pCcm=0*N.x
w1 = N.get_w_to(C)
IC = Dyadic.build(C,Ixx,Iyy,Izz)
BodyC = Body('BodyC',C,pCcm,mC,IC)
system.addforcegravity(-g*N.y)
# system.addforce(1*C.x+2*C.y+3*C.z,w1)
points = [1*C.x,0*C.x,1*C.y,0*C.y,1*C.z]
f,ma = system.getdynamics()
# func1 = system.state_space_pre_invert(f,ma)
func1 = system.state_space_post_invert(f,ma)
ini = [initialvalues[item] for item in system.get_state_variables()]
states=pynamics.integration.integrate_odeint(func1,ini,t,rtol = tol, atol=tol,args=({'constants':system.constant_values},))
po = PointsOutput(points,system)
po.calc(states,t)
po.animate(fps = 30,lw=2)
so = Output([qA,qB,qC])
so.calc(states,t)
so.plot_time()
stretch = q - q0
system.add_spring_force1(k, (stretch) * N.z, wNA)
system.addforce(-b * v2, v2)
system.addforcegravity(-g * N.y)
pos = sympy.cos(system.t * 2 * pi / 2)
eq = pos * N.x - p1
eq_d = eq.time_derivative()
eq_dd = eq_d.time_derivative()
eq_dd_scalar = []
eq_dd_scalar.append(eq_dd.dot(N.x))
system.add_constraint(AccelerationConstraint(eq_dd_scalar))
f, ma = system.getdynamics()
func1, lambda1 = system.state_space_post_invert(
f, ma, constants=system.constant_values, return_lambda=True)
states = pynamics.integration.integrate_odeint(func1,
ini,
t,
rtol=tol,
atol=tol,
args=({
'constants': {},
'alpha': 1e2,
'beta': 1e1
}, ))
lambda1_n = numpy.array([lambda1(tt, ss) for tt, ss in zip(t, states)])
plt.figure()
plt.plot(t, lambda1_n)
ParticleA = Particle(pAB, mA, 'ParticleA', system)
ParticleB = Particle(pAB2, mA, 'ParticleB', system)
system.addforce(-b * vAB, vAB)
system.addforce(-b * vAB2, vAB2)
system.addforcegravity(-g * N.y)
v = pAB2 - pNA2
u = (v.dot(v))**.5
eq1 = [(v.dot(v)) - lA**2]
eq1_dd = system.derivative(system.derivative(eq1[0]))
eq = [eq1_dd]
f, ma = system.getdynamics()
func = system.state_space_post_invert(f,
ma,
eq,
constants=system.constant_values)
states = pynamics.integration.integrate(func,
ini,
t,
rtol=1e-12,
atol=1e-12,
hmin=1e-14)
points = [pNA, pAB, pNA, pNA2, pAB2]
points_output = PointsOutput(points, system)
points_output.calc(states)
points_output.animate(fps=30, lw=2)
f
# In[24]:
ma
# ## Solve for Acceleration
#
# The next line of code solves the system of equations F=ma plus any constraint equations that have been added above. It returns one or two variables. func1 is the function that computes the velocity and acceleration given a certain state, and lambda1(optional) supplies the function that computes the constraint forces as a function of the resulting states
#
# There are a few ways of solveing for a. The below function inverts the mass matrix numerically every time step. This can be slower because the matrix solution has to be solved for, but is sometimes more tractable than solving the highly nonlinear symbolic expressions that can be generated from the previous step. The other options would be to use ```state_space_pre_invert```, which pre-inverts the equations symbolically before generating a numerical function, or ```state_space_post_invert2```, which adds Baumgarte's method for intermittent constraints.
