N = Frame('N')
A = Frame('A')
B = Frame('B')
C = Frame('C')
system.set_newtonian(N)
A.rotate_fixed_axis_directed(N, [1, 0, 0], qA, system)
B.rotate_fixed_axis_directed(A, [0, 1, 0], qB, system)
C.rotate_fixed_axis_directed(B, [0, 0, 1], qC, system)
pCcm = 0 * N.x
IC = Dyadic.build(C, Ixx, Iyy, Izz)
w1 = N.getw_(C)
w2 = wx * C.x + wy * C.y + wz * C.z
N.set_w(C, w2)
from pynamics.constraint import Constraint
eq0 = w1 - w2
eq = []
eq.append(eq0.dot(B.x))
eq.append(eq0.dot(B.y))
eq.append(eq0.dot(B.z))
c = Constraint(eq)
c.linearize(0)
system.add_constraint(c)
# for item,value in zip(system.get_state_variables(),result.x):
# initialvalues[item]=value
pAcm = pOA + lA / 2 * A.x
pBcm = pAB + lB / 2 * B.x
pCcm = pOC + lC / 2 * C.x
pDcm = pCD + lD / 2 * D.x
pEcm = pBtip - .1 * E.y
pE1 = pEcm + lE / 2 * E.x
vE1 = pE1.time_derivative(N, system)
pE2 = pEcm - lE / 2 * E.x
vE2 = pE2.time_derivative(N, system)
wOA = O.getw_(A)
wAB = A.getw_(B)
wOC = O.getw_(C)
wCD = C.getw_(D)
wBD = B.getw_(D)
wOE = O.getw_(E)
BodyO = Body('BodyO', O, pOcm, mO, Dyadic.build(O, I_main, I_main, I_main),
system)
#BodyA = Body('BodyA',A,pAcm,mA,Dyadic.build(A,I_leg,I_leg,I_leg),system)
#BodyB = Body('BodyB',B,pBcm,mB,Dyadic.build(B,I_leg,I_leg,I_leg),system)
#BodyC = Body('BodyC',C,pCcm,mC,Dyadic.build(C,I_leg,I_leg,I_leg),system)
#BodyD = Body('BodyD',D,pDcm,mD,Dyadic.build(D,I_leg,I_leg,I_leg),system)
BodyE = Body('BodyE', E, pEcm, mE, Dyadic.build(D, I_leg, I_leg, I_leg),
system)
def init_system(v, drag_direction, time_step):
import pynamics
from pynamics.frame import Frame
from pynamics.variable_types import Differentiable, Constant
from pynamics.system import System
from pynamics.body import Body
from pynamics.dyadic import Dyadic
from pynamics.output import Output, PointsOutput
from pynamics.particle import Particle
import pynamics.integration
import logging
import sympy
import numpy
import matplotlib.pyplot as plt
from math import pi
from scipy import optimize
from sympy import sin
import pynamics.tanh as tanh
from fit_qs import exp_fit
import fit_qs
# time_step = tstep
x = numpy.zeros((7, 1))
friction_perp = x[0]
friction_par = x[1]
given_b = x[2]
given_k = x[3]
given_k1 = x[4]
given_b1 = x[4]
system = System()
pynamics.set_system(__name__, system)
global_q = True
lO = Constant(7 / 1000, 'lO', system)
lA = Constant(33 / 1000, 'lA', system)
lB = Constant(33 / 1000, 'lB', system)
lC = Constant(33 / 1000, 'lC', system)
mO = Constant(10 / 1000, 'mA', system)
mA = Constant(2.89 / 1000, 'mA', system)
mB = Constant(2.89 / 1000, 'mB', system)
mC = Constant(2.89 / 1000, 'mC', system)
k = Constant(0.209, 'k', system)
k1 = Constant(0.209, 'k1', system)
friction_perp = Constant(1.2, 'f_perp', system)
friction_par = Constant(-0.2, 'f_par', system)
b_damping = Constant(given_b, 'b_damping', system)
# time_step = 1/00
if v == 0:
[
t, tinitial, tfinal, tstep, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2,
qAa3, qAb3, qAc3, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3,
qBc3, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3
] = fit_qs.fit_0_amount(time_step)
elif v == 10:
[
t, tinitial, tfinal, tstep, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2,
qAa3, qAb3, qAc3, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3,
qBc3, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3
] = fit_qs.fit_10_amount(time_step)
elif v == 20:
[
t, tinitial, tfinal, tstep, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2,
qAa3, qAb3, qAc3, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3,
qBc3, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3
] = fit_qs.fit_20_amount(time_step)
elif v == 30:
[
t, tinitial, tfinal, tstep, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2,
qAa3, qAb3, qAc3, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3,
qBc3, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3
] = fit_qs.fit_30_amount(time_step)
elif v == 40:
[
t, tinitial, tfinal, tstep, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2,
qAa3, qAb3, qAc3, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3,
qBc3, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3
] = fit_qs.fit_40_amount(time_step)
elif v == 50:
[
t, tinitial, tfinal, tstep, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2,
