def whipple_state_space(rider, speed):
""" x' = Ax + Bu + Fv
x = [phi,
delta,
phiDot,
deltaDot]
u = [Tphi,
Tdel]
v = [Fcl]
"""
bicycleModel = LinearLateralForce()
pathToData='/media/Data/Documents/School/UC Davis/Bicycle Mechanics/BicycleParameters/data/'
if rider == 'Jason':
bicycleName = 'Rigid'
elif rider == 'Charlie' or rider == 'Luke':
bicycleName = 'Rigidcl'
bike = bp.Bicycle(bicycleName, pathToData)
bike.add_rider(rider)
# set the model parameters
benchmarkPar = bp.io.remove_uncertainties(bike.parameters['Benchmark'])
benchmarkPar['xcl'] = bike.parameters['Measured']['xcl']
benchmarkPar['zcl'] = bike.parameters['Measured']['zcl']
moorePar = bicycle.benchmark_to_moore(benchmarkPar)
bicycleModel.set_parameters(moorePar)
# set the default equilibrium point
pitchAngle = bicycle.pitch_from_roll_and_steer(0., 0., moorePar['rf'],
moorePar['rr'], moorePar['d1'], moorePar['d2'], moorePar['d3'])
wheelAngSpeed = -speed / moorePar['rr']
equilibrium = np.zeros(len(bicycleModel.stateNames))
equilibrium[bicycleModel.stateNames.index('q5')] = pitchAngle
equilibrium[bicycleModel.stateNames.index('u6')] = wheelAngSpeed
bicycleModel.linear(equilibrium)
states = ['q4', 'q7', 'u4', 'u7']
inputs = ['Fcl', 'T4', 'T7']
outputs = ['q4', 'q7', 'u4', 'u7']
A, B, C, D = bicycleModel.reduce_system(states, inputs, outputs)
F = B[:, 0]
B = B[:, 1:]
return A, B, F
u_ind=[u2, u4, u5],
kd_eqs=kinematical,
q_dependent=[q3],
configuration_constraints=holonomic,
u_dependent=[u1, u3, u6],
velocity_constraints=nonholonomic,
)
# reminder: u1--yaw rate, u2--roll rate, u3--pitch rate, u4--steer rate, u5--rear wheel ang. vel., u6--front wheel ang. vel.
# kane.kindiffeq(kinematical)
(fr, frstar) = kane.kanes_equations(forceList, bodyList)
kdd = kane.kindiffdict()
bp = bi.benchmark_parameters()
mp = bi.benchmark_to_moore(bp)
rr = bp["rR"]
lam = bp["lam"]
basu_input = bi.basu_table_one_input()
mo_in = bi.basu_to_moore_input(basu_input, rr, lam)
# not include the l1, l2, mc and ic because of the rider
# which will be added into instrumented bicycle later.
para_dict = {
l1: mp["l1"],
l2: mp["l2"],
l3: mp["l3"],
l4: mp["l4"],
else:
f.close()
del f
from GyroBike import GyroBike
# create the Whipple model (with my parameters)
gyroNonLinear = GyroBike()
# load the benchmark parameters
pathToData='/media/Data/Documents/School/UC Davis/Bicycle Mechanics/BicycleParameters/data/'
gyro = bp.Bicycle('Gyro', pathToData, forceRawCalc=True)
gyro.add_rider('Child', reCalc=True)
benchmarkPar = bp.io.remove_uncertainties(gyro.parameters['Benchmark'])
# convert to my parameter set
moorePar = bicycle.benchmark_to_moore(benchmarkPar, oldMassCenter=False)
moorePar['mg'] = benchmarkPar['mD']
moorePar['ig11'] = benchmarkPar['IDxx']
moorePar['ig22'] = benchmarkPar['IDyy']
gyroNonLinear.set_parameters(moorePar)
# set the initial conditions to match Meijaard2007
speedNaught = 0.5
rollRateNaught = 0.5
pitchAngle = bicycle.pitch_from_roll_and_steer(0., 0., moorePar['rf'], moorePar['rr'],
moorePar['d1'], moorePar['d2'], moorePar['d3'])
wheelAngSpeed = -speedNaught / moorePar['rr']
gyroNonLinear.initialConditions[gyroNonLinear.stateNames.index('q5')] = pitchAngle
gyroNonLinear.initialConditions[gyroNonLinear.stateNames.index('u4')] = rollRateNaught
gyroNonLinear.initialConditions[gyroNonLinear.stateNames.index('u6')] = wheelAngSpeed
