def direct_dynamic_NE(robo):
"""Computes Direct Dynamic Model using
Newton-Euler formulation
Parameters
==========
robo : Robot
Instance of robot description container
Returns
=======
symo.sydi : dictionary
Dictionary with the information of all the sybstitution
"""
wi = ParamsInit.init_vec(robo)
# antecedent angular velocity, projected into jth frame
w = ParamsInit.init_w(robo)
jaj = ParamsInit.init_vec(robo, 6)
jTant = ParamsInit.init_mat(robo,
6) # Twist transform list of Matrices 6x6
beta_star = ParamsInit.init_vec(robo, 6)
grandJ = ParamsInit.init_mat(robo, 6)
link_acc = ParamsInit.init_vec(robo, 6)
H_inv = ParamsInit.init_scalar(robo)
juj = ParamsInit.init_vec(robo, 6) # Jj*aj / Hj
Tau = ParamsInit.init_scalar(robo)
grandVp = ParamsInit.init_vec(robo, 6)
grandVp.append(Matrix([robo.vdot0 - robo.G, robo.w0]))
symo = symbolmgr.SymbolManager()
symo.file_open(robo, 'ddm')
title = 'Direct dynamic model using Newton - Euler Algorith'
symo.write_params_table(robo, title, inert=True, dynam=True)
# init transformation
antRj, antPj = compute_rot_trans(robo, symo)
for j in xrange(1, robo.NL):
compute_omega(robo, symo, j, antRj, w, wi)
compute_screw_transform(robo, symo, j, antRj, antPj, jTant)
if robo.sigma[j] == 0:
jaj[j] = Matrix([0, 0, 0, 0, 0, 1])
elif robo.sigma[j] == 1:
jaj[j] = Matrix([0, 0, 1, 0, 0, 0])
for j in xrange(1, robo.NL):
compute_beta(robo, symo, j, w, beta_star)
compute_link_acc(robo, symo, j, antRj, antPj, link_acc, w, wi)
grandJ[j] = inertia_spatial(robo.J[j], robo.MS[j], robo.M[j])
for j in reversed(xrange(1, robo.NL)):
replace_beta_J_star(robo, symo, j, grandJ, beta_star)
compute_Tau(robo, symo, j, grandJ, beta_star, jaj, juj, H_inv, Tau)
if robo.ant[j] != -1:
compute_beta_J_star(robo, symo, j, grandJ, jaj, juj, Tau,
beta_star, jTant, link_acc)
for j in xrange(1, robo.NL):
compute_acceleration(robo, symo, j, jTant, grandVp, juj, H_inv, jaj,
Tau, link_acc)
for j in xrange(1, robo.NL):
compute_coupled_forces(robo, symo, j, grandVp, grandJ, beta_star)
symo.file_close()
return symo
def direct_dynamic_NE(robo):
"""Computes Direct Dynamic Model using
Newton-Euler formulation
Parameters
==========
robo : Robot
Instance of robot description container
Returns
=======
symo.sydi : dictionary
Dictionary with the information of all the sybstitution
"""
wi = ParamsInit.init_vec(robo)
# antecedent angular velocity, projected into jth frame
w = ParamsInit.init_w(robo)
jaj = ParamsInit.init_vec(robo, 6)
jTant = ParamsInit.init_mat(robo, 6) # Twist transform list of Matrices 6x6
beta_star = ParamsInit.init_vec(robo, 6)
grandJ = ParamsInit.init_mat(robo, 6)
link_acc = ParamsInit.init_vec(robo, 6)
H_inv = ParamsInit.init_scalar(robo)
juj = ParamsInit.init_vec(robo, 6) # Jj*aj / Hj
Tau = ParamsInit.init_scalar(robo)
grandVp = ParamsInit.init_vec(robo, 6)
grandVp.append(Matrix([robo.vdot0 - robo.G, robo.w0]))
symo = symbolmgr.SymbolManager()
symo.file_open(robo, 'ddm')
title = 'Direct dynamic model using Newton - Euler Algorith'
symo.write_params_table(robo, title, inert=True, dynam=True)
# init transformation
antRj, antPj = compute_rot_trans(robo, symo)
for j in xrange(1, robo.NL):
compute_omega(robo, symo, j, antRj, w, wi)
compute_screw_transform(robo, symo, j, antRj, antPj, jTant)
if robo.sigma[j] == 0:
jaj[j] = Matrix([0, 0, 0, 0, 0, 1])
elif robo.sigma[j] == 1:
jaj[j] = Matrix([0, 0, 1, 0, 0, 0])
for j in xrange(1, robo.NL):
compute_beta(robo, symo, j, w, beta_star)
compute_link_acc(robo, symo, j, antRj, antPj, link_acc, w, wi)
grandJ[j] = inertia_spatial(robo.J[j], robo.MS[j], robo.M[j])
for j in reversed(xrange(1, robo.NL)):
replace_beta_J_star(robo, symo, j, grandJ, beta_star)
compute_Tau(robo, symo, j, grandJ, beta_star, jaj, juj, H_inv, Tau)
if robo.ant[j] != - 1:
compute_beta_J_star(robo, symo, j, grandJ, jaj, juj, Tau,
beta_star, jTant, link_acc)
for j in xrange(1, robo.NL):
compute_acceleration(robo, symo, j, jTant, grandVp,
juj, H_inv, jaj, Tau, link_acc)
for j in xrange(1, robo.NL):
compute_coupled_forces(robo, symo, j, grandVp, grandJ, beta_star)
symo.file_close()
return symo
def direct_dynmodel(robo, symo):
"""
Compute the Direct Dynamic Model using Newton-Euler algorithm for
robots with floating and fixed base.