qAa3, qAb3, qAc3, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3,
qBc3, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3
] = fit_qs.fit_50_amount(time_step)
distance = 200 / 1000
nums = int(tfinal / tstep)
array_num = numpy.arange(0, nums)
array_num1 = numpy.repeat(array_num, nums, axis=0)
array_num1.shape = (nums, nums)
error_k = array_num1 / 8000 + numpy.ones((nums, nums))
fit_t = t
fit_qA = exp_fit(fit_t, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2, qAa3, qAb3,
qAc3)
fit_qB = exp_fit(fit_t, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3,
qBc3)
fit_qC = exp_fit(fit_t, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3,
qCc3)
fit_qAd1 = numpy.diff(fit_qA) / numpy.diff(fit_t)
fit_qAd = numpy.append(fit_qAd1[0], fit_qAd1)
fit_qBd1 = numpy.diff(fit_qB) / numpy.diff(fit_t)
fit_qBd = numpy.append(fit_qBd1[0], fit_qBd1)
fit_qCd1 = numpy.diff(fit_qC) / numpy.diff(fit_t)
fit_qCd = numpy.append(fit_qCd1[0], fit_qCd1)
fit_states1 = numpy.stack(
(fit_qA, fit_qB, fit_qC, fit_qAd, fit_qBd, fit_qCd), axis=1)
fit_states1[:, 0:3] = fit_states1[:, 0:3] - fit_states1[0, 0:3]
fit_states = -drag_direction * numpy.deg2rad(fit_states1)
# plt.plot(t,fit_states)
if drag_direction == -1:
zero_shape = fit_states.shape
fit_states = numpy.zeros(zero_shape)
fit_vel = drag_direction * distance / (tfinal)
if qAa1 == 0:
fit_vel = 0
fit_v = numpy.ones(t.shape) * fit_vel
if qAa1 == 0:
fit_d = numpy.ones(t.shape) * fit_vel
else:
fit_d = drag_direction * numpy.r_[tinitial:distance:tstep *
abs(fit_vel)]
preload0 = Constant(0 * pi / 180, 'preload0', system)
preload1 = Constant(0 * pi / 180, 'preload1', system)
preload2 = Constant(0 * pi / 180, 'preload2', system)
preload3 = Constant(0 * pi / 180, 'preload3', system)
Ixx_O = Constant(1, 'Ixx_O', system)
Iyy_O = Constant(1, 'Iyy_O', system)
Izz_O = Constant(1, 'Izz_O', system)
Ixx_A = Constant(1, 'Ixx_A', system)
Iyy_A = Constant(1, 'Iyy_A', system)
Izz_A = Constant(1, 'Izz_A', system)
Ixx_B = Constant(1, 'Ixx_B', system)
Iyy_B = Constant(1, 'Iyy_B', system)
Izz_B = Constant(1, 'Izz_B', system)
Ixx_C = Constant(1, 'Ixx_C', system)
Iyy_C = Constant(1, 'Iyy_C', system)
Izz_C = Constant(1, 'Izz_C', system)
y, y_d, y_dd = Differentiable('y', system)
qO, qO_d, qO_dd = Differentiable('qO', system)
qA, qA_d, qA_dd = Differentiable('qA', system)
qB, qB_d, qB_dd = Differentiable('qB', system)
qC, qC_d, qC_dd = Differentiable('qC', system)
initialvalues = {}
initialvalues[y] = 0 + 1e-14
initialvalues[y_d] = fit_vel + 1e-14
initialvalues[qO] = 0 + 1e-14
initialvalues[qO_d] = 0 + 1e-14
initialvalues[qA] = fit_states[0, 0] + 1e-14
initialvalues[qA_d] = fit_states[0, 3] + 1e-14
initialvalues[qB] = fit_states[0, 1] + 1e-14
initialvalues[qB_d] = fit_states[0, 4] + 1e-14
initialvalues[qC] = fit_states[0, 2] + 1e-14
initialvalues[qC_d] = fit_states[0, 5] + 1e-14
statevariables = system.get_state_variables()
ini = [initialvalues[item] for item in statevariables]
N = Frame('N')
O = Frame('O')
A = Frame('A')
B = Frame('B')
C = Frame('C')
drag_direction = drag_direction
velocity = 200 / tfinal / 1000
vSoil = drag_direction * velocity * N.y
nSoil = 1 / vSoil.length() * vSoil
system.set_newtonian(N)
if not global_q:
O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system)
A.rotate_fixed_axis_directed(O, [0, 0, 1], qA, system)
B.rotate_fixed_axis_directed(A, [0, 0, 1], qB, system)
C.rotate_fixed_axis_directed(B, [0, 0, 1], qC, system)
else:
O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system)
A.rotate_fixed_axis_directed(N, [0, 0, 1], qA, system)
B.rotate_fixed_axis_directed(N, [0, 0, 1], qB, system)
C.rotate_fixed_axis_directed(N, [0, 0, 1], qC, system)
pNO = 0 * N.x + y * N.y
pOA = lO * N.x + y * N.y
pAB = pOA + lA * A.x
pBC = pAB + lB * B.x
pCtip = pBC + lC * C.x
pOcm = pNO + lO / 2 * N.x
pAcm = pOA + lA / 2 * A.x
pBcm = pAB + lB / 2 * B.x
pCcm = pBC + lC / 2 * C.x
wNO = N.getw_(O)
wOA = N.getw_(A)
wAB = A.getw_(B)
wBC = B.getw_(C)
IO = Dyadic.build(O, Ixx_O, Iyy_O, Izz_O)
IA = Dyadic.build(A, Ixx_A, Iyy_A, Izz_A)
IB = Dyadic.build(B, Ixx_B, Iyy_B, Izz_B)
IC = Dyadic.build(C, Ixx_C, Iyy_C, Izz_C)
BodyO = Body('BodyO', O, pOcm, mO, IO, system)
BodyA = Body('BodyA', A, pAcm, mA, IA, system)
BodyB = Body('BodyB', B, pBcm, mB, IB, system)
BodyC = Body('BodyC', C, pCcm, mC, IC, system)
