def system_initialisation(l_pendulum=0.5,
m_pendulum=1.,
f_max=1500,
l_attach=0.17):
"""Generates a oscillatory system and its default initial conditions"""
# Neural parameters for oscillatory system
d = 1.
w = np.array([[0, -5, -5, 0], [-5, 0, 0, -5], [5, -5, 0, 0], [-5, 5, 0,
0]])
b = np.array([3., 3., -3., -3.])
tau = np.array([0.02, 0.02, 0.1, 0.1])
# Pendulum parameters
pendulum_params = PendulumParameters()
pendulum_params.L = l_pendulum
pendulum_params.m = m_pendulum
pendulum = PendulumSystem(pendulum_params)
# Muscles parameters
m1_param = MuscleParameters()
m1_param.f_max = f_max
m2_param = MuscleParameters()
m2_param.f_max = f_max
m1 = Muscle(m1_param)
m2 = Muscle(m2_param)
muscles = MuscleSytem(m1, m2)
# Muscle_attachment
m1_origin = np.array([-l_attach, 0.0])
m1_insertion = np.array([0.0, -l_attach])
m2_origin = np.array([l_attach, 0.0])
m2_insertion = np.array([0.0, -l_attach])
muscles.attach(np.array([m1_origin, m1_insertion]),
np.array([m2_origin, m2_insertion]))
# Neural network
n_params = NetworkParameters()
n_params.D = d
n_params.w = w
n_params.b = b
n_params.tau = tau
neural_network = NeuralSystem(n_params)
# System creation
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
sys.add_neural_system(
neural_network) # Add neural network model to the system
# Default initial conditions
x0_p = np.array([0, 0.]) # Pendulum initial condition
x0_m = np.array([0., m1.L_OPT, 0.,
m2.L_OPT]) # Muscle Model initial condition
x0_n = np.array([-0.5, 1, 0.5, 1]) # Neural Network initial condition
x0 = np.concatenate((x0_p, x0_m, x0_n)) # System initial conditions
return sys, x0
def createMuscle(self, *args, **keywordArgs):
"""
Create a new muscle.
>>> muscle = network.createMuscle(name = 'M1')
Returns the :class:`muscle <Network.Muscle.Muscle>` that is created.
"""
muscle = Muscle(self, *args, **keywordArgs)
self.addObject(muscle)
return muscle
def plotRelationLceAPForces(muscle_stretch,muscle_stimulation=1.,l_opt=0.11):
# Defination of muscles
parameters = MuscleParameters()
# Create muscle object
muscle = Muscle(parameters)
# Instatiate isometric muscle system
sys = IsometricMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
sys.muscle.L_OPT = l_opt
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT] # x0[0] --> muscle stimulation intial value
# x0[1] --> muscle contracticle length initial value
# Set the time for integration
t_start = 0.0
t_stop = 0.2
time_step = 0.001
time = np.arange(t_start, t_stop, time_step)
# Store the results
l_ce = []
active = []
passive = []
tendon = []
# Run the experiment for different length of the MTU
for l in muscle_stretch:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=muscle_stimulation,
muscle_length=l)
l_ce.append(result.l_ce[-1])
active.append(result.active_force[-1])
passive.append(result.passive_force[-1])
tendon.append(result.tendon_force[-1])
plt.figure('Active/passive forces as function of l_ce\n'+
'(activation: {}, l_opt: {})'
.format(muscle_stimulation,l_opt))
plt.plot(l_ce, active,label='active force')
plt.plot(l_ce, passive,label='passive force')
plt.plot(l_ce, tendon,label='tendon force')
plt.legend()
plt.title('Isometric muscle experiment\nActive/passive forces as function '+
'of l_ce\n(activation: {}, l_opt: {})'.format(muscle_stimulation,l_opt))
plt.xlabel('l_ce [m]')
plt.ylabel('Force [N]')
axes = plt.gca()
axes.set_xlim([0.05,0.2])
axes.set_ylim([0,1700])
plt.grid()
def isotonic_experiment(muscle_stimulation, loads,
time_param=TimeParameters()):
# Muscle
muscle_parameters = MuscleParameters()
muscle = Muscle(muscle_parameters)
# Initial conditions
x0 = [0] * StatesIsotonic.NB_STATES.value
x0[StatesIsotonic.STIMULATION.value] = 0.
x0[StatesIsotonic.L_CE.value] = muscle.L_OPT
x0[StatesIsotonic.LOAD_POS.value] = muscle.L_OPT + muscle.L_SLACK
x0[StatesIsotonic.LOAD_SPEED.value] = 0.
# Containers
v_ce = []
tendon_force = []
# Integration
pylog.info("Running the experiments (this might take a while)...")
for load in loads:
# New load definition
mass_parameters = MassParameters()
mass_parameters.mass = load
mass = Mass(mass_parameters)
# System definition
sys = IsotonicMuscleSystem()
sys.add_muscle(muscle)
sys.add_mass(mass)
result = sys.integrate(x0=x0,
time=time_param.times,
time_step=time_param.t_step,
time_stabilize=time_param.t_stabilize,
stimulation=muscle_stimulation,
load=load)
# Result processing
if result.l_mtc[-1] > x0[StatesIsotonic.LOAD_POS.value]:
# Extension
index = result.v_ce.argmax()
v_ce.append(result.v_ce.max())
tendon_force.append(result.tendon_force[index])
else:
# Contraction
index = result.v_ce.argmin()
v_ce.append(result.v_ce.min())
tendon_force.append(result.tendon_force[index])
return v_ce, tendon_force
def exercise1f():
""" Exercise 1f
What happens to the force-velocity relationship when the stimulation is varied
between [0 - 1]?"""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
# Instantiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
# Evaluate for a single load
load = 100.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT, sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 1.25
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
# ---------------------------------------------
# maximum force over stimulation
# ---------------------------------------------
# Evaluate for different muscle stimulation
muscle_stimulation = np.arange(0, 1.1, 0.1)
max_active_force = []
max_passive_force = []
max_sum_force = []
# Begin plotting
for s in muscle_stimulation:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=s,
load=load)
if abs(min(result.active_force)) > max(result.active_force):
max_active_force.append(min(result.active_force))
else:
max_active_force.append(max(result.active_force))
if abs(min(result.passive_force)) > max(result.passive_force):
max_passive_force.append(min(result.passive_force))
else:
max_passive_force.append(max(result.passive_force))
max_sum_force.append(max_active_force[-1] + max_passive_force[-1])
plt.figure('Isotonic muscle active force - stimulation [0, 1]')
plt.plot(muscle_stimulation,
max_active_force,
label='maximum active force')
plt.plot(muscle_stimulation,
max_passive_force,
label='maximum passive force')
plt.plot(muscle_stimulation, max_sum_force, label='maximum sum force')
plt.xlabel('Stimulation [-]')
plt.ylabel('Muscle sum forces [N]')
plt.legend(loc='upper right')
plt.grid()
# ---------------------------------------------
# force - velocity over stimulation
# ---------------------------------------------
muscle_stimulation = np.arange(0, 1.1, 0.1)
# Begin plotting
for s in muscle_stimulation:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=s,
load=load)
plt.figure('Isotonic muscle active force - velocity')
plt.plot(result.v_ce[200:-1],
result.active_force[200:-1],
label='stimulation {:0.1f}'.format(s))
plt.figure('Isotonic muscle passive force - velocity')
plt.plot(result.v_ce[200:-1],
result.passive_force[200:-1],
label='stimulation {:0.1f}'.format(s))
plt.figure('Isotonic muscle sum forces - velocity')
plt.plot(result.v_ce[200:-1],
result.active_force[200:-1] + result.passive_force[200:-1],
label='stimulation {:0.1f}'.format(s))
plt.figure('Isotonic muscle active force - velocity')
plt.xlabel('Velocity contractile element [m/s]')
plt.ylabel('Active force [N]')
plt.legend(loc='upper right')
plt.grid()
plt.figure('Isotonic muscle passive force - velocity')
plt.xlabel('Velocity contractile element [m/s]')
plt.ylabel('Passive force [N]')
plt.legend(loc='upper right')
plt.grid()
plt.figure('Isotonic muscle sum forces - velocity')
plt.xlabel('Velocity contractile element [m/s]')
plt.ylabel('Sum forces [N]')
plt.legend(loc='upper right')
plt.grid()
# ---------------------------------------------
# Plot velocity - tension relation
# ---------------------------------------------
muscle_stimulation = np.arange(0, 1.1, 0.25)
load = np.arange(5, 1500, 20)
plt.figure('Velocity - Tension')
# Begin plotting
for s in muscle_stimulation:
(max_vce, active_force) = ex1d_for(sys, x0, time, time_step,
time_stabilize, s, load, False)
plt.plot(load, max_vce, label="stimulation {:0.1f}".format(s))
plt.title('Velocity [m/s] - Load [N]')
plt.xlabel('Load [N]')
plt.ylabel('Velocity [m/s]')
plt.legend(loc='lower right')
plt.grid()
def exercise1a():
""" Exercise 1a
The goal of this exercise is to understand the relationship
between muscle length and tension.
Here you will re-create the isometric muscle contraction experiment.
To do so, you will have to keep the muscle at a constant length and
observe the force while stimulating the muscle at a constant activation."""