# In[25]:
func1, lambda1 = system.state_space_post_invert(
f, ma, eq_dd, return_lambda=True, variable_functions={force_var: f_force})
# ## Integrate
#
# The next line of code integrates the function calculated
# In[26]:
states = pynamics.integration.integrate_odeint(func1,
ini,
t,
rtol=tol,
atol=tol,
hmin=tol,
args=({
'constants':
f_aero_C2 = rho * vAcm.length() * (vAcm.dot(A.y)) * Area * A.y
system.addforce(-f_aero_C2, vAcm)
system.add_spring_force1(k, qA * N.z, wNA)
tin = torque * sympy.sin(2 * sympy.pi * freq * system.t)
system.addforce(tin * N.z, wNA)
f, ma = system.getdynamics()
changing_constants = [freq]
static_constants = system.constant_values.copy()
for key in changing_constants:
del static_constants[key]
func = system.state_space_post_invert(f, ma, constants=static_constants)
statevariables = system.get_state_variables()
ini = [initialvalues[item] for item in statevariables]
points = [pNA, pAcm, pAtip]
points_output = PointsOutput(points, system)
out1 = Output([tin, qA])
my_constants = {}
freq_sweep = numpy.r_[-1.5:1:20j]
freq_sweep = 1 * 10**freq_sweep
amps = []
for ff in freq_sweep:
tol = 1e-4
torque = my_signal * stall_torque
system.addforce(torque * O.z, wOA)
system.addforce(-torque * O.z, wOC)
#
eq = []
eq.append((pBtip - pDtip).dot(N.x))
eq.append((pBtip - pDtip).dot(N.y))
#eq.append((O.y.dot(N.y)))
eq_d = [system.derivative(item) for item in eq]
eq_dd = [system.derivative(item) for item in eq_d]
#
f, ma = system.getdynamics()
func1 = system.state_space_post_invert(f,
ma,
eq_dd,
constants=system.constant_values,
variable_functions={my_signal: ft2})
states = pynamics.integration.integrate_odeint(func1,
ini1,
t,
rtol=tol,
atol=tol)
KE = system.get_KE()
PE = system.getPEGravity(0 * N.x) - system.getPESprings()
energy = Output([KE - PE, toeforce, heelforce])
energy.calc(states)
energy.plot_time()
#torque_plot = Output([torque])
# ParticleB = Particle(pAB2,mA,'ParticleB',system)
# system.addforce(t*vAB,vAB)
system.addforce(torque * N.z, wNA)
# system.addforce(-b*vAB2,vAB2)
system.addforcegravity(-g * N.y)
# v = pAB2-pNA2
# u = (v.dot(v))**.5
# eq1 = [(v.dot(v)) - lA**2]
eq = []
f, ma = system.getdynamics()
func = system.state_space_post_invert(f, ma, eq)
states = pynamics.integration.integrate_odeint(func,
ini,
t,
rtol=1e-12,
atol=1e-12,
hmin=1e-14,
args=({
'constants':
system.constant_values
}, ))
points = [pNA, pAB]
points_output = PointsOutput(points, system)
points_output.calc(states)
points_output.animate(fps=30, lw=2)
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
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
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]
points = [particle1.pCM]
points_x = [item.dot(f1.x) for item in points]
points_y = [item.dot(f1.y) for item in points]
points_z = [item.dot(f1.z) for item in points]
output_x = Output(points_x)
output_y = Output(points_y)
output_z = Output(points_z)
f, ma = system.getdynamics()
func = system.state_space_post_invert(f, ma, eq_dd=eq1_dd)
t = numpy.r_[0:5:.001]
states = pynamics.integration.integrate_odeint(func,
system.get_ini(),
t,
atol=1e-5,
rtol=1e-5,
args=({
'constants':
system.constant_values
}, ))
KE = system.get_KE()
PE = system.getPEGravity(0 * f1.x) - system.getPESprings()
output = Output([KE - PE])
The last tip of the four bar mechanism (pCD) is fixed to the ground.