# BodyC = Particle(pCcm,mC,'ParticleC',system)
vOcm = pOcm.time_derivative()
vAcm = pAcm.time_derivative()
vBcm = pBcm.time_derivative()
vCcm = pCcm.time_derivative()
system.add_spring_force1(k1 + 10000 * (qA + abs(qA)),
(qA - qO - preload1) * N.z, wOA)
system.add_spring_force1(k + 10000 * (qB + abs(qB)),
(qB - qA - preload2) * N.z, wAB)
system.add_spring_force1(k + 10000 * (qC + abs(qC)),
(qC - qB - preload3) * N.z, wBC)
#new Method use nJoint
nvAcm = 1 / vAcm.length() * vAcm
nvBcm = 1 / vBcm.length() * vBcm
nvCcm = 1 / vCcm.length() * vCcm
faperp = friction_perp * nvAcm.dot(A.y) * A.y
fapar = friction_par * nvAcm.dot(A.x) * A.x
system.addforce(-(faperp + fapar), vAcm)
fbperp = friction_perp * nvBcm.dot(B.y) * B.y
fbpar = friction_par * nvBcm.dot(B.x) * B.x
system.addforce(-(fbperp + fbpar), vBcm)
fcperp = friction_perp * nvCcm.dot(C.y) * C.y
fcpar = friction_par * nvCcm.dot(C.x) * C.x
system.addforce(-(fcperp + fcpar), vCcm)
system.addforce(-b_damping * wOA, wOA)
system.addforce(-b_damping * wAB, wAB)
system.addforce(-b_damping * wBC, wBC)
eq = []
eq_d = [(system.derivative(item)) for item in eq]
eq_d.append(y_d - fit_vel)
eq_dd = [(system.derivative(item)) for item in eq_d]
f, ma = system.getdynamics()
func1 = system.state_space_post_invert(f, ma, eq_dd)
points = [pNO, pOA, pAB, pBC, pCtip]
constants = system.constant_values
return system, f, ma, func1, points, t, ini, constants, b_damping, k, k1, tstep, fit_states
statevariables = system.get_q(0) + system.get_q(1)
ini = [initialvalues[item] for item in statevariables]
N = Frame('N')
A = Frame('A')
system.set_newtonian(N)
A.rotate_fixed_axis_directed(N, [0, 0, 1], qA, system)
pNA = 0 * N.x
#pAB=pNA+lA*A.x
pAcm = pNA - lA * A.y
wNA = N.getw_(A)
IA = Dyadic.build(A, Ixx_A, Iyy_A, Izz_A)
BodyA = Body('BodyA', A, pAcm, mA, IA, system)
#BodyA = Particle(system,pAcm,mA,'ParticleA')
#ParticleB = Particle(system,pBcm,mB,'ParticleB')
#ParticleC = Particle(system,pCcm,mC,'ParticleC')
#system.addforce(-k*(qA-preload1)*N.z,wNA)
#system.addforce(-k*(qB-preload2)*A.z,wAB)
#system.addforce(-k*(qC-preload3)*B.z,wBC)
system.addforcegravity(-g * N.y)
for item in y:
plt.plot(*(item.T))
# for item,value in zip(system.get_state_variables(),result.x):
# initialvalues[item]=value
pA1cm = pOA + lA / 4 * A1.x
pB1cm = pAB + lB / 4 * B1.x
pC1cm = pOC + lC / 4 * C1.x
pD1cm = pCD + lD / 4 * D1.x
pA2cm = pA1A2 + lA / 4 * A2.x
pB2cm = pB1B2 + lB / 4 * B2.x
pC2cm = pC1C2 + lC / 4 * C2.x
pD2cm = pD1D2 + lD / 4 * D2.x
wOA1 = O.getw_(A1)
wA1A2 = A1.getw_(A2)
wA2B1 = A2.getw_(B1)
wB1B2 = B1.getw_(B2)
wOC1 = O.getw_(C1)
wC1C2 = C1.getw_(C2)
wC2D1 = C2.getw_(D1)
wD1D2 = D1.getw_(D2)
wB2D2 = B2.getw_(D2)
#BodyO = Body('BodyO',O,pOcm,mO,Dyadic.build(O,I_main,I_main,I_main),system)
#BodyA = Body('BodyA',A,pAcm,mA,Dyadic.build(A,I_leg,I_leg,I_leg),system)
#BodyB = Body('BodyB',B,pBcm,mB,Dyadic.build(B,I_leg,I_leg,I_leg),system)
#BodyC = Body('BodyC',C,pCcm,mC,Dyadic.build(C,I_leg,I_leg,I_leg),system)
#BodyD = Body('BodyD',D,pDcm,mD,Dyadic.build(D,I_leg,I_leg,I_leg),system)
#Izz_B = Constant('Izz_B',1.98358014762822e-06,system)
#Ixx_C = Constant('Ixx_C',4.39320316677997e-07,system)
#Iyy_C = Constant('Iyy_C',7.9239401855911e-07,system)
#Izz_C = Constant('Izz_C',7.9239401855911e-07,system)
IA = Dyadic.build(A,Ixx_A,Iyy_A,Izz_A)
#IB = Dyadic.build(B,Ixx_B,Iyy_B,Izz_B)
#IC = Dyadic.build(C,Ixx_C,Iyy_C,Izz_C)
BodyA = Body('BodyA',A,pm1,m1,IA,system)
#Particle1 = Particle(system,pm1,m1,'Particle1')
Particle2 = Particle(system,pm2,m2,'Particle2')
s1 = pk1.dot(N.y)*N.y
s2 = pk2.dot(N.y)*N.y
s3 = (q2-q2_command)*A.z
wNA = A.getw_(N)
wNB = B.getw_(N)
#switch1 =
system.add_spring_force(k,s1,vk1)
system.add_spring_force(k,s2,vk2)
system.add_spring_force(k_controller,s3,wNA)
system.add_spring_force(k_controller,-s3,wNB)
system.addforce(-b*vm1,vm1)
system.addforcegravity(-g*N.y)
#system.addforcegravity(-g*N.y)
#system.addforcegravity(-g*N.y)
def Cal_system(initial_states, drag_direction, tinitial, tstep, tfinal,
fit_vel, f1, f2):
g_k, g_b_damping, g_b_damping1 = [0.30867935, 1.42946955, 1.08464536]
system = System()
pynamics.set_system(__name__, system)
global_q = True
lO = Constant(7 / 1000, 'lO', system)
lA = Constant(33 / 1000, 'lA', system)
lB = Constant(33 / 1000, 'lB', system)
lC = Constant(33 / 1000, 'lC', system)