# Defination of muscles
parameters = MuscleParameters()
pylog.warning("Loading default muscle parameters")
pylog.info(parameters.showParameters())
pylog.info("Use the parameters object to change the muscle parameters")
# Create muscle object
muscle = Muscle(parameters)
pylog.warning("Isometric muscle contraction to be completed")
# Instatiate isometric muscle system
sys = IsometricMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
muscle_stretches = np.arange(.12, .30, .002)
#muscle_tendon_forces = [] #Erase or comment
muscle_active_forces = []
muscle_passive_forces = []
total_force = []
contractile_element_length = []
# Evalute for a single muscle stretch
for muscle_stretch in muscle_stretches:
# Evalute for a single muscle stimulation
muscle_stimulation = 1.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT]
# x0[0] --> muscle stimulation intial value
# x0[1] --> muscle contracticle length initial value
# Set the time for integration
t_start = 0.0
t_stop = 0.3
time_step = 0.001
time = np.arange(t_start, t_stop, time_step)
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=muscle_stimulation,
muscle_length=muscle_stretch)
# muscle_tendon_forces.append(result.tendon_force[-1])#Erase or comment
muscle_active_forces.append(result.active_force[-1])
muscle_passive_forces.append(result.passive_force[-1])
total_force.append(result.active_force[-1] + result.passive_force[-1])
contractile_element_length.append(result.l_ce[-1])
# plotXY(time,result.l_ce,'Time [s]','Contractile Element Length [m]','Active',
# 'Isometric Muscle: Contractile Element Length vs Time',
# 'Isometric Muscle: Contractile Element Length vs Time')
# plotXY(result.l_ce,result.active_force,'Contractile Element Length [m]','Active Force [N]','Active',
# 'Isometric Muscle: Contractile Element Length vs Force',
# 'Isometric Muscle: Contractile Element Length vs Force')
# plt.plot(result.l_ce, result.passive_force, label='passive')
# plt.plot(result.l_ce, result.active_force+result.passive_force, label='total')
# Plotting
plt.figure('Isometric Muscle: L_ce vs Force')
plt.plot(contractile_element_length, muscle_active_forces, label='active')
plt.plot(contractile_element_length,
muscle_passive_forces,
label='passive')
plt.plot(contractile_element_length, total_force, label='total')
plt.title('Isometric Muscle: Stretch Length vs Force')
plt.xlabel('Contractile Element Length [m]')
plt.ylabel('Muscle Force [N]')
plt.legend(loc='upper right')
plt.grid()
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
pylog.warning("Isotonic muscle contraction to be implemented")
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
# Evaluate for a single muscle stimulation
muscle_stimulation = 1.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT, sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 1.25
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
# Set max_vce
max_vce = []
# ---------------------------------------------
# Small load experiment
# ---------------------------------------------
load_table_small = [5, 10, 20, 50, 100]
# Begin plotting
plt.figure('Isotonic muscle experiment - load [10, 200] [N]')
max_vce_small = ex1d_for(sys, x0, time, time_step, time_stabilize,
muscle_stimulation, load_table_small, False)
plt.title('Isotonic muscle experiment - load [5, 140] [N]')
plt.xlabel('Time [s]')
plt.ylabel('Muscle contractile velocity [m/s]')
plt.legend(loc='upper right')
plt.grid()
# ---------------------------------------------
# Big load experiment
# ---------------------------------------------
load_table_big = [150, 200, 220, 250, 500, 1000, 1500]
# Begin plotting
plt.figure('Isotonic muscle experiment - load [150, 1500] [N]')
max_vce += ex1d_for(sys, x0, time, time_step, time_stabilize,
muscle_stimulation, load_table_big, True)
plt.title('Isotonic muscle experiment - load [150, 1500] [N]')
plt.xlabel('Time [s]')
plt.ylabel('Muscle contractile velocity [m/s]')
plt.legend(loc='upper right')
plt.grid()
# ---------------------------------------------
# Plot velocity - tension relation
# ---------------------------------------------
load = np.arange(5, 2500, 200)
(max_vce, active_force) = ex1d_for(sys, x0, time, time_step,
time_stabilize, muscle_stimulation,
load, False)
fig = plt.figure('Velocity - Tension')
ax = fig.add_subplot(111)
# Plot comments and line at 0 value
min_val = 0.0
if min(map(abs, max_vce)) not in max_vce:
min_val = -min(map(abs, max_vce))
else:
min_val = min(map(abs, max_vce))
xy = (load[max_vce.index(min_val)], min_val)
xytext = (load[max_vce.index(min_val)] + 50, min_val)
ax.annotate('load = {:0.1f}'.format(152.2), xy=xy, xytext=xytext)
plt.title('Velocity [m/s] - Tension [N]')
plt.xlabel('Tension [N]')
plt.ylabel('Velocity [m/s]')
plt.grid()
plt.plot(load, max_vce)
plt.plot(load[max_vce.index(min_val)], min_val, 'o')
def exercise3():
""" Main function to run for Exercise 3.
Parameters
----------
None
Returns
-------
None
"""
# Define and Setup your pendulum model here
# Check Pendulum.py for more details on Pendulum class
P_params = PendulumParameters() # Instantiate pendulum parameters
P_params.L = 0.5 # To change the default length of the pendulum
P_params.m = 1. # To change the default mass of the pendulum
pendulum = PendulumSystem(P_params) # Instantiate Pendulum object
#### CHECK OUT Pendulum.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
# Define and Setup your pendulum model here
# Check MuscleSytem.py for more details on MuscleSytem class
M1_param = MuscleParameters() # Instantiate Muscle 1 parameters
M1_param.f_max = 1500 # To change Muscle 1 max force
M2_param = MuscleParameters() # Instantiate Muscle 2 parameters
M2_param.f_max = 1500 # To change Muscle 2 max force
M1 = Muscle(M1_param) # Instantiate Muscle 1 object
M2 = Muscle(M2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
muscles = MuscleSytem(M1, M2) # Instantiate Muscle System with two muscles
pylog.info('Muscle system initialized \n {} \n {}'.format(
M1.parameters.showParameters(),
M2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.array([-0.17, 0.0]) # Origin of Muscle 1
m1_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 1
m2_origin = np.array([0.17, 0.0]) # Origin of Muscle 2
m2_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.array([m1_origin, m1_insertion]),
np.array([m2_origin, m2_insertion]))
##### Neural Network #####
# The network consists of four neurons
N_params = NetworkParameters() # Instantiate default network parameters
# Similarly to change w -> N_params.w = (4x4) array
# From lecture 4, slide 85 -> Generate oscillations !!
N_params.D = 2.
N_params.tau = [0.02,0.02,0.1,0.1]
N_params.b = [3.0,3.0,-3.0,-3.0]
N_params.w = [[0,-5,-5,0], # 1 <- 2
[-5,0,0,-5],
[5,-5,0,-5],
[-5,5,0,0]]
# Create a new neural network with above parameters
neural_network = NeuralSystem(N_params)
pylog.info('Neural system initialized \n {}'.format(
N_params.showParameters()))
# Create system of Pendulum, Muscles and neural network using SystemClass
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
# Add the neural network to the system
sys.add_neural_system(neural_network)
##### Time #####
t_max = 2.5 # Maximum simulation time
time = np.arange(0., t_max, 0.001) # Time vector
##### Model Initial Conditions #####
x0_P = np.array([0., 0.]) # Pendulum initial condition
# Muscle Model initial condition
x0_M = np.array([0., M1.L_OPT, 0., M2.L_OPT])
x0_N = np.array([-0.5, 1, 0.5, 1]) # Neural Network Initial Conditions
x0 = np.concatenate((x0_P, x0_M, x0_N)) # System initial conditions
##### System Simulation #####
# For more details on System Simulation check SystemSimulation.py
# SystemSimulation is used to initialize the system and integrate
# over time
sim = SystemSimulation(sys) # Instantiate Simulation object
# Add external inputs to neural network
# sim.add_external_inputs_to_network(np.ones((len(time), 4)))
#ext_in = np.ones((len(time), 4))
#ext_in[:,2] = 0.2
#ext_in[:,3] = 0.2
#sim.add_external_inputs_to_network(ext_in)
sim.initalize_system(x0, time) # Initialize the system state
# Integrate the system for the above initialized state and time
sim.simulate()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
res = sim.results()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
#res = sim.results()
# In order to obtain internal states of the muscle
# you can access the results attribute in the muscle class
muscle1_results = sim.sys.muscle_sys.Muscle1.results
muscle2_results = sim.sys.muscle_sys.Muscle2.results
# Plotting the phase
fig = plt.figure('Pendulum')
plt.title('Pendulum Phase')
plt.plot(res[:, 1], res[:, 2])
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad/s]')
plt.grid()
fig.tight_layout()
fig.savefig('graphs/PendulumPhase.png')
# Plotting the neuronal activation
# Access the neurons outputs:
# [t] theta theta. A1 lCE1 A2 lCE2 m1 m2 m3 m4
fig = plt.figure('Neuron output')
plt.title('Membrane potentials')
plt.plot(res[:, 0], res[:, 7],label='m1')
plt.plot(res[:, 0], res[:, 8],label='m2')
plt.plot(res[:, 0], res[:, 9],label='m3')
plt.plot(res[:, 0], res[:, 10],label='m4')
plt.xlabel('Time [s]')
plt.ylabel('Potential')
plt.legend()
plt.grid()
fig.tight_layout()
fig.savefig('graphs/MembranePotentials.png')
if DEFAULT["save_figures"] is False:
plt.show()
else:
figures = plt.get_figlabels()
pylog.debug("Saving figures:\n{}".format(figures))
for fig in figures:
plt.figure(fig)
save_figure(fig)
plt.close(fig)
# To animate the model, use the SystemAnimation class
# Pass the res(states) and systems you wish to animate
simulation = SystemAnimation(
res,
sim.sys.pendulum_sys,
sim.sys.muscle_sys,
sim.sys.neural_sys)
# To start the animation
simulation.animate()
# 3.b
ext_in = np.ones((len(time), 4))*0.0
plotExternalDrive(sys,x0,ext_in,typ='low')
ext_in = np.ones((len(time), 4))
plotExternalDrive(sys,x0,ext_in,typ='high')
ext_in = np.ones((len(time), 4))
ext_in[:,0] *= 0.1
ext_in[:,1] *= 0.1
plotExternalDrive(sys,x0,ext_in,typ='asymmetric')
def exercise1c():
"""describe how fiber length influences the force-length curve. Compare
a muscle comprised of short muscle fibers to a muscle comprised of
long muscle fibers. Change the parameter, you can use
system_parameters.py::MuscleParameters before instantiating the muscle
No more than 2 plots are required.