"""
# Define constraints
eq = []
eq.append(pCD.dot(N.x))
eq.append(pCD.dot(N.y))
eq_d=[(system.derivative(item)) for item in eq]
eq_dd=[(system.derivative(item)) for item in eq_d]
"""# 5. Solution: Add the code from the bottom of the pendulum example for solving for f=ma, integrating, plotting, and animating. Run the code to see your results. It should look similar to the pendulum example with constraints added, as in like a rag-doll or floppy"""
f,ma = system.getdynamics()
func1,lambda1 = system.state_space_post_invert(f,ma,eq_dd,return_lambda = True)
states=pynamics.integration.integrate(func1,ini,t,rtol=tol,atol=tol, args=({'constants':system.constant_values},))
# Plot --- output
plt.figure()
artists = plt.plot(t,states[:,:3])
plt.legend(artists,['qA','qB','qC'])
# Plot --- energy
KE = system.get_KE()
PE = system.getPEGravity(pNA) - system.getPESprings()
energy_output = Output([KE-PE],system)
energy_output.calc(states)
energy_output.plot_time()
eq_d = [item.time_derivative() for item in eq]
eq_dd = [item.time_derivative() for item in eq_d]
eq_dd_scalar = []
eq_dd_scalar.append(eq_dd[0].dot(N.x))
eq_dd_scalar.append(eq_dd[0].dot(N.y))
eq_dd_scalar.append(eq_dd[1].dot(N.y))
c = AccelerationConstraint(eq_dd_scalar)
# c.linearize(0)
system.add_constraint(c)
#
f, ma = system.getdynamics()
func1 = system.state_space_post_invert(f,
ma,
constants=constants,
variable_functions={my_signal: ft2})
states = pynamics.integration.integrate(func1, ini, t, rtol=tol, atol=tol)
KE = system.get_KE()
PE = system.getPEGravity(0 * N.x) - system.getPESprings()
energy = Output([KE - PE], constant_values=constants)
energy.calc(states, t)
energy.plot_time()
#torque_plot = Output([torque])
#torque_plot.calc(states,t)
#torque_plot.plot_time()
points = [pDtip, pCD, pOC, pOA, pAB, pBtip]
points = PointsOutput(points, constant_values=constants)
f, ma = system.getdynamics()
# # ## Solve for Acceleration
# #
# # The next line of code solves the system of equations F=ma plus any constraint equations that have been added above. It returns one or two variables. func1 is the function that computes the velocity and acceleration given a certain state, and lambda1(optional) supplies the function that computes the constraint forces as a function of the resulting states
# #
# # There are a few ways of solveing for a. The below function inverts the mass matrix numerically every time step. This can be slower because the matrix solution has to be solved for, but is sometimes more tractable than solving the highly nonlinear symbolic expressions that can be generated from the previous step. The other options would be to use ```state_space_pre_invert```, which pre-inverts the equations symbolically before generating a numerical function, or ```state_space_post_invert2```, which adds Baumgarte's method for intermittent constraints.
static_constants = [
rho, lA, lB, lC, lS, mA, mB, mC, mS, r2, Ixx_A, Iyy_A, Izz_A, Ixx_B, Iyy_B,
Izz_B, Ixx_A, Iyy_B, Izz_B, Ixx_C, Iyy_C, Izz_C, Ixx_S, Iyy_S, Izz_S
]
static_constants = dict([(key, system.constant_values[key])
for key in static_constants])
func1 = system.state_space_post_invert(f,
ma,
return_lambda=False,
constants=static_constants)
# %%
statevariables = system.get_state_variables()
ini = [initialvalues[item] for item in statevariables]
# %%
# # ## Integrate
# #
# # The next line of code integrates the function calculated
tol = 1e-7
tinitial = 0
tfinal = 3
fps = 30
def Cal_robot(direction, given_l, given_arm_l, omega1, t1, t2, ini_states,
name1, video_on, x1, x2):
system1 = System()
time_a = time.time()
pynamics.set_system(__name__, system1)