mO = Constant(10 / 1000, 'mA', system)
mA = Constant(2.89 / 1000, 'mA', system)
mB = Constant(2.89 / 1000, 'mB', system)
mC = Constant(2.89 / 1000, 'mC', system)
k = Constant(g_k, 'k', system)
k1 = Constant(0.4, 'k1', system)
friction_perp = Constant(f1, 'f_perp', system)
friction_par = Constant(f2, 'f_par', system)
b_damping = Constant(g_b_damping, 'b_damping', system)
b_damping1 = Constant(g_b_damping1, 'b_damping1', system)
preload0 = Constant(0 * pi / 180, 'preload0', system)
preload1 = Constant(0 * pi / 180, 'preload1', system)
preload2 = Constant(0 * pi / 180, 'preload2', system)
preload3 = Constant(0 * pi / 180, 'preload3', system)
Ixx_O = Constant(1, 'Ixx_O', system)
Iyy_O = Constant(1, 'Iyy_O', system)
Izz_O = Constant(1, 'Izz_O', system)
Ixx_A = Constant(1, 'Ixx_A', system)
Iyy_A = Constant(1, 'Iyy_A', system)
Izz_A = Constant(1, 'Izz_A', system)
Ixx_B = Constant(1, 'Ixx_B', system)
Iyy_B = Constant(1, 'Iyy_B', system)
Izz_B = Constant(1, 'Izz_B', system)
Ixx_C = Constant(1, 'Ixx_C', system)
Iyy_C = Constant(1, 'Iyy_C', system)
Izz_C = Constant(1, 'Izz_C', system)
y, y_d, y_dd = Differentiable('y', system)
qO, qO_d, qO_dd = Differentiable('qO', system)
qA, qA_d, qA_dd = Differentiable('qA', system)
qB, qB_d, qB_dd = Differentiable('qB', system)
qC, qC_d, qC_dd = Differentiable('qC', system)
fit_states = initial_states
initialvalues = {}
initialvalues[y] = fit_states[0]
initialvalues[y_d] = fit_states[5]
initialvalues[qO] = 0
initialvalues[qO_d] = 0
initialvalues[qA] = fit_states[2]
initialvalues[qA_d] = fit_states[7]
initialvalues[qB] = fit_states[3]
initialvalues[qB_d] = fit_states[8]
initialvalues[qC] = fit_states[4]
initialvalues[qC_d] = fit_states[9]
statevariables = system.get_state_variables()
ini = [initialvalues[item] for item in statevariables]
N = Frame('N')
O = Frame('O')
A = Frame('A')
B = Frame('B')
C = Frame('C')
system.set_newtonian(N)
if not global_q:
O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system)
A.rotate_fixed_axis_directed(O, [0, 0, 1], qA, system)
B.rotate_fixed_axis_directed(A, [0, 0, 1], qB, system)
C.rotate_fixed_axis_directed(B, [0, 0, 1], qC, system)
else:
O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system)
A.rotate_fixed_axis_directed(N, [0, 0, 1], qA, system)
B.rotate_fixed_axis_directed(N, [0, 0, 1], qB, system)
C.rotate_fixed_axis_directed(N, [0, 0, 1], qC, system)
pNO = 0 * N.x + y * N.y
pOA = lO * N.x + y * N.y
pAB = pOA + lA * A.x
pBC = pAB + lB * B.x
pCtip = pBC + lC * C.x
pOcm = pNO + lO / 2 * N.x
pAcm = pOA + lA / 2 * A.x
pBcm = pAB + lB / 2 * B.x
pCcm = pBC + lC / 2 * C.x
wNO = N.getw_(O)
wOA = N.getw_(A)
wAB = A.getw_(B)
wBC = B.getw_(C)
IO = Dyadic.build(O, Ixx_O, Iyy_O, Izz_O)
IA = Dyadic.build(A, Ixx_A, Iyy_A, Izz_A)
IB = Dyadic.build(B, Ixx_B, Iyy_B, Izz_B)
IC = Dyadic.build(C, Ixx_C, Iyy_C, Izz_C)
BodyO = Body('BodyO', O, pOcm, mO, IO, system)
BodyA = Body('BodyA', A, pAcm, mA, IA, system)
BodyB = Body('BodyB', B, pBcm, mB, IB, system)
BodyC = Body('BodyC', C, pCcm, mC, IC, system)
# vOcm = pOcm.time_derivative()
vAcm = pAcm.time_derivative()
vBcm = pBcm.time_derivative()
vCcm = pCcm.time_derivative()
# system.add_spring_force1(k1+10000*(qA+abs(qA)),(qA-qO-preload1)*N.z,wOA)
# system.add_spring_force1(k+10000*(qB+abs(qB)),(qB-qA-preload2)*N.z,wAB)
# system.add_spring_force1(k+10000*(qC+abs(qC)),(qC-qB-preload3)*N.z,wBC)
system.add_spring_force1(k1, (qA - qO - preload1) * N.z, wOA)
system.add_spring_force1(k, (qB - qA - preload2) * N.z, wAB)
system.add_spring_force1(k, (qC - qB - preload3) * N.z, wBC)
#new Method use nJoint
nvAcm = 1 / vAcm.length() * vAcm
nvBcm = 1 / vBcm.length() * vBcm
nvCcm = 1 / vCcm.length() * vCcm
vSoil = drag_direction * 1 * N.y
nSoil = 1 / vSoil.length() * vSoil
if fit_vel == 0:
vSoil = 1 * 1 * N.y
nSoil = 1 / vSoil.length() * vSoil
faperp = friction_perp * nSoil.dot(A.y) * A.y
fapar = friction_par * nSoil.dot(A.x) * A.x
system.addforce(-(faperp + fapar), vAcm)
fbperp = friction_perp * nSoil.dot(B.y) * B.y
fbpar = friction_par * nSoil.dot(B.x) * B.x
system.addforce(-(fbperp + fbpar), vBcm)
fcperp = friction_perp * nSoil.dot(C.y) * C.y
fcpar = friction_par * nSoil.dot(C.x) * C.x
system.addforce(-(fcperp + fcpar), vCcm)
else:
faperp = friction_perp * nvAcm.dot(A.y) * A.y