gyroNonLinear.initialConditions[gyroNonLinear.stateNames.index('u9')] = -5000. / 60. * 2 * pi
alparse.alparse('Whipple', 'Whipple', code='Python')
else:
f.close()
del f
from Whipple import LinearWhipple
# create the Whipple model (with my parameters)
whip = LinearWhipple()
# load the benchmark parameters
pathToData = '/media/Data/Documents/School/UC Davis/Bicycle Mechanics/BicycleParameters/data/'
benchmark = bp.Bicycle('Benchmark', pathToData)
benchmarkPar = bp.io.remove_uncertainties(benchmark.parameters['Benchmark'])
# convert to my parameter set
moorePar = bicycle.benchmark_to_moore(benchmarkPar, oldMassCenter=False)
whip.set_parameters(moorePar)
# set the initial conditions to match Meijaard2007
speedNaught = 4.6
u6Naught = -speedNaught / moorePar['rr']
rollRateNaught = 0.5
pitchAngle = bicycle.pitch_from_roll_and_steer(0., 0., moorePar['rf'],
moorePar['rr'], moorePar['d1'],
moorePar['d2'], moorePar['d3'])
# linearize about the nominal configuration
equilibrium = np.zeros(len(whip.stateNames))
equilibrium[whip.stateNames.index('q5')] = pitchAngle
equilibrium[whip.stateNames.index('u6')] = u6Naught
whip.linear(equilibrium)
riderPar = {
'IBxx': humanInertia[0, 0],
'IByy': humanInertia[1, 1],
'IBzz': humanInertia[2, 2],
'IBxz': humanInertia[2, 0],
'mB': humanMass,
'xB': humanCoM[0][0],
'yB': humanCoM[1][0],
'zB': humanCoM[2][0]
}
rigid = bp.Bicycle(bikeName, forceRawCalc=True, pathToData=pathToParameters)
benchmark = bp.rider.combine_bike_rider(rigid.parameters['Benchmark'],
riderPar)
benchmark = bp.io.remove_uncertainties(benchmark)
par = bicycle.benchmark_to_moore(benchmark)
# get the arm parameters
# note that the right and left arms have the same parameters due to symmetry, I
# should probably reduce the number of parameters in the analytical model to
# reflect this
# right upper arm, G
par['mg'] = h.B1.Mass
par['l5'] = h.B1.relCOM[2][0]
IG = h.B1.relInertia
par['ig11'] = IG[0, 0]
par['ig33'] = IG[2, 2]
par['d12'] = h.B1.length
# shoulders
else:
f.close()
del f
from GyroBike import LinearGyroBike
# create the linear gyrobike model
gyrobike = LinearGyroBike()
# create the gyro bike
pathToData = '/media/Data/Documents/School/UC Davis/Bicycle Mechanics/BicycleParameters/data/'
gyro = bp.Bicycle('Gyro', pathToData, forceRawCalc=True)
# set the model parameters
benchmarkPar = bp.io.remove_uncertainties(gyro.parameters['Benchmark'])
moorePar = bicycle.benchmark_to_moore(benchmarkPar)
moorePar['mg'] = benchmarkPar['mD']
moorePar['ig11'] = benchmarkPar['IDxx']
moorePar['ig22'] = benchmarkPar['IDyy']
gyrobike.set_parameters(moorePar)
# set the default equilibrium point
speedNaught = 0.5 # just over 1 mph, really slow walking
pitchAngle = bicycle.pitch_from_roll_and_steer(0., 0., moorePar['rf'],
moorePar['rr'], moorePar['d1'],
moorePar['d2'], moorePar['d3'])
wheelAngSpeed = -speedNaught / moorePar['rr']
equilibrium = np.zeros(len(gyrobike.stateNames))
equilibrium[gyrobike.stateNames.index('q5')] = pitchAngle
equilibrium[gyrobike.stateNames.index('u6')] = wheelAngSpeed
[u4, u6, u7], # roll rate, rear wheel rate, steer rate
kd_eqs=kinematical,
q_dependent=[q5], # pitch angle
configuration_constraints=[holonomic],
u_dependent=[u3, u5, u8], # yaw rate, pitch rate, front wheel rate
velocity_constraints=nonholonomic)
fr, frstar = kane.kanes_equations(forces, bodies)
# Validation of non-linear equations
print('Loading numerical input parameters.')
