations.relative_jacobian_fun()"
)
return self.rbdalgos.relative_jacobian(frame, joint_positions).array
[docs]
def jacobian_dot(
self,
frame: str,
base_transform: cs.SX,
joint_positions: cs.SX,
base_velocity: cs.SX,
joint_velocities: cs.SX,
) -> cs.SX:
"""Returns the Jacobian derivative relative to the specified frame
Args:
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
joint_velocities (cs.SX): The joint velocities
Returns:
Jdot (cs.SX): The Jacobian derivative relative to the frame
"""
if (
isinstance(base_transform, cs.MX)
and isinstance(joint_positions, cs.MX)
and isinstance(base_velocity, cs.MX)
and isinstance(joint_velocities, cs.MX)
):
raise ValueError(
"You are using casadi MX. Please use the function KinDynComputations.jacobian_dot_fun()"
)
return self.rbdalgos.jacobian_dot(
frame, base_transform, joint_positions, base_velocity, joint_velocities
).array
[docs]
def forward_kinematics(
self,
frame: str,
base_transform: cs.SX,
joint_positions: cs.SX,
):
"""Computes the forward kinematics relative to the specified frame
Args:
frame (str): The frame to which the fk will be computed
base_transform (cs.SX): The homogenous transform from base to world frame
joint_positions (cs.SX): The joints position
Returns:
H (cs.SX): The fk represented as Homogenous transformation matrix
"""
if isinstance(base_transform, cs.MX) and isinstance(joint_positions, cs.MX):
raise ValueError(
"You are using casadi MX. Please use the function KinDynComputations.forward_kinematics_fun()"
)
return self.rbdalgos.forward_kinematics(
frame, base_transform, joint_positions
).array
[docs]
def jacobian(self, frame: str, base_transform, joint_positions):
"""Returns the Jacobian relative to the specified frame
Args:
base_transform (cs.SX): The homogenous transform from base to world frame
s (cs.SX): The joints position
frame (str): The frame to which the jacobian will be computed
Returns:
J_tot (cs.SX): The Jacobian relative to the frame
"""
if isinstance(base_transform, cs.MX) and isinstance(joint_positions, cs.MX):
raise ValueError(
"You are using casadi MX. Please use the function KinDynComputations.jacobian_fun()"
)
return self.rbdalgos.jacobian(frame, base_transform, joint_positions).array
[docs]
def bias_force(
self,
base_transform: cs.SX,
joint_positions: cs.SX,
base_velocity: cs.SX,
joint_velocities: cs.SX,
) -> cs.SX:
"""Returns the bias force of the floating-base dynamics equation,
using a reduced RNEA (no acceleration and external forces)
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
joint_velocities (cs.SX): The joints velocity
Returns:
h (cs.SX): the bias force
"""
if (
isinstance(base_transform, cs.MX)
and isinstance(joint_positions, cs.MX)
and isinstance(base_velocity, cs.MX)
and isinstance(joint_velocities, cs.MX)
):
raise ValueError(
"You are using casadi MX. Please use the function KinDynComputations.bias_force_fun()"
)
return self.rbdalgos.rnea(
base_transform, joint_positions, base_velocity, joint_velocities, self.g
).array
[docs]
def coriolis_term(
self,
base_transform: cs.SX,
joint_positions: cs.SX,
base_velocity: cs.SX,
joint_velocities: cs.SX,
) -> cs.SX:
"""Returns the coriolis term of the floating-base dynamics equation,
using a reduced RNEA (no acceleration and external forces)
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
joint_velocities (cs.SX): The joints velocity
Returns:
C (cs.SX): the Coriolis term
"""
if (
isinstance(base_transform, cs.MX)
and isinstance(joint_positions, cs.MX)
and isinstance(base_velocity, cs.MX)
and isinstance(joint_velocities, cs.MX)
):
raise ValueError(
"You are using casadi MX. Please use the function KinDynComputations.coriolis_term_fun()"
)
return self.rbdalgos.rnea(
base_transform,
joint_positions,
base_velocity.reshape(6, 1),
joint_velocities,
np.zeros(6),
).array
[docs]
def gravity_term(self, base_transform: cs.SX, joint_positions: cs.SX) -> cs.SX:
"""Returns the gravity term of the floating-base dynamics equation,
using a reduced RNEA (no acceleration and external forces)
Args:
base_transform (cs.SX): The homogenous transform from base to world frame
joint_positions (cs.SX): The joints position
Returns:
G (cs.SX): the gravity term
"""
if isinstance(base_transform, cs.MX) and isinstance(joint_positions, cs.MX):
raise ValueError(
"You are using casadi MX. Please use the function KinDynComputations.gravity_term_fun()"
)
return self.rbdalgos.rnea(
base_transform,
joint_positions,
np.zeros(6).reshape(6, 1),
np.zeros(self.NDoF),
self.g,
).array
[docs]
def CoM_position(self, base_transform: cs.SX, joint_positions: cs.SX) -> cs.SX:
"""Returns the CoM position
Args:
base_transform (cs.SX): The homogenous transform from base to world frame
joint_positions (cs.SX): The joints position
Returns:
CoM (cs.SX): The CoM position
"""
if isinstance(base_transform, cs.MX) and isinstance(joint_positions, cs.MX):
raise ValueError(
"You are using casadi MX. Please use the function KinDynComputations.CoM_position_fun()"
)
return self.rbdalgos.CoM_position(base_transform, joint_positions).array
[docs]
def CoM_jacobian(self, base_transform: cs.SX, joint_positions: cs.SX) -> cs.SX:
"""Returns the CoM Jacobian
Args:
base_transform (cs.SX): The homogenous transform from base to world frame
joint_positions (cs.SX): The joints position
Returns:
J_com (cs.SX): The CoM Jacobian
"""
if isinstance(base_transform, cs.MX) and isinstance(joint_positions, cs.MX):
raise ValueError(
"You are using casadi MX. Please use the function KinDynComputations.CoM_jacobian_fun()"
)
return self.rbdalgos.CoM_jacobian(base_transform, joint_positions).array