fapar = friction_par * nvAcm.dot(A.x) * A.x
system.addforce(-(faperp + fapar), vAcm)
fbperp = friction_perp * nvBcm.dot(B.y) * B.y
fbpar = friction_par * nvBcm.dot(B.x) * B.x
system.addforce(-(fbperp + fbpar), vBcm)
fcperp = friction_perp * nvCcm.dot(C.y) * C.y
fcpar = friction_par * nvCcm.dot(C.x) * C.x
system.addforce(-(fcperp + fcpar), vCcm)
system.addforce(-b_damping1 * wOA, wOA)
system.addforce(-b_damping * wAB, wAB)
system.addforce(-b_damping * wBC, wBC)
eq = []
eq_d = [(system.derivative(item)) for item in eq]
eq_d.append(y_d - fit_vel)
eq_dd = [(system.derivative(item)) for item in eq_d]
f, ma = system.getdynamics()
func1 = system.state_space_post_invert(f, ma, eq_dd)
points = [pNO, pOA, pAB, pBC, pCtip]
constants = system.constant_values
states = pynamics.integration.integrate_odeint(func1,
ini,
t,
args=({
'constants': constants
}, ))
points_output = PointsOutput(points, system, constant_values=constants)
y = points_output.calc(states)
final = numpy.asarray(states[-1, :])
time1 = time.time()
points_output.animate(fps=30,
movie_name=str(time1) + 'video_1.mp4',
lw=2,
marker='o',
color=(1, 0, 0, 1),
linestyle='-')
return final, states, y, system
state = numpy.array([ini, result.x])
ini1 = list(result.x)
y = points.calc(state)
y = y.reshape((-1, 6, 2))
plt.figure()
for item in y:
plt.plot(*(item.T))
# for item,value in zip(system.get_state_variables(),result.x):
# initialvalues[item]=value
pAcm = pOA + lA / 2 * A.x
pBcm = pAB + lB / 2 * B.x
pCcm = pOC + lC / 2 * C.x
pDcm = pCD + lD / 2 * D.x
wOMA = O.getw_(MA)
wOA = O.getw_(A)
wAB = A.getw_(B)
wOMC = O.getw_(MC)
wOC = O.getw_(C)
wCD = C.getw_(D)
wBD = B.getw_(D)
wNMA = N.getw_(MA)
aNMA = wNMA.time_derivative()
wNMC = N.getw_(MC)
aNMC = wNMC.time_derivative()
I_motorA = Dyadic.build(MA, Im, Im, Im)
I_motorC = Dyadic.build(MC, Im, Im, Im)
y = y.reshape((-1, len(points), 2))
plt.figure()
for item in y:
plt.plot(*(item.T))
# for item,value in zip(system.get_state_variables(),result.x):
# initialvalues[item]=value
pA1cm = pOA + lA / 4 * A1.x
pC1cm = pOC + lC / 4 * C1.x
pBcm = pAB + lB / 2 * B.x
pDcm = pCD + lD / 2 * D.x
pA2cm = pA1A2 + lA / 4 * A2.x
pC2cm = pC1C2 + lC / 4 * C2.x
wOMA = O.getw_(MA)
wOMC = O.getw_(MC)
wOA1 = O.getw_(A1)
wA1A2 = A1.getw_(A2)
wA2B = A2.getw_(B)
#wB1B2 = B1.getw_(B2)
wOC1 = O.getw_(C1)
wC1C2 = C1.getw_(C2)
wC2D = C2.getw_(D)
#wD1D2 = D1.getw_(D2)
wBD = B.getw_(D)
wNMA = N.getw_(MA)
aNMA = wNMA.time_derivative()
wNMC = N.getw_(MC)
def Cal_robot(direction, given_l, omega1, t1, t2, ini_states, name1, system,
video_on, x1):
time_a = time.time()
pynamics.set_system(__name__, system)
given_k, given_b = x1
global_q = True
damping_r = 0
tinitial = 0
tfinal = (t1 - t2) / omega1
tstep = 1 / 30
t = numpy.r_[tinitial:tfinal:tstep]
tol_1 = 1e-6
tol_2 = 1e-6
lO = Constant(27.5 / 1000, 'lO', system)
lR = Constant(40.5 / 1000, 'lR', system)
lA = Constant(given_l / 1000, 'lA', system)
lB = Constant(given_l / 1000, 'lB', system)
lC = Constant(given_l / 1000, 'lC', system)
mO = Constant(154.5 / 1000, 'mO', system)
mR = Constant(9.282 / 1000, 'mR', system)
mA = Constant(given_l * 2.75 * 0.14450000000000002 / 1000, 'mA', system)
mB = Constant(given_l * 2.75 * 0.14450000000000002 / 1000, 'mB', system)
mC = Constant(given_l * 2.75 * 0.14450000000000002 / 1000, 'mC', system)
k = Constant(given_k, 'k', system)
friction_perp = Constant(13 / 3, 'f_perp', system)
friction_par = Constant(-2 / 3, 'f_par', system)
friction_arm_perp = Constant(5.6, 'fr_perp', system)
friction_arm_par = Constant(-0.2, 'fr_par', system)
b_damping = Constant(given_b, 'b_damping', system)
preload0 = Constant(0 * pi / 180, 'preload0', system)
preload1 = Constant(0 * pi / 180, 'preload1', system)
preload2 = Constant(0 * pi / 180, 'preload2', system)
preload3 = Constant(0 * pi / 180, 'preload3', system)
Ixx_O = Constant(1, 'Ixx_O', system)
Iyy_O = Constant(1, 'Iyy_O', system)
Izz_O = Constant(1, 'Izz_O', system)
Ixx_R = Constant(1, 'Ixx_R', system)
Iyy_R = Constant(1, 'Iyy_R', system)
Izz_R = Constant(1, 'Izz_R', system)
Ixx_A = Constant(1, 'Ixx_A', system)
Iyy_A = Constant(1, 'Iyy_A', system)
Izz_A = Constant(1, 'Izz_A', system)
Ixx_B = Constant(1, 'Ixx_B', system)
Iyy_B = Constant(1, 'Iyy_B', system)
Izz_B = Constant(1, 'Izz_B', system)
Ixx_C = Constant(1, 'Ixx_C', system)
Iyy_C = Constant(1, 'Iyy_C', system)