"""
# Defination of muscles
parameters = MuscleParameters()
pylog.warning("Loading default muscle parameters")
pylog.info(parameters.showParameters())
pylog.info("Use the parameters object to change the muscle parameters")
# Create muscle object
muscle = Muscle(parameters)
pylog.warning("Isometric muscle contraction to be completed")
# Instatiate isometric muscle system
sys = IsometricMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
muscle_lengths = np.arange(.1, .26, .03)
max_muscle_active_forces = []
max_muscle_passive_forces = []
max_total_force = []
max_force_stretch = []
# Evalute for a single muscle stretch
for muscle_length in muscle_lengths:
parameters.l_opt = muscle_length
muscle = Muscle(parameters)
pylog.warning("Isometric muscle contraction to be completed")
# Instatiate isometric muscle system
sys = IsometricMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
if muscle_length < .16:
start_stretch_length = .16
else:
start_stretch_length = muscle_length
muscle_stretches = np.arange(
start_stretch_length, 1.2 * muscle_length + .16,
(1.2 * muscle_length + .16 - start_stretch_length) / 40)
muscle_active_forces = []
muscle_passive_forces = []
total_force = []
# Evalute for a single muscle stretch
for muscle_stretch in muscle_stretches:
# Evalute for a single muscle stimulation
muscle_stimulation = 1.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT]
# x0[0] --> muscle stimulation intial value
# x0[1] --> muscle contracticle length initial value
# Set the time for integration
t_start = 0.0
t_stop = 0.3
time_step = 0.001
time = np.arange(t_start, t_stop, time_step)
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=muscle_stimulation,
muscle_length=muscle_stretch)
muscle_active_forces.append(result.active_force[-1])
muscle_passive_forces.append(result.passive_force[-1])
total_force.append(result.active_force[-1] +
result.passive_force[-1])
max_muscle_active_forces.append(max(muscle_active_forces))
active_max_index = muscle_active_forces.index(
max(muscle_active_forces))
max_muscle_passive_forces.append(
muscle_passive_forces[active_max_index])
max_total_force.append(total_force[active_max_index])
max_force_stretch.append(muscle_stretches[active_max_index])
# Plotting max force for each muscle length over different stretch values. Uncomment to see (adds ~8 plots)
# plt.figure('Isometric muscle experiment. L_opt = %.2f'%(muscle_length))
# plt.plot(muscle_stretches, muscle_active_forces, label='active')
# plt.plot(muscle_stretches, muscle_passive_forces, label='passive')
# plt.plot(muscle_stretches, total_force, label='total')
# plt.title('Isometric muscle experiment 1C, L_opt = %.2f'%(muscle_length))
# plt.xlabel('Stretch Length [m]')
# plt.ylabel('Muscle Force [N]')
# plt.legend(loc='upper left')
# plt.grid()
# Plotting active on its own
plt.figure('Isometric muscle experiment, Active Force')
plt.plot(muscle_stretches,
muscle_active_forces,
label=('L_opt = %.2f' % (muscle_length)))
plt.title('Isometric muscle experiment: Active Force vs L_Opt')
plt.xlabel('Stretch Length [m]')
plt.ylabel('Active Muscle Force [N]')
plt.legend(loc='upper left')
plt.grid()
# Plotting passive on its own
plt.figure('Isometric muscle experiment, Passive Force')
plt.plot(muscle_stretches,
muscle_passive_forces,
label=('L_opt = %.2f' % (muscle_length)))
plt.title('Isometric muscle experiment: Passive Force vs L_Opt')
plt.xlabel('Stretch Length [m]')
plt.ylabel('Passive Muscle Force [N]')
plt.legend(loc='upper left')
plt.grid()
# Plot max vals
plt.figure('Isometric muscle experiment max Force')
plt.plot(muscle_lengths, max_muscle_active_forces, label='active')
#plt.plot(muscle_lengths, max_muscle_passive_forces, label='passive')
#plt.plot(muscle_lengths, max_total_force, label='total')
plt.title('Isometric muscle experiment 1C, Max')
plt.xlabel('Muscle Optimal Length [m]')
plt.ylabel('Max Muscle Force [N]')
plt.legend(loc='upper left')
plt.grid()
# print(max_muscle_active_forces)
# Plot max stretch lengths of max vals
plt.figure('Isometric muscle experiment max Force stretch')
plt.plot(muscle_lengths, max_force_stretch, label='active')
#plt.plot(muscle_lengths, max_muscle_passive_forces, label='passive')
#plt.plot(muscle_lengths, max_total_force, label='total')
plt.title('Isometric muscle experiment 1C, Max Stretch')
plt.xlabel('Muscle Optimal Length [m]')
plt.ylabel('Muscle Stretch of Max Force [m]')
plt.legend(loc='upper left')
plt.grid()
def exercise2b():
""" Main function to run for Exercise 2b.
Parameters
----------
None
Returns
-------
None
"""
# Define and Setup your pendulum model here
# Check PendulumSystem.py for more details on Pendulum class
pendulum_params = PendulumParameters() # Instantiate pendulum parameters
pendulum_params.L = 0.5 # To change the default length of the pendulum
pendulum_params.m = 1. # To change the default mass of the pendulum
pendulum = PendulumSystem(pendulum_params) # Instantiate Pendulum object
#### CHECK OUT PendulumSystem.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
# Define and Setup your pendulum model here
# Check MuscleSytem.py for more details on MuscleSytem class
M1_param = MuscleParameters() # Instantiate Muscle 1 parameters
M1_param.f_max = 1500 # To change Muscle 1 max force
M2_param = MuscleParameters() # Instantiate Muscle 2 parameters
M2_param.f_max = 1500 # To change Muscle 2 max force
M1 = Muscle(M1_param) # Instantiate Muscle 1 object
M2 = Muscle(M2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
muscles = MuscleSytem(M1, M2) # Instantiate Muscle System with two muscles
pylog.info('Muscle system initialized \n {} \n {}'.format(
M1.parameters.showParameters(), M2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.array([-0.17, 0.0]) # Origin of Muscle 1
m1_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 1
m2_origin = np.array([0.17, 0.0]) # Origin of Muscle 2
m2_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.array([m1_origin, m1_insertion]),
np.array([m2_origin, m2_insertion]))
# Create a system with Pendulum and Muscles using the System Class
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
##### Time #####
t_max = 20 # Maximum simulation time
time = np.arange(0., t_max, 0.005) # Time vector
##### Model Initial Conditions #####
x0_P = np.array([np.pi / 4, 0.]) # Pendulum initial condition
# Muscle Model initial condition
x0_M = np.array([0., M1.L_OPT, 0., M2.L_OPT])
x0 = np.concatenate((x0_P, x0_M)) # System initial conditions
##### System Simulation #####
# For more details on System Simulation check SystemSimulation.py
# SystemSimulation is used to initialize the system and integrate
# over time
sim1 = SystemSimulation(sys) # Instantiate Simulation object
# Add muscle activations to the simulation
# Here you can define your muscle activation vectors
# that are time dependent
#act1 = np.ones((len(time), 1)) * 1.
#act2 = np.ones((len(time), 1)) * 0.05
act1 = np.array([np.sin(time)]).T
act2 = np.array([-np.sin(time)]).T
activations = np.hstack((act1, act2))
# Method to add the muscle activations to the simulation
sim1.add_muscle_activations(activations)
# Simulate the system for given time
sim1.initalize_system(x0, time) # Initialize the system state
#: If you would like to perturb the pedulum model then you could do
# so by
#sim.sys.pendulum_sys.parameters.PERTURBATION = True
# The above line sets the state of the pendulum model to zeros between
# time interval 1.2 < t < 1.25. You can change this and the type of
# perturbation in
# pendulum_system.py::pendulum_system function
# Integrate the system for the above initialized state and time
sim1.simulate()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
res1 = sim1.results()
sim2 = SystemSimulation(sys) # Instantiate Simulation object
sim2.add_muscle_activations(activations)
# Simulate the system for given time
sim2.initalize_system(x0, time) # Initialize the system state
#add perturbation
sim2.sys.pendulum_sys.parameters.PERTURBATION = True
# Integrate the system for the above initialized state and time
sim2.simulate()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
res2 = sim2.results()
# In order to obtain internal states of the muscle
# you can access the results attribute in the muscle class
muscle1_results = sim1.sys.muscle_sys.Muscle1.results
muscle2_results = sim1.sys.muscle_sys.Muscle2.results
# Plotting the results
plt.figure('Pendulum')
plt.title('Pendulum Phase')
plt.plot(res1[:, 1], res1[:, 2])
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad.s]')
plt.grid()
plt.figure('Pendulum with perturbation')
plt.title('Pendulum Phase')
plt.plot(res2[:, 1], res2[:, 2])
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad.s]')
plt.grid()
plt.figure('Activation Wave Forms')
plt.title('Activation Wave Forms')
plt.plot(time, act1)
plt.plot(time, act2)
plt.xlabel('Time [s]')
plt.ylabel('Activation')
plt.legend(('Actication muscle 1', 'Activation muscle 2'))
plt.grid
poincare_crossings(res1, 0.5, 1, "poincare_cross")
# To animate the model, use the SystemAnimation class
# Pass the res(states) and systems you wish to animate
simulation1 = SystemAnimation(res1, pendulum, muscles)
simulation2 = SystemAnimation(res2, pendulum, muscles)
# To start the animation
if DEFAULT["save_figures"] is False:
simulation1.animate()
simulation2.animate()
def exercise2c():
pendulum_params = PendulumParameters() # Instantiate pendulum parameters
pendulum_params.L = 0.5 # To change the default length of the pendulum
pendulum_params.m = 1. # To change the default mass of the pendulum
pendulum = PendulumSystem(pendulum_params) # Instantiate Pendulum object
#### CHECK OUT PendulumSystem.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
# Define and Setup your pendulum model here
# Check MuscleSytem.py for more details on MuscleSytem class
M1_param = MuscleParameters() # Instantiate Muscle 1 parameters
M1_param.f_max = 1500 # To change Muscle 1 max force
M2_param = MuscleParameters() # Instantiate Muscle 2 parameters
M2_param.f_max = 1500 # To change Muscle 2 max force
M1 = Muscle(M1_param) # Instantiate Muscle 1 object
M2 = Muscle(M2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
muscles = MuscleSytem(M1, M2) # Instantiate Muscle System with two muscles
pylog.info('Muscle system initialized \n {} \n {}'.format(