given_k, given_b = x1
f1, f2, f3 = x2
global_q = True
damping_r = 0
tinitial = 0
tfinal = (t1 - t2) / omega1
tstep = 1 / 50
t = numpy.r_[tinitial:tfinal:tstep]
tol_1 = 1e-6
tol_2 = 1e-6
lO = Constant(27.5 / 1000, 'lO', system1)
# given_arm_l = 65
lR = Constant(given_arm_l / 1000, 'lR', system1)
# lR = Constant(40.5/1000,'lR',system11)
lA = Constant(given_l / 1000, 'lA', system1)
lB = Constant(given_l / 1000, 'lB', system1)
lC = Constant(given_l / 1000, 'lC', system1)
mO = Constant(1e0 * 154.5 / 1000, 'mO', system1)
# mR = Constant(9.282/1000 ,'mR',system1)
mR = Constant((1.158 + 0.1445 * given_arm_l) / 1000, 'mR', system1)
mA = Constant(given_l * 2.75 * 0.14450000000000002 / 1000, 'mA', system1)
mB = Constant(given_l * 2.75 * 0.14450000000000002 / 1000, 'mB', system1)
mC = Constant(given_l * 2.75 * 0.14450000000000002 / 1000, 'mC', system1)
k = Constant(given_k, 'k', system1)
friction_perp = Constant(f1, 'f_perp', system1)
friction_par = Constant(-1, 'f_par', system1)
friction_arm_perp = Constant(2 + given_arm_l * f3, 'fr_perp', system1)
friction_arm_par = Constant(-0.3, 'fr_par', system1)
b_damping = Constant(given_b, 'b_damping', system1)
preload0 = Constant(0 * pi / 180, 'preload0', system1)
preload1 = Constant(0 * pi / 180, 'preload1', system1)
preload2 = Constant(0 * pi / 180, 'preload2', system1)
preload3 = Constant(0 * pi / 180, 'preload3', system1)
Ixx_O = Constant(1, 'Ixx_O', system1)
Iyy_O = Constant(1, 'Iyy_O', system1)
Izz_O = Constant(1, 'Izz_O', system1)
Ixx_R = Constant(1, 'Ixx_R', system1)
Iyy_R = Constant(1, 'Iyy_R', system1)
Izz_R = Constant(1, 'Izz_R', system1)
Ixx_A = Constant(1, 'Ixx_A', system1)
Iyy_A = Constant(1, 'Iyy_A', system1)
Izz_A = Constant(1, 'Izz_A', system1)
Ixx_B = Constant(1, 'Ixx_B', system1)
Iyy_B = Constant(1, 'Iyy_B', system1)
Izz_B = Constant(1, 'Izz_B', system1)
Ixx_C = Constant(1, 'Ixx_C', system1)
Iyy_C = Constant(1, 'Iyy_C', system1)
Izz_C = Constant(1, 'Izz_C', system1)
y, y_d, y_dd = Differentiable('y', system1)
qO, qO_d, qO_dd = Differentiable('qO', system1)
qR, qR_d, qR_dd = Differentiable('qR', system1)
qA, qA_d, qA_dd = Differentiable('qA', system1)
qB, qB_d, qB_dd = Differentiable('qB', system1)
qC, qC_d, qC_dd = Differentiable('qC', system1)
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 = system1.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')
system1.set_newtonian(N)
if not global_q:
O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system1)
R.rotate_fixed_axis_directed(O, [0, 0, 1], qR, system1)
A.rotate_fixed_axis_directed(O, [0, 0, 1], qA, system1)
B.rotate_fixed_axis_directed(A, [0, 0, 1], qB, system1)
C.rotate_fixed_axis_directed(B, [0, 0, 1], qC, system1)
else:
O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system1)
R.rotate_fixed_axis_directed(N, [0, 0, 1], qR, system1)
A.rotate_fixed_axis_directed(N, [0, 0, 1], qA, system1)
B.rotate_fixed_axis_directed(N, [0, 0, 1], qB, system1)
C.rotate_fixed_axis_directed(N, [0, 0, 1], qC, system1)
pNO = 0 * N.x + y * N.y
pOR = pNO + lO * N.x
# 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
pOcm = pNO
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, system1)
BodyR = Body('BodyR', R, pRcm, mR, IR, system1)
BodyA = Body('BodyA', A, pAcm, mA, IA, system1)
BodyB = Body('BodyB', B, pBcm, mB, IB, system1)
BodyC = Body('BodyC', C, pCcm, mC, IC, system1)
j_tol = 0 * pi / 180
inv_k = 1e2
alw = 1
system1.add_spring_force1(
k + inv_k * (qA - qR + alw * abs(qA - qR - j_tol)),
(qA - qR - preload1) * N.z, wRA)
system1.add_spring_force1(
k + inv_k * (qB - qA + alw * abs(qB - qA - j_tol)),
(qB - qA - preload2) * N.z, wAB)