Izz_C = Constant(1, 'Izz_C', system)
y, y_d, y_dd = Differentiable('y', system)
qO, qO_d, qO_dd = Differentiable('qO', system)
qR, qR_d, qR_dd = Differentiable('qR', system)
qA, qA_d, qA_dd = Differentiable('qA', system)
qB, qB_d, qB_dd = Differentiable('qB', system)
qC, qC_d, qC_dd = Differentiable('qC', system)
initialvalues = {}
initialvalues[y] = ini_states[0] + tol_1
initialvalues[qO] = ini_states[1] + tol_1
initialvalues[qR] = ini_states[2] + tol_1
initialvalues[qA] = ini_states[3] + tol_1
initialvalues[qB] = ini_states[4] + tol_1
initialvalues[qC] = ini_states[5] + tol_1
initialvalues[y_d] = ini_states[6] + tol_1
initialvalues[qO_d] = ini_states[7] + tol_1
initialvalues[qR_d] = ini_states[8] + tol_1
initialvalues[qA_d] = ini_states[9] + tol_1
initialvalues[qB_d] = ini_states[10] + tol_1
initialvalues[qC_d] = ini_states[11] + tol_1
statevariables = system.get_state_variables()
ini = [initialvalues[item] for item in statevariables]
N = Frame('N')
O = Frame('O')
R = Frame('R')
A = Frame('A')
B = Frame('B')
C = Frame('C')
system.set_newtonian(N)
if not global_q:
O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system)
R.rotate_fixed_axis_directed(O, [0, 0, 1], qR, system)
A.rotate_fixed_axis_directed(R, [0, 0, 1], qA, system)
B.rotate_fixed_axis_directed(A, [0, 0, 1], qB, system)
C.rotate_fixed_axis_directed(B, [0, 0, 1], qC, system)
else:
O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system)
R.rotate_fixed_axis_directed(N, [0, 0, 1], qR, system)
A.rotate_fixed_axis_directed(N, [0, 0, 1], qA, system)
B.rotate_fixed_axis_directed(N, [0, 0, 1], qB, system)
C.rotate_fixed_axis_directed(N, [0, 0, 1], qC, system)
pNO = 0 * N.x + y * N.y
pOR = pNO + lO * N.x
pRA = pOR + lR * R.x
pAB = pRA + lA * A.x
pBC = pAB + lB * B.x
pCtip = pBC + lC * C.x
pOcm = pNO + lO / 2 * N.x
pRcm = pOR + lR / 2 * R.x
pAcm = pRA + lA / 2 * A.x
pBcm = pAB + lB / 2 * B.x
pCcm = pBC + lC / 2 * C.x
wNO = N.getw_(O)
wOR = N.getw_(R)
wRA = R.getw_(A)
wAB = A.getw_(B)
wBC = B.getw_(C)
IO = Dyadic.build(O, Ixx_O, Iyy_O, Izz_O)
IR = Dyadic.build(R, Ixx_R, Iyy_R, Izz_R)
IA = Dyadic.build(A, Ixx_A, Iyy_A, Izz_A)
IB = Dyadic.build(B, Ixx_B, Iyy_B, Izz_B)
IC = Dyadic.build(C, Ixx_C, Iyy_C, Izz_C)
BodyO = Body('BodyO', O, pOcm, mO, IO, system)
BodyR = Body('BodyR', R, pRcm, mR, IR, system)
BodyA = Body('BodyA', A, pAcm, mA, IA, system)
BodyB = Body('BodyB', B, pBcm, mB, IB, system)
BodyC = Body('BodyC', C, pCcm, mC, IC, system)
j_tol = 3 * pi / 180
inv_k = 10
system.add_spring_force1(k + inv_k * (qA - qR + abs(qA - qR - j_tol)),
(qA - qR - preload1) * N.z, wRA)
system.add_spring_force1(k + inv_k * (qB - qA + abs(qB - qA - j_tol)),
(qB - qA - preload2) * N.z, wAB)
system.add_spring_force1(k + inv_k * (qC - qB + abs(qC - qB - j_tol)),
(qC - qB - preload3) * N.z, wBC)
vOcm = y_d * N.y
vRcm = pRcm.time_derivative()
vAcm = pAcm.time_derivative()
vBcm = pBcm.time_derivative()
vCcm = pCcm.time_derivative()
nvRcm = 1 / (vRcm.length() + tol_1) * vRcm
nvAcm = 1 / (vAcm.length() + tol_1) * vAcm
nvBcm = 1 / (vBcm.length() + tol_1) * vBcm
nvCcm = 1 / (vCcm.length() + tol_1) * vCcm
vSoil = -direction * 1 * N.y
nSoil = 1 / vSoil.length() * vSoil
foperp = 8 * nSoil
system.addforce(-foperp, vOcm)
frperp = friction_arm_perp * nvRcm.dot(R.y) * R.y
frpar = friction_arm_par * nvRcm.dot(R.x) * R.x
system.addforce(-(frperp + frpar), vRcm)
faperp = friction_perp * nvAcm.dot(A.y) * A.y
fapar = friction_par * nvAcm.dot(A.x) * A.x
system.addforce(-(faperp + fapar), vAcm)
fbperp = friction_perp * nvBcm.dot(B.y) * B.y
fbpar = friction_par * nvBcm.dot(B.x) * B.x
system.addforce(-(fbperp + fbpar), vBcm)
fcperp = friction_perp * nvCcm.dot(C.y) * C.y
fcpar = friction_par * nvCcm.dot(C.x) * C.x
system.addforce(-(fcperp + fcpar), vCcm)
system.addforce(-b_damping * 1 * wRA, wRA)
system.addforce(-b_damping * 1 * wAB, wAB)
system.addforce(-b_damping * 1 * wBC, wBC)
eq = []
eq_d = [(system.derivative(item)) for item in eq]
eq_d.append(qR_d - omega1)
eq_dd = [(system.derivative(item)) for item in eq_d]
f, ma = system.getdynamics()
func1 = system.state_space_post_invert(f, ma, eq_dd)
points = [pNO, pOR, pRA, pAB, pBC, pCtip]
constants = system.constant_values
states = pynamics.integration.integrate_odeint(func1,
ini,
t,
args=({
'constants': constants
}, ))