Parameters:
robo: Robot - instance of robot description container
symo: symbolmgr.SymbolManager - instance of symbol manager
"""
# antecedent angular velocity, projected into jth frame
# j^omega_i
wi = ParamsInit.init_vec(robo)
# j^omega_j
w = ParamsInit.init_w(robo)
# j^a_j -- joint axis in screw form
jaj = ParamsInit.init_vec(robo, 6)
# Twist transform list of Matrices 6x6
grandJ = ParamsInit.init_mat(robo, 6)
jTant = ParamsInit.init_mat(robo, 6)
gamma = ParamsInit.init_vec(robo, 6)
beta = ParamsInit.init_vec(robo, 6)
zeta = ParamsInit.init_vec(robo, 6)
h_inv = ParamsInit.init_scalar(robo)
jah = ParamsInit.init_vec(robo, 6) # Jj*aj*Hinv_j
tau = ParamsInit.init_scalar(robo)
star_inertia = ParamsInit.init_mat(robo, 6)
star_beta = ParamsInit.init_vec(robo, 6)
qddot = ParamsInit.init_scalar(robo)
grandVp = ParamsInit.init_vec(robo, 6)
react_wrench = ParamsInit.init_vec(robo, 6)
torque = ParamsInit.init_scalar(robo)
# init transformation
antRj, antPj = compute_rot_trans(robo, symo)
# first forward recursion
for j in xrange(1, robo.NL):
# compute spatial inertia matrix for use in backward recursion
grandJ[j] = inertia_spatial(robo.J[j], robo.MS[j], robo.M[j])
# set jaj vector
if robo.sigma[j] == 0:
jaj[j] = Matrix([0, 0, 0, 0, 0, 1])
elif robo.sigma[j] == 1:
jaj[j] = Matrix([0, 0, 1, 0, 0, 0])
# compute j^omega_j and j^omega_i
compute_omega(robo, symo, j, antRj, w, wi)
# compute j^S_i : screw transformation matrix
compute_screw_transform(robo, symo, j, antRj, antPj, jTant)
# compute j^gamma_j : gyroscopic acceleration (6x1)
compute_gamma(robo, symo, j, antRj, antPj, w, wi, gamma)
# compute j^beta_j : external+coriolis+centrifugal wrench (6x1)
compute_beta(robo, symo, j, w, beta)
# decide first link
first_link = 0 if robo.is_floating else 1
# first backward recursion - initialisation step
for j in reversed(xrange(first_link, robo.NL)):
if j == first_link and robo.is_floating:
# compute spatial inertia matrix for base
grandJ[j] = inertia_spatial(robo.J[j], robo.MS[j], robo.M[j])
# compute 0^beta_0
compute_beta(robo, symo, j, w, beta)
replace_star_terms(
symo, grandJ, beta, j, star_inertia, star_beta
)
# second backward recursion - compute star terms
for j in reversed(xrange(first_link, robo.NL)):
replace_star_terms(
symo, star_inertia, star_beta, j,
star_inertia, star_beta, replace=True
)
if j == 0:
continue
compute_tau(robo, symo, j, jaj, star_beta, tau)
compute_star_terms(
robo, symo, j, jaj, jTant, gamma, tau,
h_inv, jah, star_inertia, star_beta
)
if j == first_link:
continue
# compute base acceleration : this returns the correct value for
# fixed base and floating base robots
compute_base_accel(
robo, symo, star_inertia, star_beta, grandVp
)
# second forward recursion
for j in xrange(1, robo.NL):
# compute qddot_j : joint acceleration
compute_joint_accel(
robo, symo, j, jaj, jTant, h_inv, jah, gamma,
tau, grandVp, star_beta, star_inertia, qddot
)
# compute j^zeta_j : relative acceleration (6x1)
compute_zeta(robo, symo, j, gamma, jaj, zeta, qddot)
# compute j^Vdot_j : link acceleration
compute_link_accel(robo, symo, j, jTant, zeta, grandVp)
# compute j^F_j : reaction wrench
compute_reaction_wrench(
robo, symo, j, grandVp,
star_inertia, star_beta, react_wrench
)
def composite_inverse_dynmodel(robo, symo):
"""
Compute the Inverse Dynamic Model using Composite link Newton-Euler
algorithm for tree structure robots with fixed and floating base.