system1.add_spring_force1(
k + inv_k * (qC - qB + alw * abs(qC - qB - j_tol)),
(qC - qB - preload3) * N.z, wBC)
# system1.add_spring_force1(k,(qA-qR-preload1)*N.z,wRA)
# system1.add_spring_force1(k,(qB-qA-preload2)*N.z,wAB)
# system1.add_spring_force1(k,(qC-qB-preload3)*N.z,wBC)
vOcm = y_d * N.y
# vOcm = pOcm.time_derivative()
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
# reff = abs( abs(y_d+0.01)-abs(y_d-0.01))*1/0.02*9.75
# foperp = reff*nSoil
foperp = f2 * nSoil
system1.addforce(foperp, vOcm)
# system1.addforce(9.75*1*nSoil,vOcm)
# system1.addforce(9.75*1*nSoil*y_d,vOcm)
# system1.addforce(-100*N.x, y_d*N.x)
frperp = friction_arm_perp * nvRcm.dot(R.y) * R.y
frpar = friction_arm_par * nvRcm.dot(R.x) * R.x
system1.addforce(-(frperp + frpar), vRcm)
faperp = friction_perp * nvAcm.dot(A.y) * A.y
fapar = friction_par * nvAcm.dot(A.x) * A.x
system1.addforce(-(faperp + fapar), vAcm)
fbperp = friction_perp * nvBcm.dot(B.y) * B.y
fbpar = friction_par * nvBcm.dot(B.x) * B.x
system1.addforce(-(fbperp + fbpar), vBcm)
fcperp = friction_perp * nvCcm.dot(C.y) * C.y
fcpar = friction_par * nvCcm.dot(C.x) * C.x
system1.addforce(-(fcperp + fcpar), vCcm)
system1.addforce(-b_damping * 1 * wRA, wRA)
system1.addforce(-b_damping * 1 * wAB, wAB)
system1.addforce(-b_damping * 1 * wBC, wBC)
eq = []
eq_d = [(system1.derivative(item)) for item in eq]
eq_d.append(qR_d - omega1)
# eq_dd= [(system1.derivative(item)) for item in eq_d]
eq_dd = [system1.derivative(eq_d[0])]
f, ma = system1.getdynamics()
func1 = system1.state_space_post_invert(f, ma, eq_dd)
points = [pNO, pOR, pRA, pAB, pBC, pCtip]
constants = system1.constant_values
states = pynamics.integration.integrate_odeint(func1,
ini,
t,
args=({
'constants': constants
}, ))
final = numpy.asarray(states[-1, :])
logger1 = logging.getLogger('pynamics.system1')
logger2 = logging.getLogger('pynamics.integration')
logger3 = logging.getLogger('pynamics.output')
logger1.disabled = True
logger2.disabled = True
logger3.disabled = True
points_output = PointsOutput(points, system1, 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])
y_d1 = states[:, 6]
# force1 = abs( abs(y_d1+0.1)-abs(y_d1-0.1))*40
# plt.plot(t,force1)
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
sol = sympy.solve(zero,torques)
sol2 = [sol[item] for item in torques]
# sol2 = sympy.Matrix([sol[item] for item in torques])
f_torques = sympy.lambdify(system.get_q(0)+system.get_q(1)+system.get_q(2),sol2)
res = numpy.array(f_torques(*(states_exp.T))).T
ft1 = scipy.interpolate.interp1d(t,res[:,0],fill_value = 'extrapolate', kind='quadratic')
ft2 = scipy.interpolate.interp1d(t,res[:,1],fill_value = 'extrapolate', kind='quadratic')
ft3 = scipy.interpolate.interp1d(t,res[:,2],fill_value = 'extrapolate', kind='quadratic')
plt.figure()
plt.plot(t,numpy.array([ft1(t),ft2(t),ft3(t)]).T,'-o')
variable_functions = {t1:ft1,t2:ft2,t3:ft3}
func1 = system.state_space_post_invert(f,ma,variable_functions=variable_functions)
# # func1,lambda1 = system.state_space_post_invert(f,ma,eq_dd,return_lambda = True)
states=pynamics.integration.integrate_odeint(func1,ini,t,rtol=tol,atol=tol,args=({'constants':system.constant_values},) )
# lambda2 = numpy.array([lambda1(item1,item2,system.constant_values) for item1,item2 in zip(t,states)])
KE = system.get_KE()
PE = system.getPEGravity(pNA) - system.getPESprings()
points = [pNA,pAB,pBC,pCtip]
#points = [item for item2 in points for item in [item2.dot(system.newtonian.x),item2.dot(system.newtonian.y)]]
points_output = PointsOutput(points,system)
y = points_output.calc(states)
#y.resize(y.shape[0],int(y.shape[1]/2),2)
plt.figure()