final = numpy.asarray(states[-1, :])
logger1 = logging.getLogger('pynamics.system')
logger2 = logging.getLogger('pynamics.integration')
logger3 = logging.getLogger('pynamics.output')
logger1.disabled = True
logger2.disabled = True
logger3.disabled = True
points_output = PointsOutput(points, system, constant_values=constants)
y1 = points_output.calc(states)
if video_on == 1:
plt.figure()
plt.plot(*(y1[::int(len(y1) / 20)].T) * 1000)
plt.axis('equal')
plt.axis('equal')
plt.title("Plate Configuration vs Distance")
plt.xlabel("Configuration")
plt.ylabel("Distance (mm)")
plt.figure()
plt.plot(t, numpy.rad2deg(states[:, 2]))
plt.plot(t, numpy.rad2deg(states[:, 8]))
plt.legend(["qR", "qR_d"])
plt.hlines(numpy.rad2deg(t1), tinitial, tfinal)
plt.hlines(numpy.rad2deg(t2), tinitial, tfinal)
plt.title("Robot Arm angle and velocitues (qR and qR_d) over Time")
plt.xlabel("Time (s)")
plt.ylabel("Angles,Velocities (deg, deg/s)")
plt.figure()
q_states = numpy.c_[(states[:, 2], states[:, 3], states[:,
4], states[:,
5])]
plt.plot(t, numpy.rad2deg(q_states))
plt.title("Joint Angule over Time")
plt.xlabel("Time (s)")
plt.ylabel("Joint Angles (deg)")
plt.legend(["Arm", "Joint 1", "Joint 2", "Joint 3"])
plt.figure()
qd_states = numpy.c_[(states[:, 8], states[:,
9], states[:,
10], states[:,
11])]
plt.plot(t, numpy.rad2deg(qd_states))
plt.legend(["qR_d", "qA_d", "qB_d", "qC_d"])
plt.title("Joint Angular Velocities over Time")
plt.xlabel("Time (s)")
plt.ylabel("Joint Angular Velocities (deg/s)")
plt.legend(["Arm", "Joint 1", "Joint 2", "Joint 3"])
plt.figure()
plt.plot(t, states[:, 0], '--')
plt.plot(t, states[:, 6])
plt.title("Robot Distance and Velocity over time")
plt.xlabel("Time (s)")
plt.ylabel("Distance (mm)")
plt.legend(["Distance", "Velocity of the robot"])
points_output.animate(fps=1 / tstep,
movie_name=name1,
lw=2,
marker='o',
color=(1, 0, 0, 1),
linestyle='-')
else:
pass
return final, states, y1
B2.rotate_fixed_axis_directed(B12, [1, 0, 0], qB2, system) B23.rotate_fixed_axis_directed(B2, [0, 0, 1], -t3, system) ################################################ #Define particles at the center of mass of each body pNO = 0 * N.x ParticleA1 = Particle(A1.x + A12.x, m, 'ParticleA1', system) ParticleA2 = Particle(A2.x + A23.x, m, 'ParticleA2', system) # ParticleA3 = Particle(A3.x+A34.x,m/2,'ParticleA3',system) ParticleB1 = Particle(B1.x + B12.x, m, 'ParticleB1', system) ParticleB2 = Particle(B2.x + B23.x, m, 'ParticleB2', system) ################################################ #Get the relative rotational velocity between frames wA1 = N.getw_(A1) wA2 = A12.getw_(A2) wA3 = A23.getw_(A3) wB1 = NB1.getw_(B1) wB2 = B12.getw_(B2) ################################################ #Add damping between joints system.addforce(-b * wA1, wA1) system.addforce(-b * wA2, wA2) system.addforce(-b * wA3, wA3) system.addforce(-b * wB1, wB1) system.addforce(-b * wB2, wB2) #system.addforce(1*A1.x,wA1)
statevariables = system.get_state_variables()
ini = [initialvalues[item] for item in statevariables]
N = Frame('N')
#A = Frame('A')
B = Frame('B')
M = Frame('M')
system.set_newtonian(N)
#A.rotate_fixed_axis_directed(N,[0,0,1],qA,system)
B.rotate_fixed_axis_directed(N, [0, 0, 1], qB, system)
pO = 0 * N.x
#wNA = N.getw_(A)
wNB = N.getw_(B)
wNA = G * wNB
aNA = wNA.time_derivative()
#wNB = wB*B.z
#aNB = wB_d*B.z
I_motor = Dyadic.build(B, Im, Im, Im)
I_load = Dyadic.build(B, Il, Il, Il)
#Motor = Body('Motor',A,pO,0,I_motor,system)
Motor = Body('Motor', B, pO, 0, I_motor, system, wNBody=wNA, alNBody=aNA)
Inductor = PseudoParticle(0 * M.x,
L,
name='Inductor',
vCM=i * M.x,
aCM=i_d * M.x)
ini = [initialvalues[item] for item in statevariables]
A = Frame('A')
B = Frame('B')
C = Frame('C')
D = Frame('D')
system.set_newtonian(A)
B.rotate_fixed_axis_directed(A, [0, 0, 1], H, system)
C.rotate_fixed_axis_directed(B, [1, 0, 0], -L, system)
D.rotate_fixed_axis_directed(C, [0, 1, 0], Q, system)
pNA = 0 * A.x
pAD = pNA + x * A.x + y * A.y
pBcm = pAD + r * C.z
pDA = pBcm - r * D.z
wAD = A.getw_(D)
II = Dyadic.build(B, J, I, J)
BodyD = Body('BodyD', D, pBcm, m, II, system)
#ParticleA = Particle(pAcm,mA,'ParticleA',system)
#ParticleB = Particle(pBcm,mB,'ParticleB',system)
#ParticleC = Particle(pCcm,mC,'ParticleC',system)
system.addforcegravity(-g * A.z)