from dtk import bicycle
bp = bicycle.benchmark_parameters()
mp = bicycle.benchmark_to_moore(bp)
# load the input values specified in table one of Basu-Mandal2007
basu_input = bicycle.basu_table_one_input()
# convert the values to my coordinates and speeds
moore_input = bicycle.basu_to_moore_input(basu_input, bp['rR'], bp['lam'])
constant_substitutions = {}
for k, v in mp.items():
try:
exec('constant_substitutions[{}] = v'.format(k))
except NameError:
pass
dynamic_substitutions = {}
for k, v in moore_input.items():
else:
f.close()
del f
from GyroBike import LinearGyroBike
# create the linear gyrobike model
gyrobike = LinearGyroBike()
# create the gyro bike
pathToData='/media/Data/Documents/School/UC Davis/Bicycle Mechanics/BicycleParameters/data/'
gyro = bp.Bicycle('Gyro', pathToData, forceRawCalc=True)
# set the model parameters
benchmarkPar = bp.io.remove_uncertainties(gyro.parameters['Benchmark'])
moorePar = bicycle.benchmark_to_moore(benchmarkPar)
moorePar['mg'] = benchmarkPar['mD']
moorePar['ig11'] = benchmarkPar['IDxx']
moorePar['ig22'] = benchmarkPar['IDyy']
gyrobike.set_parameters(moorePar)
# set the default equilibrium point
speedNaught = 0.5 # just over 1 mph, really slow walking
pitchAngle = bicycle.pitch_from_roll_and_steer(0., 0., moorePar['rf'],
moorePar['rr'], moorePar['d1'], moorePar['d2'], moorePar['d3'])
wheelAngSpeed = -speedNaught / moorePar['rr']
equilibrium = np.zeros(len(gyrobike.stateNames))
equilibrium[gyrobike.stateNames.index('q5')] = pitchAngle
equilibrium[gyrobike.stateNames.index('u6')] = wheelAngSpeed
figDir = '../../../figures/extensions/'
# find the inertia of the humans without arms, this is with respect to the
# benchmark coordinate system and about the CoM of the subset of parts
humanMass, humanCoM, humanInertia = h.combine_inertia(('P', 'T', 'C', 'K1', 'K2', 'J1', 'J2'))
riderPar = {'IBxx': humanInertia[0, 0],
'IByy': humanInertia[1, 1],
'IBzz': humanInertia[2, 2],
'IBxz': humanInertia[2, 0],
'mB': humanMass,
'xB': humanCoM[0][0],
'yB': humanCoM[1][0],
'zB': humanCoM[2][0]}
rigid = bp.Bicycle(bikeName, forceRawCalc=True, pathToData=pathToParameters)
benchmark = bp.rider.combine_bike_rider(rigid.parameters['Benchmark'], riderPar)
benchmark = bp.io.remove_uncertainties(benchmark)
par = bicycle.benchmark_to_moore(benchmark)
# get the arm parameters
# note that the right and left arms have the same parameters due to symmetry, I
# should probably reduce the number of parameters in the analytical model to
# reflect this
# right upper arm, G
par['mg'] = h.B1.Mass
par['l5'] = h.B1.relCOM[2][0]
IG = h.B1.relInertia
par['ig11'] = IG[0, 0]
par['ig33'] = IG[2, 2]
par['d12'] = h.B1.length
# shoulders
[u4, u6, u7], # roll rate, rear wheel rate, steer rate
kd_eqs=kinematical,
q_dependent=[q5], # pitch angle
configuration_constraints=[holonomic],
u_dependent=[u3, u5, u8], # yaw rate, pitch rate, front wheel rate
velocity_constraints=nonholonomic)
fr, frstar = kane.kanes_equations(forces, bodies)
# Validation of non-linear equations
print('Loading numerical input parameters.')
from dtk import bicycle
bp = bicycle.benchmark_parameters()
mp = bicycle.benchmark_to_moore(bp)
# load the input values specified in table one of Basu-Mandal2007
basu_input = bicycle.basu_table_one_input()
# convert the values to my coordinates and speeds
moore_input = bicycle.basu_to_moore_input(basu_input, bp['rR'],
bp['lam'])
constant_substitutions = {}
for k, v in mp.items():
try:
exec('constant_substitutions[{}] = v'.format(k))
except NameError:
pass
dynamic_substitutions = {}