Parameters:
robo: Robot - instance of robot description container
symo: symbolmgr.SymbolManager - instance of symbol manager
"""
# antecedent angular velocity, projected into jth frame
# j^omega_i
wi = ParamsInit.init_vec(robo)
# j^omega_j
w = ParamsInit.init_w(robo)
# j^a_j -- joint axis in screw form
jaj = ParamsInit.init_vec(robo, 6)
# Twist transform list of Matrices 6x6
grandJ = ParamsInit.init_mat(robo, 6)
jTant = ParamsInit.init_mat(robo, 6)
gamma = ParamsInit.init_vec(robo, 6)
beta = ParamsInit.init_vec(robo, 6)
zeta = ParamsInit.init_vec(robo, 6)
composite_inertia = ParamsInit.init_mat(robo, 6)
composite_beta = ParamsInit.init_vec(robo, 6)
comp_inertia3, comp_ms, comp_mass = ParamsInit.init_jplus(robo)
grandVp = ParamsInit.init_vec(robo, 6)
react_wrench = ParamsInit.init_vec(robo, 6)
torque = ParamsInit.init_scalar(robo)
# init transformation
antRj, antPj = compute_rot_trans(robo, symo)
# first forward recursion
for j in xrange(1, robo.NL):
# compute spatial inertia matrix for use in backward recursion
grandJ[j] = inertia_spatial(robo.J[j], robo.MS[j], robo.M[j])
# set jaj vector
if robo.sigma[j] == 0:
jaj[j] = Matrix([0, 0, 0, 0, 0, 1])
elif robo.sigma[j] == 1:
jaj[j] = Matrix([0, 0, 1, 0, 0, 0])
# compute j^omega_j and j^omega_i
compute_omega(robo, symo, j, antRj, w, wi)
# compute j^S_i : screw transformation matrix
compute_screw_transform(robo, symo, j, antRj, antPj, jTant)
# first forward recursion (still)
for j in xrange(1, robo.NL):
# compute j^gamma_j : gyroscopic acceleration (6x1)
compute_gamma(robo, symo, j, antRj, antPj, w, wi, gamma)
# compute j^beta_j : external+coriolis+centrifugal wrench (6x1)
compute_beta(robo, symo, j, w, beta)
# compute j^zeta_j : relative acceleration (6x1)
compute_zeta(robo, symo, j, gamma, jaj, zeta)
# first backward recursion - initialisation step
for j in reversed(xrange(0, robo.NL)):
if j == 0:
# compute spatial inertia matrix for base
grandJ[j] = inertia_spatial(robo.J[j], robo.MS[j], robo.M[j])
# compute 0^beta_0
compute_beta(robo, symo, j, w, beta)
replace_composite_terms(
symo, grandJ, beta, j, composite_inertia, composite_beta
)
# second backward recursion - compute composite term
for j in reversed(xrange(0, robo.NL)):
replace_composite_terms(
symo, composite_inertia, composite_beta, j,
composite_inertia, composite_beta, replace=True
)
if j == 0:
continue
compute_composite_inertia(
robo, symo, j, antRj, antPj,
comp_inertia3, comp_ms, comp_mass, composite_inertia
)
compute_composite_beta(
robo, symo, j, jTant, zeta, composite_inertia, composite_beta
)
# compute base acceleration : this returns the correct value for
# fixed base and floating base robots
compute_base_accel_composite(
robo, symo, composite_inertia, composite_beta, grandVp
)
# second forward recursion
for j in xrange(1, robo.NL):
# compute j^Vdot_j : link acceleration
compute_link_accel(robo, symo, j, jTant, zeta, grandVp)
# compute j^F_j : reaction wrench
compute_reaction_wrench(
robo, symo, j, grandVp,
composite_inertia, composite_beta, react_wrench
)
# second forward recursion still - to make the output pretty
for j in xrange(1, robo.NL):
# compute torque
compute_torque(robo, symo, j, jaj, react_wrench, torque)
def direct_dynmodel(robo, symo):
"""
Compute the Direct Dynamic Model using Newton-Euler algorithm for
robots with floating and fixed base.