f, ma = system.getdynamics()
vAB = pAB.time_derivative(N,system)
aAB = vAB.time_derivative(N,system)
vBA = pBA.time_derivative(N,system)
aBA = vBA.time_derivative(N,system)
#constraint1 = pNA-pAN
#constraint1_d = vectorderivative(constraint1,N)
#constraint1_dd = vectorderivative(constraint1_d,N)
#
constraint2 = pAB-pBA
constraint2_d = constraint2.time_derivative(N,system)
constraint2_dd = constraint2_d.time_derivative(N,system)
wNA = N.getw_(A)
wAB = A.getw_(B)
IA = Dyadic.build(A,Ixx_A,Iyy_A,Izz_A)
IB = Dyadic.build(A,Ixx_B,Iyy_B,Izz_B)
Body('BodyA',A,pAcm,mA,IA,system)
Body('BodyB',B,pBcm,mB,IB,system)
system.addforce(-b*wNA,wNA)
system.addforce(-b*wAB,wAB)
system.addforce(-k*qA*N.z,wNA)
system.addforce(-k*qB*A.z,wAB)
#system.addforce(fNAx*N.x+fNAy*N.y,vNA)
f1 = Frame()
f2 = Frame()
f3 = Frame()
f4 = Frame()
#f5 = Frame()
system.set_newtonian(f1)
f2.rotate_fixed_axis_directed(f1, [0, 0, 1], q1)
f3.rotate_fixed_axis_directed(f2, [1, 0, 0], q2)
f4.rotate_fixed_axis_directed(f3, [0, 1, 0], q3)
p1 = x * f1.x + y * f1.y + z * f1.z
p2 = -l1 * f4.x
#v1=p1.time_derivative(f1)
wNA = f1.getw_(f2)
particle1 = Particle(p1, mp1)
body1 = Body('body1', f4, p1, mp1, Dyadic.build(f4, 1, 1, 1), system=None)
#system.addforce(-b*v1,v1)
system.addforcegravity(-g * f1.z)
#system.add_spring_force1(k,(q1)*f1.z,wNA)
eq1 = []
#eq1.append(p2.dot(p2))
eq1.append(p2.dot(f1.x))
eq1.append(p2.dot(f1.y))
eq1.append(p2.dot(f1.z))
eq1_d = [system.derivative(item) for item in eq1]
eq1_dd = [system.derivative(item) for item in eq1_d]
# In[15]:
pAcm = pNA - lA / 2 * A.y
pBcm = pAB - lB / 2 * B.y
pCcm = pBC
# ## Calculating Velocity
#
# The angular velocity between frames, and the time derivatives of vectors are extremely useful in calculating the equations of motion and for determining many of the forces that need to be applied to your system (damping, drag, etc). Thus, it is useful, once kinematics have been defined, to take or find the derivatives of some of those vectors for calculating linear or angular velocity vectors
#
# ### Angular Velocity
# The following three lines of code computes and returns the angular velocity between frames N and A (${}^N\omega^A$), A and B (${}^A\omega^B$), and B and C (${}^B\omega^C$). In other cases, if the derivative expression is complex or long, you can supply pynamics with a given angular velocity between frames to speed up computation time.
# In[16]:
wNA = N.getw_(A)
wAB = A.getw_(B)
wBC = B.getw_(C)
# ### Vector derivatives
# The time derivatives of vectors may also be
# vCtip = pCtip.time_derivative(N,system)
# ### Define Inertias and Bodies
# The next several lines compute the inertia dyadics of each body and define a rigid body on each frame. In the case of frame C, we represent the mass as a particle located at point pCcm.
# In[17]:
IA = Dyadic.build(A, Ixx_A, Iyy_A, Izz_A)
IB = Dyadic.build(B, Ixx_B, Iyy_B, Izz_B)
pCcm = pBC + lC / 2 * C.x
vAcm = pAcm.time_derivative()
vCcm = pCcm.time_derivative()
# ## Calculating Velocity
#
# The angular velocity between frames, and the time derivatives of vectors are extremely useful in calculating the equations of motion and for determining many of the forces that need to be applied to your system (damping, drag, etc). Thus, it is useful, once kinematics have been defined, to take or find the derivatives of some of those vectors for calculating linear or angular velocity vectors
#
# ### Angular Velocity
# The following three lines of code computes and returns the angular velocity between frames N and A (${}^N\omega^A$), A and B (${}^A\omega^B$), and B and C (${}^B\omega^C$). In other cases, if the derivative expression is complex or long, you can supply pynamics with a given angular velocity between frames to speed up computation time.
# In[16]:
#wNA3 = N.getw_(A3)
wA3B1 = A3.getw_(B1)
wB2C = B2.getw_(C)
# ### Vector derivatives
# The time derivatives of vectors may also be
# vCtip = pCtip.time_derivative(N,system)
# ### Define Inertias and Bodies
# The next several lines compute the inertia dyadics of each body and define a rigid body on each frame. In the case of frame C, we represent the mass as a particle located at point pCcm.
# In[17]:
IA = Dyadic.build(A3, Ixx_A, Iyy_A, Izz_A)
IB = Dyadic.build(B1, Ixx_B, Iyy_B, Izz_B)
IC = Dyadic.build(C, Ixx_C, Iyy_C, Izz_C)