def jacobian_determinant(robo, n, i, j, rows, cols):
symo = Symoro(None)
J, L = _jac(robo, symo, n, i, j, trig_subs=False)
J_reduced = zeros(len(rows), len(cols))
for i, i_old in enumerate(rows):
for j, j_old in enumerate(cols):
J_reduced[i, j] = J[i_old, j_old]
symo.file_open(robo, 'det')
symo.write_params_table(robo, 'Jacobian determinant for frame %s' % n)
symo.write_line(_jac_det(robo, symo, J=J_reduced))
symo.file_close()
return symo
def accelerations(robo):
symo = Symoro(None)
symo.file_open(robo, 'acc')
symo.write_params_table(robo, 'Link accelerations')
antRj, antPj = compute_rot_trans(robo, symo)
compute_vel_acc(robo, symo, antRj, antPj, forced=True, gravity=False)
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 = Init.init_vec(robo)
# antecedent angular velocity, projected into jth frame
w = Init.init_w(robo)
jaj = Init.init_vec(robo, 6)
jTant = Init.init_mat(robo, 6) # Twist transform list of Matrices 6x6
beta_star = Init.init_vec(robo, 6)
grandJ = Init.init_mat(robo, 6)
link_acc = Init.init_vec(robo, 6)
H_inv = Init.init_scalar(robo)
juj = Init.init_vec(robo, 6) # Jj*aj / Hj
Tau = Init.init_scalar(robo)
grandVp = Init.init_vec(robo, 6)
grandVp.append(Matrix([robo.vdot0 - robo.G, robo.w0]))
symo = Symoro()
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 igm_Paul(robo, T_ref, n):
if isinstance(T_ref, list):
T_ref = Matrix(4, 4, T_ref)
symo = Symoro()
symo.file_open(robo, "igm")
symo.write_params_table(robo, "Inverse Geometrix Model for frame %s" % n)
_paul_solve(robo, symo, T_ref, 0, n)
symo.file_close()
return symo
def jacobian(robo, n, i, j):
symo = Symoro()
symo.file_open(robo, 'jac')
title = "Jacobian matrix for frame %s\n"
title += "Projection frame %s, intermediat frame %s"
symo.write_params_table(robo, title % (n, i, j))
_jac(robo, symo, n, i, j, forced=True)
symo.file_close()
return symo
def inverse_dynamic_NE(robo):
"""Computes Inverse 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
"""
symo = Symoro()
symo.file_open(robo, 'idm')
title = 'Inverse dynamic model using Newton - Euler Algorith'
symo.write_params_table(robo, title, inert=True, dynam=True)
Newton_Euler(robo, symo)
symo.file_close()
return symo
def direct_geometric_fast(robo, i, j):
"""Computes trensformation matrix iTj.
Parameters
==========
robo: Robot
Instance of robot description container
i: int
the to-frame
j: int
the from-frame
Returns
=======
symo: Symoro
Instance that contains all the relations of the computed model
"""
symo = Symoro()
symo.file_open(robo, 'fgm')
symo.write_params_table(robo, 'Direct Geometrix model')
dgm(robo, symo, i, j, fast_form=True, forced=True)
symo.file_close()
return symo
def pseudo_force_NE(robo):
"""Computes Coriolis, Centrifugal, Gravity, Friction and external
torques using Newton-Euler formulation
Parameters
==========
robo : Robot
Instance of robot description container
Returns
=======
symo.sydi : dictionary
Dictionary with the information of all the sybstitution
"""
robo_pseudo = deepcopy(robo)
robo_pseudo.qddot = sympy.zeros(robo_pseudo.NL, 1)
symo = Symoro()
symo.file_open(robo, 'ccg')
title = 'Pseudo forces using Newton - Euler Algorith'
symo.write_params_table(robo, title, inert=True, dynam=True)
Newton_Euler(robo_pseudo, symo)
symo.file_close()
return symo
def direct_geometric(robo, frames, trig_subs):
"""Computes trensformation matrix iTj.