Parameters:
robo: Robot - instance of robot description container
symo: symbolmgr.SymbolManager - instance of symbol manager
"""
# antecedent angular velocity, projected into jth frame
# j^omega_i
wi = ParamsInit.init_vec(robo)
# j^omega_j
w = ParamsInit.init_w(robo)
# j^a_j -- joint axis in screw form
jaj = ParamsInit.init_vec(robo, 6)
# Twist transform list of Matrices 6x6
grandJ = ParamsInit.init_mat(robo, 6)
jTant = ParamsInit.init_mat(robo, 6)
gamma = ParamsInit.init_vec(robo, 6)
beta = ParamsInit.init_vec(robo, 6)
zeta = ParamsInit.init_vec(robo, 6)
h_inv = ParamsInit.init_scalar(robo)
jah = ParamsInit.init_vec(robo, 6) # Jj*aj*Hinv_j
tau = ParamsInit.init_scalar(robo)
star_inertia = ParamsInit.init_mat(robo, 6)
star_beta = ParamsInit.init_vec(robo, 6)
qddot = ParamsInit.init_scalar(robo)
grandVp = ParamsInit.init_vec(robo, 6)
react_wrench = ParamsInit.init_vec(robo, 6)
torque = ParamsInit.init_scalar(robo)
# init transformation
antRj, antPj = compute_rot_trans(robo, symo)
# first forward recursion
for j in xrange(1, robo.NL):
# compute spatial inertia matrix for use in backward recursion
grandJ[j] = inertia_spatial(robo.J[j], robo.MS[j], robo.M[j])
# set jaj vector
if robo.sigma[j] == 0:
jaj[j] = Matrix([0, 0, 0, 0, 0, 1])
elif robo.sigma[j] == 1:
jaj[j] = Matrix([0, 0, 1, 0, 0, 0])
# compute j^omega_j and j^omega_i
compute_omega(robo, symo, j, antRj, w, wi)
# compute j^S_i : screw transformation matrix
compute_screw_transform(robo, symo, j, antRj, antPj, jTant)
# compute j^gamma_j : gyroscopic acceleration (6x1)
compute_gamma(robo, symo, j, antRj, antPj, w, wi, gamma)
# compute j^beta_j : external+coriolis+centrifugal wrench (6x1)
compute_beta(robo, symo, j, w, beta)
# decide first link
first_link = 0 if robo.is_floating else 1
# first backward recursion - initialisation step
for j in reversed(xrange(first_link, robo.NL)):
if j == first_link and robo.is_floating:
# compute spatial inertia matrix for base
grandJ[j] = inertia_spatial(robo.J[j], robo.MS[j], robo.M[j])
# compute 0^beta_0
compute_beta(robo, symo, j, w, beta)
replace_star_terms(symo, grandJ, beta, j, star_inertia, star_beta)
# second backward recursion - compute star terms
for j in reversed(xrange(first_link, robo.NL)):
replace_star_terms(symo,
star_inertia,
star_beta,
j,
star_inertia,
star_beta,
replace=True)
if j == 0:
continue
compute_tau(robo, symo, j, jaj, star_beta, tau)
compute_star_terms(robo, symo, j, jaj, jTant, gamma, tau, h_inv, jah,
star_inertia, star_beta)
if j == first_link:
continue
# compute base acceleration : this returns the correct value for
# fixed base and floating base robots
compute_base_accel(robo, symo, star_inertia, star_beta, grandVp)
# second forward recursion
for j in xrange(1, robo.NL):
# compute qddot_j : joint acceleration
compute_joint_accel(robo, symo, j, jaj, jTant, h_inv, jah, gamma, tau,
grandVp, star_beta, star_inertia, qddot)
# compute j^zeta_j : relative acceleration (6x1)
compute_zeta(robo, symo, j, gamma, jaj, zeta, qddot)
# compute j^Vdot_j : link acceleration
compute_link_accel(robo, symo, j, jTant, zeta, grandVp)
# compute j^F_j : reaction wrench
compute_reaction_wrench(robo, symo, j, grandVp, star_inertia,
star_beta, react_wrench)
def composite_inverse_dynmodel(robo, symo):
"""
Compute the Inverse Dynamic Model using Composite link Newton-Euler
algorithm for tree structure robots with fixed and floating base.