M1.parameters.showParameters(), M2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.array([-0.17, 0.0]) # Origin of Muscle 1
m1_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 1
m2_origin = np.array([0.17, 0.0]) # Origin of Muscle 2
m2_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.array([m1_origin, m1_insertion]),
np.array([m2_origin, m2_insertion]))
# Create a system with Pendulum and Muscles using the System Class
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
##### Model Initial Conditions #####
x0_P = np.array([0, 0.]) # Pendulum initial condition
# Muscle Model initial condition
x0_M = np.array([0., M1.L_OPT, 0., M2.L_OPT])
x0 = np.concatenate((x0_P, x0_M)) # System initial conditions
##### System Simulation #####
# For more details on System Simulation check SystemSimulation.py
# SystemSimulation is used to initialize the system and integrate
# over time
sim = SystemSimulation(sys) # Instantiate Simulation object
#Frequency effect :
stim_frequency = np.array([0.05, 0.1, 0.5, 1, 5, 10, 50, 100, 500]) #in Hz
stim_amplitude = 1 # belongs to 0-1
phase = np.pi
frequency_pendelum = np.zeros(len(stim_frequency))
amplitude_pendelum = np.zeros(len(stim_frequency))
for j, frequency in enumerate(stim_frequency):
t_max = 5 / frequency # Maximum simulation time
time_step = 0.001 * (1 / frequency)
time = np.arange(0., t_max, time_step) # Time vector
act1 = np.zeros((len(time), 1))
act2 = np.zeros((len(time), 1))
act1[:,
0] = stim_amplitude * (1 +
np.sin(2 * np.pi * frequency * time)) / 2
act2[:, 0] = stim_amplitude * (
1 + np.sin(2 * np.pi * frequency * time + phase)) / 2
activations = np.hstack((act1, act2))
sim.add_muscle_activations(activations)
sim.initalize_system(x0, time) # Initialize the system state
sim.simulate()
res = sim.results()
#computing the freuquency and amplitude
angular_position = res[:, 1]
#signal_stat = signal[index_start:len(signal)]
start_index = int(len(angular_position) / 2)
final_index = (len(angular_position))
index_zeros = np.where(
np.diff(np.sign(angular_position[start_index:final_index])))[
0] #np.where(signal_stat==0)[0]
deltas = np.diff(index_zeros)
delta = np.mean(deltas)
frequency_pendelum[j] = 1 / (2 * delta * time_step)
signal = angular_position[start_index:len(angular_position)]
amplitude = (np.max(signal) - np.min(signal)) / 2
amplitude_pendelum[j] = amplitude
plt.figure()
plt.subplot(121)
plt.loglog(stim_frequency, frequency_pendelum)
plt.grid()
plt.xlabel('Stimulation Frequency [Hz]')
plt.ylabel('Pendulum Oscillation Frequency [Hz]')
plt.subplot(122)
plt.loglog(stim_frequency, amplitude_pendelum)
plt.grid()
plt.xlabel('Stimulation Frequency [Hz]')
plt.ylabel('Pendulum Oscillation Amplitude [rad]')
plt.savefig('2c.png')
plt.show()
stim_frequency = 10 #in Hz
stim_amplitude = np.arange(0, 1.1, 0.1)
frequency_pendelum = np.zeros(len(stim_amplitude))
amplitude_pendelum = np.zeros(len(stim_amplitude))
for j, amplitude_ in enumerate(stim_amplitude):
t_max = 5 / stim_frequency # Maximum simulation time
time_step = 0.001 * (1 / stim_frequency)
time = np.arange(0., t_max, time_step) # Time vector
act1 = np.zeros((len(time), 1))
act2 = np.zeros((len(time), 1))
act1[:,
0] = amplitude_ * (1 +
np.sin(2 * np.pi * stim_frequency * time)) / 2
act2[:, 0] = amplitude_ * (
1 + np.sin(2 * np.pi * stim_frequency * time + phase)) / 2
activations = np.hstack((act1, act2))
sim.add_muscle_activations(activations)
sim.initalize_system(x0, time) # Initialize the system state
sim.simulate()
res = sim.results()
#computing the freuquency and amplitude
angular_position = res[:, 1]
#signal_stat = signal[index_start:len(signal)]
start_index = int(len(angular_position) / 2)
final_index = (len(angular_position))
index_zeros = np.where(
np.diff(np.sign(angular_position[start_index:final_index])))[
0] #np.where(signal_stat==0)[0]
deltas = np.diff(index_zeros)
delta = np.mean(deltas)
frequency_pendelum[j] = 1 / (2 * delta * time_step)
signal = angular_position[start_index:len(angular_position)]
amplitude = (np.max(signal) - np.min(signal)) / 2
amplitude_pendelum[j] = amplitude
frequency_pendelum[0] = 0
plt.figure()
plt.subplot(121)
plt.plot(stim_amplitude, frequency_pendelum)
plt.grid()
plt.xlabel('Stimulation Amplitude [rad]')
plt.ylabel('Pendulum Oscillation Frequency [Hz]')
plt.subplot(122)
plt.plot(stim_amplitude, amplitude_pendelum)
plt.grid()
plt.xlabel('Stimulation Amplitude[rad]')
plt.ylabel('Pendulum Oscillation Amplitude [rad]')
plt.savefig('2c_amplitude.png')
plt.show()
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
pylog.warning("Isotonic muscle contraction to be implemented")
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
# Evalute for a single load
load = 100.
# Evalute for a single muscle stimulation
muscle_stimulation = 1.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT, sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.5
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
loads = np.arange(20, 351, 10)
velocities = []
for index, load in enumerate(loads):
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=load)
if (result.l_mtc[-1] < sys.muscle.L_OPT + sys.muscle.L_SLACK):
velocities.append(np.max(result.v_ce))
print('max')
else:
velocities.append(np.min(result.v_ce))
print('min')
#Muscle contracile Velocity - Tension (load) relationship
plt.figure('Isotonic muscle experiment')
plt.title('Isotonic muscle experiment')
plt.xlabel('Muscle Contractile Velocity [m/s]')
plt.ylabel('Tension (load) [N]')
plt.plot(velocities, loads)
plt.grid()
#For different stimulations 1.f
muscle_stimulation = np.arange(0, 1.1, 0.2)
plt.figure('Isotonic muscle exp with different stimulations')
plt.title('Isotonic muscle experiment with different stimulations')
for stim in muscle_stimulation:
velocities = []
for index, load in enumerate(loads):
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=stim,
load=load)
if (result.l_mtc[-1] < sys.muscle.L_OPT + sys.muscle.L_SLACK):
velocities.append(np.max(result.v_ce))
else:
velocities.append(np.min(result.v_ce))
plt.xlabel('Muscle Contractile Velocity [m/s]')
plt.ylabel('Tension (load) [N]')
plt.plot(velocities, loads)
plt.legend(('0', '0.2', '0.4', '0.6', '0.8', '1.0'))
plt.grid()
def exercise1a():
""" Exercise 1a
The goal of this exercise is to understand the relationship
between muscle length and tension.
Here you will re-create the isometric muscle contraction experiment.
To do so, you will have to keep the muscle at a constant length and
observe the force while stimulating the muscle at a constant activation."""
# Defination of muscles
parameters = MuscleParameters()
pylog.warning("Loading default muscle parameters")
pylog.info(parameters.showParameters())
pylog.info("Use the parameters object to change the muscle parameters")
# Create muscle object
muscle = Muscle(parameters)
# Instatiate isometric muscle system
sys = IsometricMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT]
# x0[0] --> muscle stimulation intial value
# x0[1] --> muscle contracticle length initial value
# Set the time for integration
t_start = 0.0
t_stop = 0.5
time_step = 0.001
time = np.arange(t_start, t_stop, time_step)
# Evalute for a single muscle stimulation
muscle_stimulation = np.arange(0, 1., 0.2)
# Several muscle stretch
muscle_stretches = np.arange(0, 0.3, 0.01)
active_active = []
for stim in muscle_stimulation:
active_forces = []
passive_forces = []
total = []
lengths = []
for stretch in muscle_stretches:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=stim,
muscle_length=stretch)
active_forces.append(result.active_force[-1])
passive_forces.append(result.passive_force[-1])
total.append(result.active_force[-1] + result.passive_force[-1])
lengths.append(result.l_ce[-1])
active_active.append(active_forces)
# Plotting
plt.figure('Isometric muscle experiment 1')
plt.plot(lengths, active_forces)
plt.plot(lengths, passive_forces)
plt.plot(lengths, total)
plt.title('Isometric muscle experiment stimulation')
plt.xlabel('Muscle stretch')
plt.ylabel('Muscle force')
plt.legend(('Active', 'Passive', 'Total'))
plt.grid()
plt.show()
# Plotting
plt.figure('Isometric muscle experiment 2')
for i in range(len(muscle_stimulation)):
plt.plot(lengths, active_active[i])
plt.title('Isometric muscle experiment')
plt.xlabel('Muscle stretch')
plt.ylabel('Muscle force')
plt.legend(muscle_stimulation)
plt.grid()
plt.show()
# Plotting
#plt.figure('Isotonic muscle experiment')
#plt.plot(result.time, result.v_ce)
#plt.title('Isotonic muscle experiment')
#plt.xlabel('Time [s]')
#plt.ylabel('Muscle contractilve velocity')
#plt.grid()
#muscle with longer l_opt
muscle.L_OPT = 0.5
muscle_stimulation = 1.
lce = []
totalF = []
activeF = []
passiveF = []
for stretch in muscle_stretches:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=muscle_stimulation,
muscle_length=stretch)
activeF.append(result.active_force[-1])
passiveF.append(result.passive_force[-1])
lce.append(result.l_ce[-1])
totalF.append(result.active_force[-1] + result.passive_force[-1])
plt.figure('muscle with l_opt=0.5')
plt.title('muscle with l_opt=0.5')
plt.plot(lce, activeF)
plt.plot(lce, passiveF)
plt.plot(lce, totalF)
plt.xlabel('Muscle Stretch')
plt.ylabel('Force')
plt.ylim((0, 4000))
plt.legend(('Active Force', 'Passive Force', 'Total Force'))
plt.grid()
#muscle with shorter l_opt
t_start = 0.0
t_stop = 1
time_step = 0.005
time = np.arange(t_start, t_stop, time_step)
muscle_stretches = np.arange(0, 0.3, 0.01)
muscle.L_OPT = 0.075
muscle_stimulation = 1.
lce = []
totalF = []
activeF = []
passiveF = []
plt.figure('muscle with l_opt=0.075')
for stretch in muscle_stretches:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=muscle_stimulation,
muscle_length=stretch)
activeF.append(result.active_force[-1])
passiveF.append(result.passive_force[-1])
lce.append(result.l_ce[-1])
totalF.append(result.active_force[-1] + result.passive_force[-1])
plt.title('muscle with l_opt=0.075')
plt.plot(lce, activeF)
plt.plot(lce, passiveF)
plt.plot(lce, totalF)
plt.xlabel('Muscle Stretch')
plt.ylabel('Force')
plt.ylim((0, 4000))
plt.legend(('Active Force', 'Passive Force', 'Total Force'))
plt.grid()
def exercise1a():
""" Exercise 1a
The goal of this exercise is to understand the relationship
between muscle length and tension.