Parameters
==========
robo: Robot
Instance of robot description container
frames: list of tuples of type (i,j)
Defines list of required transformation matrices iTj
trig_subs: bool, optional
If True, all the sin(x) and cos(x) will be replaced by symbols
SX and CX with adding them to the dictionary
Returns
=======
symo: Symoro
Instance that contains all the relations of the computed model
"""
symo = Symoro()
symo.file_open(robo, 'trm')
symo.write_params_table(robo, 'Direct Geometrix model')
for i, j in frames:
symo.write_line('Tramsformation matrix %s T %s' % (i, j))
print dgm(robo, symo, i, j, fast_form=False,
forced=True, trig_subs=trig_subs)
symo.write_line()
symo.file_close()
return symo
def dynamic_identification_NE(robo):
"""Computes Dynamic Identification 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
"""
# init forces vectors
Fjnt = Init.init_vec(robo)
Njnt = Init.init_vec(robo)
# init file output, writing the robot description
symo = Symoro()
symo.file_open(robo, 'dim')
title = "Dynamic identification model using Newton - Euler Algorith"
symo.write_params_table(robo, title, inert=True, dynam=True)
# init transformation
antRj, antPj = compute_rot_trans(robo, symo)
# init velocities and accelerations
w, wdot, vdot, U = compute_vel_acc(robo, symo, antRj, antPj)
# virtual robot with only one non-zero parameter at once
robo_tmp = deepcopy(robo)
robo_tmp.IA = sympy.zeros(robo.NL, 1)
robo_tmp.FV = sympy.zeros(robo.NL, 1)
robo_tmp.FS = sympy.zeros(robo.NL, 1)
for k in xrange(1, robo.NL):
param_vec = robo.get_inert_param(k)
F = Init.init_vec(robo)
N = Init.init_vec(robo)
for i in xrange(10):
if param_vec[i] == ZERO:
continue
# change link names according to current non-zero parameter
robo_tmp.num = [str(l) + str(param_vec[i])
for l in xrange(k + 1)]
# set the parameter to 1
mask = sympy.zeros(10, 1)
mask[i] = 1
robo_tmp.put_inert_param(mask, k)
# compute the total forcec of the link k
compute_wrench(robo_tmp, symo, k, w, wdot, U, vdot, F, N)
# init external forces
Fex = copy(robo.Fex)
Nex = copy(robo.Nex)
for j in reversed(xrange(k + 1)):
compute_joint_wrench(robo_tmp, symo, j, antRj, antPj,
vdot, Fjnt, Njnt, F, N, Fex, Nex)
for j in xrange(k + 1):
compute_torque(robo_tmp, symo, j, Fjnt, Njnt, 'DG')
# reset all the parameters to zero
robo_tmp.put_inert_param(sympy.zeros(10, 1), k)
# compute model for the joint parameters
compute_joint_torque_deriv(symo, robo.IA[k],
robo.qddot[k], k)
compute_joint_torque_deriv(symo, robo.FS[k],
sympy.sign(robo.qdot[k]), k)
compute_joint_torque_deriv(symo, robo.FV[k],
robo.qdot[k], k)
# closing the output file
symo.file_close()
return symo
def base_paremeters(robo_orig):
"""Computes grouped inertia parameters. New parametrization
contains less parameters but generates the same dynamic model
Parameters
==========
robo : Robot
Instance of robot description container
Returns
=======
symo.sydi : dictionary
Dictionary with the information of all the sybstitution
"""
robo = copy(robo_orig)
lam = [0 for i in xrange(robo.NL)]
symo = Symoro()
symo.file_open(robo, 'regp')
title = 'Base parameters computation'
symo.write_params_table(robo, title, inert=True, dynam=True)
# init transformation
antRj, antPj = compute_rot_trans(robo, symo)
for j in reversed(xrange(1, robo.NL)):
if robo.sigma[j] == 0:
# general grouping
compute_lambda(robo, symo, j, antRj, antPj, lam)
group_param_rot(robo, symo, j, lam)
# special grouping
group_param_rot_spec(robo, symo, j, lam, antRj)
pass
elif robo.sigma[j] == 1:
# general grouping
group_param_prism(robo, symo, j, antRj)
# special grouping
group_param_prism_spec(robo, symo, j, antRj, antPj)
pass
elif robo.sigma[j] == 2:
# fixed joint, group everuthing
compute_lambda(robo, symo, j, antRj, antPj)
group_param_fix(robo, symo, j, lam)
pass
symo.write_line('*=*')
symo.write_line()
title = robo.name + ' grouped inertia parameters'
symo.write_params_table(robo, title, inert=True, equations=False)
symo.file_close()
return robo, symo.sydi
def inertia_matrix(robo):
"""Computes Inertia Matrix using composed link
Parameters
==========
robo : Robot
Instance of robot description container
Returns
=======
symo.sydi : dictionary
Dictionary with the information of all the sybstitution
"""
Jplus, MSplus, Mplus = Init.init_Jplus(robo)
AJE1 = Init.init_vec(robo)
f = Init.init_vec(robo, ext=1)
n = Init.init_vec(robo, ext=1)
A = sympy.zeros(robo.NL, robo.NL)
symo = Symoro()
symo.file_open(robo, 'inm')
title = 'Inertia Matrix using composite links'
symo.write_params_table(robo, title, inert=True, dynam=True)
# init transformation
antRj, antPj = compute_rot_trans(robo, symo)
for j in reversed(xrange(-1, robo.NL)):
replace_Jplus(robo, symo, j, Jplus, MSplus, Mplus)
if j != - 1:
compute_Jplus(robo, symo, j, antRj, antPj,
Jplus, MSplus, Mplus, AJE1)
for j in xrange(1, robo.NL):
compute_A_diagonal(robo, symo, j, Jplus, MSplus, Mplus, f, n, A)
ka = j
while ka != - 1:
k = ka
ka = robo.ant[ka]
compute_A_triangle(robo, symo, j, k, ka,
antRj, antPj, f, n, A, AJE1)
symo.mat_replace(A, 'A', forced=True, symmet=True)
J_base = inertia_spatial(Jplus[-1], MSplus[-1], Mplus[-1])
symo.mat_replace(J_base, 'JP', 0, forced=True, symmet=True)
symo.file_close()
return symo
def kinematic_constraints(robo):
symo = Symoro(None)
res = _kinematic_loop_constraints(robo, symo)
if res == FAIL:
return FAIL
W_a, W_p, W_ac, W_pc, W_c = res
symo.file_open(robo, 'ckel')
symo.write_params_table(robo, 'Constraint kinematic equations of loop',
equations=False)
symo.write_line('Active joint variables')
symo.write_line([robo.get_q(i) for i in robo.indx_active])
symo.write_line()
symo.write_line('Passive joints variables')
symo.write_line([robo.get_q(i) for i in robo.indx_passive])
symo.write_line()
symo.write_line('Cut joints variables')
symo.write_line([robo.get_q(i) for i in robo.indx_cut])
symo.write_line()
symo.mat_replace(W_a, 'WA', forced=True)
symo.mat_replace(W_p, 'WP', forced=True)
symo.mat_replace(W_ac, 'WPA', forced=True)
symo.mat_replace(W_pc, 'WPC', forced=True)
symo.mat_replace(W_c, 'WC', forced=True)
symo.file_close()
return symo
def jdot_qdot(robo):
symo = Symoro(None)
symo.file_open(robo, 'jpqp')
symo.write_params_table(robo, 'JdotQdot')
antRj, antPj = compute_rot_trans(robo, symo)
w = Init.init_w(robo)
wdot, vdot = Init.init_wv_dot(robo, gravity=False)
U = Init.init_U(robo)
for j in xrange(1, robo.NL):
jRant = antRj[j].T
qdj = Z_AXIS * robo.qdot[j]
qddj = Z_AXIS * ZERO
wi = _omega_i(robo, symo, j, jRant, w)
symo.mat_replace(wi, 'WI', j)
w[j] = _omega_j(robo, j, jRant, w, wi, qdj)
symo.mat_replace(w[j], 'W', j)
_omega_dot_j(robo, j, jRant, w, wi, wdot, qdj, qddj)
symo.mat_replace(wdot[j], 'WPJ', j, forced=True)
_v_dot_j(robo, symo, j, jRant, antPj, w, wi, wdot, U, vdot, qdj, qddj)
symo.mat_replace(vdot[j], 'VPJ', j, forced=True)
symo.file_close()
return symo
def velocities(robo):
symo = Symoro(None)
symo.file_open(robo, 'vel')
symo.write_params_table(robo, 'Link velocities')
antRj, antPj = compute_rot_trans(robo, symo)
w = Init.init_w(robo)
v = Init.init_v(robo)
for j in xrange(1, robo.NL):
jRant = antRj[j].T
qdj = Z_AXIS * robo.qdot[j]
wi = _omega_i(robo, symo, j, jRant, w)
w[j] = _omega_j(robo, j, jRant, w, wi, qdj)
symo.mat_replace(w[j], 'W', j, forced=True)
_v_j(robo, j, antPj, jRant, v, w, qdj)
symo.mat_replace(v[j], 'V', j, forced=True)
symo.file_close()
return symo