Parameters:
robo: Robot - instance of robot description container
symo: symbolmgr.SymbolManager - instance of symbol manager
"""
# antecedent angular velocity, projected into jth frame
# j^omega_i
wi = ParamsInit.init_vec(robo)
# j^omega_j
w = ParamsInit.init_w(robo)
# j^a_j -- joint axis in screw form
jaj = ParamsInit.init_vec(robo, 6)
# Twist transform list of Matrices 6x6
grandJ = ParamsInit.init_mat(robo, 6)
jTant = ParamsInit.init_mat(robo, 6)
gamma = ParamsInit.init_vec(robo, 6)
beta = ParamsInit.init_vec(robo, 6)
zeta = ParamsInit.init_vec(robo, 6)
composite_inertia = ParamsInit.init_mat(robo, 6)
composite_beta = ParamsInit.init_vec(robo, 6)
comp_inertia3, comp_ms, comp_mass = ParamsInit.init_jplus(robo)
grandVp = ParamsInit.init_vec(robo, 6)
react_wrench = ParamsInit.init_vec(robo, 6)
torque = ParamsInit.init_scalar(robo)
# init transformation
antRj, antPj = compute_rot_trans(robo, symo)
# first forward recursion
for j in xrange(1, robo.NL):
# compute spatial inertia matrix for use in backward recursion
grandJ[j] = inertia_spatial(robo.J[j], robo.MS[j], robo.M[j])
# set jaj vector
if robo.sigma[j] == 0:
jaj[j] = Matrix([0, 0, 0, 0, 0, 1])
elif robo.sigma[j] == 1:
jaj[j] = Matrix([0, 0, 1, 0, 0, 0])
# compute j^omega_j and j^omega_i
compute_omega(robo, symo, j, antRj, w, wi)
# compute j^S_i : screw transformation matrix
compute_screw_transform(robo, symo, j, antRj, antPj, jTant)
# first forward recursion (still)
for j in xrange(1, robo.NL):
# compute j^gamma_j : gyroscopic acceleration (6x1)
compute_gamma(robo, symo, j, antRj, antPj, w, wi, gamma)
# compute j^beta_j : external+coriolis+centrifugal wrench (6x1)
compute_beta(robo, symo, j, w, beta)
# compute j^zeta_j : relative acceleration (6x1)
compute_zeta(robo, symo, j, gamma, jaj, zeta)
# first backward recursion - initialisation step
for j in reversed(xrange(0, robo.NL)):
if j == 0:
# compute spatial inertia matrix for base
grandJ[j] = inertia_spatial(robo.J[j], robo.MS[j], robo.M[j])
# compute 0^beta_0
compute_beta(robo, symo, j, w, beta)
replace_composite_terms(symo, grandJ, beta, j, composite_inertia,
composite_beta)
# second backward recursion - compute composite term
for j in reversed(xrange(0, robo.NL)):
replace_composite_terms(symo,
composite_inertia,
composite_beta,
j,
composite_inertia,
composite_beta,
replace=True)
if j == 0:
continue
compute_composite_inertia(robo, symo, j, antRj, antPj, comp_inertia3,
comp_ms, comp_mass, composite_inertia)
compute_composite_beta(robo, symo, j, jTant, zeta, composite_inertia,
composite_beta)
# compute base acceleration : this returns the correct value for
# fixed base and floating base robots
compute_base_accel_composite(robo, symo, composite_inertia, composite_beta,
grandVp)
# second forward recursion
for j in xrange(1, robo.NL):
# compute j^Vdot_j : link acceleration
compute_link_accel(robo, symo, j, jTant, zeta, grandVp)
# compute j^F_j : reaction wrench
compute_reaction_wrench(robo, symo, j, grandVp, composite_inertia,
composite_beta, react_wrench)
# second forward recursion still - to make the output pretty
for j in xrange(1, robo.NL):
# compute torque
compute_torque(robo, symo, j, jaj, react_wrench, torque)