Here you will re-create the isometric muscle contraction experiment.
To do so, you will have to keep the muscle at a constant length and
observe the force while stimulating the muscle at a constant activation."""
# Defination of muscles
parameters = MuscleParameters()
pylog.warning("Loading default muscle parameters")
pylog.info(parameters.showParameters())
pylog.info("Use the parameters object to change the muscle parameters")
# Create muscle object
muscle = Muscle(parameters)
pylog.warning("Isometric muscle contraction to be completed")
# Instatiate isometric muscle system
sys = IsometricMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.l_opt # To get the muscle optimal length
#x0 = [0.0, sys.muscle.L_OPT]
# Evalute for a single muscle stretch
muscle_stretch = 0.2
# Evalute for a single muscle stimulation
muscle_stimulation = 1.
# Set the initial condition
x0 = [0.0, sys.muscle.l_opt]
# x0[0] --> muscle stimulation intial value
# x0[1] --> muscle contracticle length initial value
# Set the time for integration
t_start = 0.0
t_stop = 0.2
time_step = 0.001
time = np.arange(t_start, t_stop, time_step)
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=muscle_stimulation,
muscle_length=muscle_stretch)
# Plotting
plt.figure('Isometric muscle experiment')
plt.plot(result.time, result.l_ce)
plt.title('Isometric muscle experiment')
plt.xlabel('Time [s]')
plt.ylabel('Muscle contracticle length [m]')
plt.grid()
muscle_stretches = np.arange(0, muscle_stretch, 0.001)
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### code for 1a
pylog.info(
"1a. relationship between forces and contractile element length")
length_start = 0.0
length_stop = 0.3
length_step = 0.005
muscle_lengths = np.arange(length_start, length_stop, length_step)
active_forces = []
passive_forces = []
total_forces = []
element_lengths = []
for temp_length in muscle_lengths:
temp_result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=muscle_stimulation,
muscle_length=temp_length)
temp_active_force = temp_result.active_force[-1]
temp_passive_force = temp_result.passive_force[-1]
tenp_total_force = temp_active_force + temp_passive_force
temp_element_length = temp_result.l_ce[-1]
active_forces = active_forces + [temp_active_force]
passive_forces = passive_forces + [temp_passive_force]
total_forces = total_forces + [tenp_total_force]
element_lengths = element_lengths + [temp_element_length]
plt.figure("1a. Isometric muscle experiment (muscle_stimulation == 1)")
plt.plot(element_lengths, active_forces)
plt.plot(element_lengths, passive_forces)
plt.plot(element_lengths, total_forces)
plt.title('Isometric Muscle Experiment (muscle_stimulation == 1)')
plt.xlabel('Muscle contracticle length [m]')
plt.ylabel('Tension [N]')
plt.legend(("Active Force", "Passive Force", "Total force"))
plt.grid()
plt.show()
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### code for 1b
pylog.info(
"1b. relationship between forces and contractile element length with different stimulations"
)
length_start = 0.0
length_stop = 0.3
length_step = 0.005
muscle_lengths = np.arange(length_start, length_stop, length_step)
muscle_stimulations = np.arange(0, muscle_stimulation + 0.1, 0.1)
all_active_forces = []
all_passive_forces = []
all_total_forces = []
all_element_lengths = []
for temp_muscle_stimulation in muscle_stimulations:
temp_active_forces = []
temp_passive_forces = []
temp_total_forces = []
temp_element_lengths = []
for temp_length in muscle_lengths:
temp_result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=temp_muscle_stimulation,
muscle_length=temp_length)
temp_active_force = temp_result.active_force[-1]
temp_passive_force = temp_result.passive_force[-1]
tenp_total_force = temp_active_force + temp_passive_force
temp_element_length = temp_result.l_ce[-1]
temp_active_forces = temp_active_forces + [temp_active_force]
temp_passive_forces = temp_passive_forces + [temp_passive_force]
temp_total_forces = temp_total_forces + [tenp_total_force]
temp_element_lengths = temp_element_lengths + [temp_element_length]
all_active_forces = all_active_forces + [temp_active_forces]
all_passive_forces = all_passive_forces + [temp_passive_forces]
all_total_forces = all_total_forces + [temp_total_forces]
all_element_lengths = all_element_lengths + [temp_element_lengths]
plt.figure(
'1b. Isometric muscle experiment for active forces with different stimulations'
)
for i in range(len(muscle_stimulations)):
plt.plot(all_element_lengths[i], all_active_forces[i])
plt.title(
'Isometric muscle experiment for active forces with different stimulations'
)
plt.xlabel('Muscle contracticle length [m]')
plt.ylabel('Tension [N]')
temp_legends = [
'stimulation = ' + format((temp_stimulation), '.1f')
for temp_stimulation in muscle_stimulations
]
plt.legend(temp_legends)
plt.grid()
plt.show()
plt.figure(
'1b. Isometric muscle experiment for passive forces with different stimulations'
)
for i in range(len(muscle_stimulations)):
plt.plot(all_element_lengths[i], all_passive_forces[i])
plt.title(
'Isometric muscle experiment for passive forces with different stimulations'
)
plt.xlabel('Muscle contracticle length [m]')
plt.ylabel('Tension [N]')
temp_legends = [
'stimulation = ' + format((temp_stimulation), '.1f')
for temp_stimulation in muscle_stimulations
]
plt.legend(temp_legends)
plt.grid()
plt.show()
plt.figure(
'1b. Isometric muscle experiment for total forces with different stimulations'
)
for i in range(len(muscle_stimulations)):
plt.plot(all_element_lengths[i], all_total_forces[i])
plt.title(
'Isometric muscle experiment for total forces with different stimulations'
)
plt.xlabel('Muscle contracticle length [m]')
plt.ylabel('Tension [N]')
temp_legends = [
'stimulation = ' + format((temp_stimulation), '.1f')
for temp_stimulation in muscle_stimulations
]
plt.legend(temp_legends)
plt.grid()
plt.show()
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### code for 1c
pylog.info(
"1c. relationship between forces and contractile element length with different fiber lengths"
)
short_opt = 0.05
medium_opt = 0.1
long_opt = 0.15
opt_range = [short_opt, medium_opt, long_opt]
muscle_stimulation = 1.
length_start = 0.0
length_stop = 0.3
length_step = 0.005
muscle_lengths = np.arange(length_start, length_stop, length_step)
for temp_opt in opt_range:
parameters = MuscleParameters(l_opt=temp_opt)
muscle = Muscle(parameters)
sys = IsometricMuscleSystem()
sys.add_muscle(muscle)
#muscle.L_OPT = temp_opt
temp_active_forces = []
temp_passive_forces = []
temp_total_forces = []
temp_element_lengths = []
for temp_length in muscle_lengths:
temp_result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=muscle_stimulation,
muscle_length=temp_length)
temp_active_force = temp_result.active_force[-1]
temp_passive_force = temp_result.passive_force[-1]
tenp_total_force = temp_active_force + temp_passive_force
temp_element_length = temp_result.l_ce[-1]
temp_active_forces = temp_active_forces + [temp_active_force]
temp_passive_forces = temp_passive_forces + [temp_passive_force]
temp_total_forces = temp_total_forces + [tenp_total_force]
temp_element_lengths = temp_element_lengths + [temp_element_length]
plt.figure(
"1c. Isometric muscle experiment with musle fiber length = " +
format((temp_opt), '.2f'))
plt.plot(temp_element_lengths, temp_active_forces)
plt.plot(temp_element_lengths, temp_passive_forces)
plt.plot(temp_element_lengths, temp_total_forces)
plt.xlabel('Muscle contracticle length [m]')
plt.ylabel('Tension [N]')
plt.title("Isometric muscle experiment with musle fiber length = " +
format((temp_opt), '.2f'))
plt.legend(("Active Force", "Passive Force ", "Total Force "))
plt.grid()
plt.show()
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
pylog.warning("Isotonic muscle contraction to be implemented")
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.l_opt # To get the muscle optimal length
# Evalute for a single load
load = 250 / 9.81
# Evalute for a single muscle stimulation
muscle_stimulation = 1.0
# Set the initial condition
x0 = [0.0, sys.muscle.l_opt, sys.muscle.l_opt + sys.muscle.l_slack, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.4
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=load)
# Plotting
plt.figure('Isotonic muscle experiment')
plt.plot(result.time, result.v_ce)
plt.title('Isotonic muscle experiment')
plt.xlabel('Time [s]')
plt.ylabel('Muscle contracticle velocity [lopts/s]')
plt.grid()
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### code for 1d
pylog.info(
"1d. relationship between muscle contractile velocity and external load"
)
load_start = 1
load_stop = 501
load_step = 10
load_range = np.arange(load_start, load_stop, load_step)
muscle_stimulation = 1.0
vels = []
tendon_forces = []
active_forces = []
passive_forces = []
total_forces = []
for temp_load in load_range:
temp_result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=temp_load)
temp_tendon_force = temp_result.tendon_force[-1]
temp_active_force = temp_result.active_force[-1]
temp_passive_force = temp_result.passive_force[-1]
temp_total_force = temp_active_force + temp_passive_force
tendon_forces = tendon_forces + [temp_tendon_force]
active_forces = active_forces + [temp_active_force]
passive_forces = passive_forces + [temp_passive_force]
total_forces = total_forces + [temp_total_force]
temp_l_mtu = temp_result.l_mtu[-1]
if temp_l_mtu < sys.muscle.l_opt + sys.muscle.l_slack:
vels = vels + [np.min(temp_result.v_ce)]
else:
vels = vels + [np.max(temp_result.v_ce)]
plt.figure(
'1d. Isotonic muscle experiment for tension and contractile velocities'
)
plt.plot(vels, tendon_forces)
plt.plot(vels, load_range)
plt.plot(vels, active_forces)
plt.plot(vels, passive_forces)
plt.plot(vels, total_forces)
plt.title(
'Isotonic muscle experiment for tension and contractile velocities')
plt.xlabel('Muscle contracticle velocity [lopts/s]')
plt.ylabel('Tension [N]')
plt.legend(("Tendon Force", "Load", "Active Force", "Passive Force",
"Total force"))
plt.grid()
plt.show()
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### code for 1f
pylog.info(
"1f. relationship between muscle contractile velocity and external load with different stimulations"
)
muscle_stimulations = np.arange(0, muscle_stimulation + 0.1, 0.1)
load_start = 1
load_stop = 501
load_step = 10
load_range = np.arange(load_start, load_stop, load_step)
all_vels = []
all_tendon_forces = []
for temp_muscle_stimulation in muscle_stimulations:
temp_vels = []
temp_tendon_forces = []
for temp_load in load_range:
temp_result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=temp_muscle_stimulation,
load=temp_load)
temp_tendon_force = temp_result.tendon_force[-1]
temp_tendon_forces = temp_tendon_forces + [temp_tendon_force]
temp_l_mtu = temp_result.l_mtu[-1]
if temp_l_mtu < sys.muscle.l_opt + sys.muscle.l_slack:
temp_vels = temp_vels + [np.min(temp_result.v_ce)]
else:
temp_vels = temp_vels + [np.max(temp_result.v_ce)]
all_vels = all_vels + [temp_vels]
all_tendon_forces = all_tendon_forces + [temp_tendon_forces]
plt.figure(
'1f. Isotonic muscle experiment for loads and contractile velocities with different stimulations'
)
for i in range(len(muscle_stimulations)):
plt.plot(all_vels[i], load_range)
plt.title(
'Isotonic muscle experiment for loads and contractile velocities with different stimulations'
)
plt.xlabel('Muscle contracticle velocity [lopts/s]')
plt.ylabel('Tension [N]')
temp_legends = [
'stimulation = ' + format((temp_stimulation), '.1f')
for temp_stimulation in muscle_stimulations
]
plt.legend(temp_legends)
plt.grid()
plt.show()
plt.figure(
'1f. Isotonic muscle experiment for tendon forces and contractile velocities with different stimulations'
)
for i in range(len(muscle_stimulations)):
plt.plot(all_vels[i], all_tendon_forces[i])
plt.title(
'Isotonic muscle experiment for tendon forces and contractile velocities with different stimulations'
)
plt.xlabel('Muscle contracticle velocity [lopts/s]')
plt.ylabel('Tension [N]')
temp_legends = [
'stimulation = ' + format((temp_stimulation), '.1f')
for temp_stimulation in muscle_stimulations
]
plt.legend(temp_legends)
plt.grid()
plt.show()
def system_init():
"""Initialize default system."""
########## PENDULUM ##########
# Define and Setup your pendulum model here
# Check Pendulum.py for more details on Pendulum class
P_params = PendulumParameters() # Instantiate pendulum parameters
P_params.L = 1.0 # To change the default length of the pendulum
P_params.m = 0.25 # To change the default mass of the pendulum
pendulum = PendulumSystem(P_params) # Instantiate Pendulum object
#### CHECK OUT Pendulum.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
########## MUSCLES ##########
# Define and Setup your muscle model here
# Check MuscleSystem.py for more details on MuscleSystem class
m1_param = MuscleParameters() # Instantiate Muscle 1 parameters
m1_param.f_max = 200. # To change Muscle 1 max force
m1_param.l_opt = 0.4
m1_param.l_slack = 0.45
m2_param = MuscleParameters() # Instantiate Muscle 2 parameters
m2_param.f_max = 200. # To change Muscle 2 max force
m2_param.l_opt = 0.4
m2_param.l_slack = 0.45
m1 = Muscle('m1', m1_param) # Instantiate Muscle 1 object
m2 = Muscle('m2', m2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
# Instantiate Muscle System with two muscles
muscles = MuscleSystem(m1, m2)
pylog.info('Muscle system initialized \n {} \n {}'.format(
m1.parameters.showParameters(), m2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.asarray([0.0, 0.9]) # Origin of Muscle 1
m1_insertion = np.asarray([0.0, 0.15]) # Insertion of Muscle 1
m2_origin = np.asarray([0.0, 0.8]) # Origin of Muscle 2
m2_insertion = np.asarray([0.0, -0.3]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.asarray([m1_origin, m1_insertion]),
np.asarray([m2_origin, m2_insertion]))
########## ADD SYSTEMS ##########
# Create a system with Pendulum and Muscles using the System Class
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
########## INITIALIZATION ##########
t_max = 2 # Maximum simulation time
time = np.arange(0., t_max, 0.001) # Time vector
##### Model Initial Conditions #####
x0_P = np.asarray([np.pi / 2, 0.0]) # Pendulum initial condition
# Muscle Model initial condition
l_ce_0 = sys.muscle_sys.initialize_muscle_length(np.pi / 2)
x0_M = np.asarray([0.05, l_ce_0[0], 0.05, l_ce_0[1]])
x0 = np.concatenate((x0_P, x0_M)) # System initial conditions
########## System Simulation ##########
sim = SystemSimulation(sys) # Instantiate Simulation object
# Simulate the system for given time
sim.initalize_system(x0, time) # Initialize the system state
return sim
def exercise2():
""" Main function to run for Exercise 2.
Parameters
----------
None
Returns
-------
None
"""
'''
sim = system_init()
# Add muscle activations to the simulation
# Here you can define your muscle activation vectors
# that are time dependent
act1 = np.ones((len(sim.time), 1)) * 0.05
act2 = np.ones((len(sim.time), 1)) * 0.05
activations = np.hstack((act1, act2))
# Method to add the muscle activations to the simulation
sim.add_muscle_stimulations(activations)
#: If you would like to perturb the pedulum model then you could do
# so by
sim.sys.pendulum_sys.parameters.PERTURBATION = True
# The above line sets the state of the pendulum model to zeros between
# time interval 1.2 < t < 1.25. You can change this and the type of
# perturbation in
# pendulum_system.py::pendulum_system function
# Integrate the system for the above initialized state and time
sim.simulate()
# Obtain the states of the system after integration
# res is np.asarray [time, states]
# states vector is in the same order as x0
res = sim.results()
# In order to obtain internal states of the muscle
# you can access the results attribute in the muscle class
muscle_1_results = sim.sys.muscle_sys.muscle_1.results
muscle_2_results = sim.sys.muscle_sys.muscle_2.results
# Plotting the results
plt.figure('Pendulum')
plt.title('Pendulum Phase')
plt.plot(res[:, 1], res[:, 2])
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad.s]')
plt.grid()
'''
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### code for 2a
pylog.info("2a")
theta = np.arange(np.pi / 4, np.pi * 3 / 4, 0.001)
temp_a1 = 0.35
ratios = [
0.2,
0.5,
1.,
2.,
5.,
]
L2_s = []
h2_s = []
for temp_ratio in ratios:
temp_a2 = temp_a1 * temp_ratio
temp_L2 = np.sqrt(temp_a1 * temp_a1 + temp_a2 * temp_a2 +
2 * temp_a1 * temp_a2 * np.cos(theta))
temp_h2 = (temp_a1 * temp_a2 * np.sin(theta)) / temp_L2
L2_s = L2_s + [temp_L2]
h2_s = h2_s + [temp_h2]
plt.figure(
'2a. Relationship between muscle length and pendulum angular position')
plt.title(
'Relationship between muscle length and pendulum angular position')
for i in range(len(ratios)):
plt.plot(theta, L2_s[i])
plt.xlabel('Angular Position [rad]')
plt.ylabel('Muscle Length [m]')
temp_legends = [
'ratio of a2/a1 = ' + format((temp_ratio), '.2f')
for temp_ratio in ratios
]
plt.legend(temp_legends)
plt.grid()
plt.show()
plt.figure(
'2a. Relationship between moment arm and pendulum angular position')
plt.title('Relationship between moment arm and pendulum angular position')
for i in range(len(ratios)):
plt.plot(theta, h2_s[i])
plt.xlabel('Angular Position [rad]')
plt.ylabel('Moment Arm [m]')
temp_legends = [
'ratio of a2/a1 = ' + format((temp_ratio), '.2f')
for temp_ratio in ratios
]
plt.legend(temp_legends)
plt.grid()
plt.show()
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### code for 2b
pylog.info("2b")
#initialization
P_params = PendulumParameters() # Instantiate pendulum parameters
P_params.L = 1.0 # To change the default length of the pendulum
P_params.m = 0.25 # To change the default mass of the pendulum
pendulum = PendulumSystem(P_params) # Instantiate Pendulum object
#### CHECK OUT Pendulum.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
########## MUSCLES ##########
# Define and Setup your muscle model here
# Check MuscleSystem.py for more details on MuscleSystem class
m1_param = MuscleParameters() # Instantiate Muscle 1 parameters
m1_param.f_max = 200. # To change Muscle 1 max force
m1_param.l_opt = 0.4
m1_param.l_slack = 0.45
m2_param = MuscleParameters() # Instantiate Muscle 2 parameters
m2_param.f_max = 200. # To change Muscle 2 max force
m2_param.l_opt = 0.4
m2_param.l_slack = 0.45
m1 = Muscle('m1', m1_param) # Instantiate Muscle 1 object
m2 = Muscle('m2', m2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
# Instantiate Muscle System with two muscles
muscles = MuscleSystem(m1, m2)
pylog.info('Muscle system initialized \n {} \n {}'.format(
m1.parameters.showParameters(), m2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.asarray([0.0, 0.9]) # Origin of Muscle 1
m1_insertion = np.asarray([0.0, 0.15]) # Insertion of Muscle 1
m2_origin = np.asarray([0.0, 0.8]) # Origin of Muscle 2
m2_insertion = np.asarray([0.0, -0.3]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.asarray([m1_origin, m1_insertion]),
np.asarray([m2_origin, m2_insertion]))
########## ADD SYSTEMS ##########
# Create a system with Pendulum and Muscles using the System Class
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
########## INITIALIZATION ##########
t_max = 2 # Maximum simulation time
time = np.arange(0., t_max, 0.001) # Time vector
##### Model Initial Conditions #####
x0_P = np.asarray([np.pi / 2, 0.0]) # Pendulum initial condition
# Muscle Model initial condition
l_ce_0 = sys.muscle_sys.initialize_muscle_length(np.pi / 2)
x0_M = np.asarray([0.05, l_ce_0[0], 0.05, l_ce_0[1]])
x0 = np.concatenate((x0_P, x0_M)) # System initial conditions
########## System Simulation ##########
sim = SystemSimulation(sys) # Instantiate Simulation object
# Simulate the system for given time
sim.initalize_system(x0, time) # Initialize the system state
omega = 1.5
sin_act_1 = np.sin(2 * np.pi * omega * time).reshape(len(time), 1)
sin_act_1[sin_act_1 < 0] = 0
#sin_act_2=np.sin(2*np.pi*omega*time+np.pi/2).reshape(len(time),1)
sin_act_2 = -np.sin(2 * np.pi * omega * time).reshape(len(time), 1)
sin_act_2[sin_act_2 < 0] = 0
activations = np.hstack((sin_act_1, sin_act_2))
plt.figure('2b. Activation wave')
plt.title('Activation wave')
plt.plot(time, sin_act_1, label='Activation 1')
plt.plot(time, sin_act_2, label='Activation 2')
plt.xlabel('Time [s]')
plt.ylabel('Activation')
plt.grid()
plt.legend()
# without pertubation
sim.add_muscle_stimulations(activations)
sim.initalize_system(x0, time)
sim.sys.pendulum_sys.parameters.PERTURBATION = False
sim.simulate()
res = sim.results()
muscle1_results = sim.sys.muscle_sys.muscle_1.results
muscle2_results = sim.sys.muscle_sys.muscle_2.results
plt.figure('2b. Limit cycle without pertubation')
plt.title('Pendulum Phase without pertubation')
plt.plot(
res[:, 1],
res[:, 2],
)
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad/s]')
plt.grid()
plt.legend()
# with pertubation
sim.add_muscle_stimulations(activations)
sim.initalize_system(x0, time)
sim.sys.pendulum_sys.parameters.PERTURBATION = True
sim.simulate()
res = sim.results()
muscle1_results = sim.sys.muscle_sys.muscle_1.results
muscle2_results = sim.sys.muscle_sys.muscle_2.results
plt.figure('2b. Limit cycle with pertubation')
plt.title('Pendulum Phase with pertubation')
plt.plot(
res[:, 1],
res[:, 2],
)
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad/s]')
plt.grid()
plt.legend()
###########################################################
###########################################################
###########################################################
###########################################################
###########################################################
### code for 2c
pylog.info("2c")
# different frequencies
omegas = 1.5 * np.array([0.5, 2.])
positions = []
vels = []
for temp_omega in omegas:
sin_act_1 = np.sin(2 * np.pi * temp_omega * time).reshape(len(time), 1)
sin_act_1[sin_act_1 < 0] = 0
sin_act_2 = -np.sin(2 * np.pi * temp_omega * time).reshape(
len(time), 1)
sin_act_2[sin_act_2 < 0] = 0
activations = np.hstack((sin_act_1, sin_act_2))
sim.add_muscle_stimulations(activations)
sim.initalize_system(x0, time)
sim.sys.pendulum_sys.parameters.PERTURBATION = False
sim.simulate()
res = sim.results()
muscle1_results = sim.sys.muscle_sys.muscle_1.results
muscle2_results = sim.sys.muscle_sys.muscle_2.results
positions = positions + [res[:, 1]]
vels = vels + [res[:, 2]]
plt.figure('2c.Pendulum phase plane with stimulation frequencies')
plt.title('Pendulum phase plane with stimulation frequencies')
for i in range(len(omegas)):
plt.plot(positions[i], vels[i])
plt.xlabel('Angular Position [rad]')
plt.ylabel('Velocity [rad/s]')
temp_legends = [
'ratio of frequency = ' + format((temp_omega / 1.5), '.2f')
for temp_omega in omegas
]
plt.legend(temp_legends)
plt.grid()
plt.show()
'''
# different frequencies
omegas=1.5*np.array([0.2,0.5,1.,2.,5.])
positions=[]
vels=[]
for temp_omega in omegas:
sin_act_1=np.sin(2*np.pi*temp_omega*time).reshape(len(time),1)
sin_act_1[sin_act_1<0]=0
sin_act_2=np.sin(2*np.pi*temp_omega*(np.pi/6+time)).reshape(len(time),1)
sin_act_2[sin_act_2<0]=0
activations = np.hstack((sin_act_1,sin_act_2))
sim.add_muscle_stimulations(activations)
sim.initalize_system(x0, time)
sim.sys.pendulum_sys.parameters.PERTURBATION = False
sim.simulate()
res = sim.results()
muscle1_results = sim.sys.muscle_sys.muscle_1.results
muscle2_results = sim.sys.muscle_sys.muscle_2.results
positions=positions+[res[:, 1]]
vels=vels+[res[:,2]]
plt.figure('2c.Pendulum phase plane with stimulation frequencies')
plt.title('Pendulum phase plane with stimulation frequencies')
for i in range(len(ratios)):
plt.plot(positions[i], vels[i])
plt.xlabel('Angular Position [rad]')
plt.ylabel('Muscle Length [m]')
temp_legends=['ratio of frequency = '+ format((temp_omega/1.5),'.2f') for temp_omega in omegas]
plt.legend(temp_legends)
plt.grid()
plt.show()
'''
# To animate the model, use the SystemAnimation class
# Pass the res(states) and systems you wish to animate
simulation = SystemAnimation(res, sim.sys.pendulum_sys, sim.sys.muscle_sys)
if not DEFAULT["save_figures"]:
# To start the animation
simulation.animate()
plt.show()
else:
figures = plt.get_figlabels()
pylog.debug("Saving figures:\n{}".format(figures))
for fig in figures:
plt.figure(fig)
save_figure(fig)
plt.close(fig)
def exercise2():
""" Main function to run for Exercise 2.
Parameters
----------
None
Returns
-------
None
"""
# Define and Setup your pendulum model here
# Check PendulumSystem.py for more details on Pendulum class
pendulum_params = PendulumParameters() # Instantiate pendulum parameters
pendulum_params.L = 0.5 # To change the default length of the pendulum
pendulum_params.m = 1. # To change the default mass of the pendulum
pendulum = PendulumSystem(pendulum_params) # Instantiate Pendulum object
#### CHECK OUT PendulumSystem.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
# Define and Setup your pendulum model here
# Check MuscleSytem.py for more details on MuscleSytem class
M1_param = MuscleParameters() # Instantiate Muscle 1 parameters
M1_param.f_max = 1500 # To change Muscle 1 max force
M2_param = MuscleParameters() # Instantiate Muscle 2 parameters
M2_param.f_max = 1500 # To change Muscle 2 max force
M1 = Muscle(M1_param) # Instantiate Muscle 1 object
M2 = Muscle(M2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
muscles = MuscleSytem(M1, M2) # Instantiate Muscle System with two muscles
pylog.info('Muscle system initialized \n {} \n {}'.format(
M1.parameters.showParameters(), M2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.array([-0.17, 0.0]) # Origin of Muscle 1
m1_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 1
m2_origin = np.array([0.17, 0.0]) # Origin of Muscle 2
m2_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.array([m1_origin, m1_insertion]),
np.array([m2_origin, m2_insertion]))
############Exercise 2A ###############################################
# rigth after creating and attaching both muscles:
print(m1_origin, m2_origin)
m1a1 = abs(abs(m1_origin[0]) - abs(m1_origin[1]))
m1a2 = abs(abs(m1_insertion[0]) - abs(m1_insertion[1]))
m1a1 = m1_origin[0] - m1_origin[1]
m1a2 = m1_insertion[0] - m1_insertion[1]
m2a1 = m2_origin[0] - m2_origin[1]
m2a2 = m2_insertion[0] - m2_insertion[1]
print(m1a1, m1a2)
fromtheta(M1, m1a1, m1a2, 1)
fromtheta(M2, m2a1, m2a2, 2)
# Create a system with Pendulum and Muscles using the System Class
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
##### Time #####
t_max = 5 # Maximum simulation time
time = np.arange(0., t_max, 0.002) # Time vector
##### Model Initial Conditions #####
x0_P = np.array([np.pi / 4, 0.]) # Pendulum initial condition
x0_P = np.array([0., 0.]) # Pendulum initial condition
# Muscle Model initial condition
x0_M = np.array([0., M1.L_OPT, 0., M2.L_OPT])
x0 = np.concatenate((x0_P, x0_M)) # System initial conditions
##### System Simulation #####
# For more details on System Simulation check SystemSimulation.py
# SystemSimulation is used to initialize the system and integrate
# over time
sim = SystemSimulation(sys) # Instantiate Simulation object
# Add muscle activations to the simulation
# Here you can define your muscle activation vectors
# that are time dependent
wave_h1 = np.sin(time * 3) * 1 #makes a sinusoidal wave from 'time'
wave_h2 = np.sin(time * 3 +
np.pi) * 1 #makes a sinusoidal wave from 'time'
wave_h1[wave_h1 < 0] = 0 #formality of passing negative values to zero
wave_h2[wave_h2 < 0] = 0 #formality of passing negative values to zero
act1 = wave_h1.reshape(len(time), 1) #makes a vertical array like act1
act2 = wave_h2.reshape(len(time), 1) #makes a vertical array like act1
# Plotting the waveforms
plt.figure('Muscle Activations')
plt.title('Muscle Activation Functions')
plt.plot(time, wave_h1, label='Muscle 1')
plt.plot(time, wave_h2, label='Muscle 2')
plt.xlabel('Time [s]')
plt.ylabel('Muscle Excitation')
plt.legend(loc='upper right')
plt.grid()
activations = np.hstack((act1, act2))
# Method to add the muscle activations to the simulation
sim.add_muscle_activations(activations)
# Simulate the system for given time
sim.initalize_system(x0, time) # Initialize the system state
#: If you would like to perturb the pedulum model then you could do
# so by
sim.sys.pendulum_sys.parameters.PERTURBATION = False
# The above line sets the state of the pendulum model to zeros between
# time interval 1.2 < t < 1.25. You can change this and the type of
# perturbation in
# pendulum_system.py::pendulum_system function
# Integrate the system for the above initialized state and time
sim.simulate()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
res = sim.results()
# In order to obtain internal states of the muscle
# you can access the results attribute in the muscle class
muscle1_results = sim.sys.muscle_sys.Muscle1.results
muscle2_results = sim.sys.muscle_sys.Muscle2.results
# Plotting the results
plt.figure('Pendulum_phase')
plt.title('Pendulum Phase')
plt.plot(res[:, 1], res[:, 2])
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad.s]')
plt.grid()
# Plotting the results: Amplidute stimulation
plt.figure('Amplidute stimulation')
plt.title('Amplidute stimulation')
plt.plot(time, res[:, 1], label='Stimul. 0.2')
plt.xlabel('time [s]')
plt.ylabel('Position [rad]')
plt.legend(loc='upper left')
plt.grid()
# Plotting the results: frequency stimulation
plt.figure('Frequency stimulation')
plt.title('Frequency stimulation')
plt.plot(time, res[:, 1], label='w: 3 rad/s')
plt.xlabel('time [s]')
plt.ylabel('Position [rad]')
plt.legend(loc='upper left')
plt.grid()
poincare_crossings(res, -2, 1, "Pendulum")
# To animate the model, use the SystemAnimation class
# Pass the res(states) and systems you wish to animate
simulation = SystemAnimation(res, pendulum, muscles)
# To start the animation
if DEFAULT["save_figures"] is False:
simulation.animate()
if not DEFAULT["save_figures"]:
plt.show()
else:
figures = plt.get_figlabels()
pylog.debug("Saving figures:\n{}".format(figures))
for fig in figures:
plt.figure(fig)
save_figure(fig)
plt.close(fig)
def exercise2():
""" Main function to run for Exercise 2.
"""
# Define and Setup your pendulum model here
# Check PendulumSystem.py for more details on Pendulum class
pendulum_params = PendulumParameters() # Instantiate pendulum parameters
pendulum_params.L = 0.5 # To change the default length of the pendulum
pendulum_params.m = 1. # To change the default mass of the pendulum
pendulum = PendulumSystem(pendulum_params) # Instantiate Pendulum object
#### CHECK OUT PendulumSystem.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
# Define and Setup your pendulum model here
# Check MuscleSytem.py for more details on MuscleSytem class
M1_param = MuscleParameters() # Instantiate Muscle 1 parameters
M1_param.f_max = 1500 # To change Muscle 1 max force
M2_param = MuscleParameters() # Instantiate Muscle 2 parameters
M2_param.f_max = 1500 # To change Muscle 2 max force
M1 = Muscle(M1_param) # Instantiate Muscle 1 object
M2 = Muscle(M2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
muscles = MuscleSytem(M1, M2) # Instantiate Muscle System with two muscles
pylog.info('Muscle system initialized \n {} \n {}'.format(
M1.parameters.showParameters(),
M2.parameters.showParameters()))
# 2a : set of muscle 1 attachment points
m1_origin = np.array([[-0.17, 0.0]]) # Origin of Muscle 1
m1_insertion = np.array([[0.0, -0.17], [0.0, -0.3], [0.0, -0.4], [0.0, -0.5]]) # Insertion of Muscle 1
theta = np.linspace(-np.pi/2,np.pi/2)
m_lengths = np.zeros((len(m1_insertion),len(theta)))
m_moment_arms = np.zeros((len(m1_insertion),len(theta)))
leg=[]
for i in range(0,len(m1_insertion)):
m_lengths[i,:]=np.sqrt(m1_origin[0,0]**2 + m1_insertion[i,1]**2 +
2 * np.abs(m1_origin[0,0]) * np.abs(m1_insertion[i,1]) * np.sin(theta))
m_moment_arms[i,:]= m1_origin[0,0] * m1_insertion[i,1] * np.cos(theta) / m_lengths[i,:]
leg.append('Origin: {}m, Insertion: {}m'.format(m1_origin[0,0],m1_insertion[i,1]))
# Plotting
plt.figure('2a length')
plt.title('Length of M1 with respect to the position of the limb')
for i in range(0,len(m_lengths)):
plt.plot(theta*180/np.pi, m_lengths[i,:])
plt.plot((theta[0]*180/np.pi,theta[len(theta)-1]*180/np.pi),(0.11,0.11), ls='dashed')
leg.append('l_opt')
plt.plot((theta[0]*180/np.pi,theta[len(theta)-1]*180/np.pi),(0.13,0.13), ls='dashed')
leg.append('l_slack')
plt.xlabel('Position [deg]')
plt.ylabel('Muscle length [m]')
plt.legend(leg)
plt.grid()
plt.savefig('2_a_length.png')
plt.figure('2a moment')
plt.title('Moment arm over M1 with respect to the position of the limb')
for i in range(0,len(m_moment_arms)):
plt.plot(theta*180/np.pi, m_moment_arms[i,:])
plt.xlabel('Position [deg]')
plt.ylabel('Moment arm [m]')
plt.legend(leg)
plt.grid()
plt.savefig('2_a_moment.png')
# 2b : simple activation wave forms
# Muscle 2 attachement point
m2_origin = np.array([0.17, 0.0]) # Origin of Muscle 2
m2_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.array([m1_origin[0,:], m1_insertion[0,:]]),
np.array([m2_origin, m2_insertion]))
# Create a system with Pendulum and Muscles using the System Class
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
##### Time #####
t_max = 2.5 # Maximum simulation time
time = np.arange(0., t_max, 0.001) # Time vector
##### Model Initial Conditions #####
x0_P = np.array([np.pi/4, 0.]) # Pendulum initial condition
# Muscle Model initial condition
x0_M = np.array([0., M1.L_OPT, 0., M2.L_OPT])
x0 = np.concatenate((x0_P, x0_M)) # System initial conditions
##### System Simulation #####
# For more details on System Simulation check SystemSimulation.py
# SystemSimulation is used to initialize the system and integrate
# over time
sim = SystemSimulation(sys) # Instantiate Simulation object
# Add muscle activations to the simulation
# Here you can define your muscle activation vectors
# that are time dependent
sin_frequency = 2 #Hz
amp_stim = 1
phase_shift = np.pi
act1 = np.zeros((len(time),1))
act2 = np.zeros((len(time),1))
for i in range(0,len(time)):
act1[i,0] = amp_stim*(1+np.sin(2*np.pi*sin_frequency*time[i]))/2
act2[i,0] = amp_stim*(1+ np.sin(2*np.pi*sin_frequency*time[i] + phase_shift))/2
plt.figure('2b activation')
plt.plot(time,act1)
plt.plot(time,act2)
plt.legend(["Activation for muscle 1", "Activation for muscle 2"])
plt.title('Activation for muscle 1 and 2 with simple activation wave forms')
plt.xlabel("Time [s]")
plt.ylabel("Activation")
plt.savefig('2_b_activation.png')
plt.show()
activations = np.hstack((act1, act2))
# Method to add the muscle activations to the simulation
sim.add_muscle_activations(activations)
# Simulate the system for given time
sim.initalize_system(x0, time) # Initialize the system state
#: If you would like to perturb the pedulum model then you could do
# so by
sim.sys.pendulum_sys.parameters.PERTURBATION = True
# The above line sets the state of the pendulum model to zeros between
# time interval 1.2 < t < 1.25. You can change this and the type of
# perturbation in
# pendulum_system.py::pendulum_system function
# Integrate the system for the above initialized state and time
sim.simulate()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
res = sim.results()
# Plotting the results
plt.figure('2b phase')
plt.title('Pendulum Phase')
plt.plot(res[:, 1], res[:, 2])
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad/s]')
plt.grid()
plt.savefig('2_b_phase.png')
plt.show()
plt.figure('2b oscillations')
plt.title('Pendulum Oscillations')
plt.plot(time,res[:, 1])
plt.xlabel('Time [s]')
plt.ylabel('Position [rad]')
plt.grid()
plt.savefig('2_b_oscillations.png')
plt.show()
# To animate the model, use the SystemAnimation class
# Pass the res(states) and systems you wish to animate
simulation = SystemAnimation(res, pendulum, muscles)
# To start the animation
if DEFAULT["save_figures"] is False:
simulation.animate()
if not DEFAULT["save_figures"]:
plt.show()
else:
figures = plt.get_figlabels()
pylog.debug("Saving figures:\n{}".format(figures))
for fig in figures:
plt.figure(fig)
save_figure(fig)
plt.close(fig)
# 2c : relationship between stimulation frequency and amplitude
# Effect of frequency
stim_frequency_range = np.array([0.05,0.1,0.5,1,5,10,50,100,500]) #Hz
stim_amp = 1
phase_shift = np.pi
frequency_pend=np.zeros(len(stim_frequency_range))
amplitude_pend=np.zeros(len(stim_frequency_range))
for j,stim_frequency in enumerate(stim_frequency_range):
period = 1/stim_frequency
t_max = 10*period # Maximum simulation time
time = np.arange(0., t_max, 0.001*period) # Time vector
act1 = np.zeros((len(time),1))
act2 = np.zeros((len(time),1))
act1[:,0] = stim_amp*(1 + np.sin(2*np.pi*stim_frequency*time))/2
act2[:,0] = stim_amp*(1+ np.sin(2*np.pi*stim_frequency*time + phase_shift))/2
activations = np.hstack((act1, act2))
sim.add_muscle_activations(activations)
sim.initalize_system(x0, time) # Initialize the system state
sim.simulate()
res = sim.results()
# computing the frequency and amplitude
angular_position = res[:,1]
signal_stat = angular_position[int(len(angular_position)/2):len(angular_position)]
index_zeros = np.where(np.diff(np.sign(signal_stat)))[0]
deltas = np.diff(index_zeros)
delta = np.mean(deltas)
period = 2*delta*0.001*period
frequency_pend[j] = 1/period
amplitude_pend[j] = (np.max(signal_stat)-np.min(signal_stat))/2
# Plotting
plt.figure('2c : effect of frequency')
plt.subplot(121)
plt.loglog(stim_frequency_range,frequency_pend)
plt.grid()
plt.xlabel('Stimulation Frequency in Hz')
plt.ylabel('Pendulum Oscillation Frequency [Hz]')
plt.subplot(122)
plt.loglog(stim_frequency_range,amplitude_pend)
plt.grid()
plt.xlabel('Stimulation Frequency in Hz')
plt.ylabel('Pendulum Oscillation Amplitude [rad]')
plt.savefig('2c_frequency.png')
plt.show()
# Effect of amplitude
stim_frequency = 10 #Hz
stim_amp_range = np.arange(0,1.1,0.1)
phase_shift = np.pi
frequency_pend=np.zeros(len(stim_amp_range))
amplitude_pend=np.zeros(len(stim_amp_range))
for j,stim_amp in enumerate(stim_amp_range):
period = 1/stim_frequency
t_max = 5*period # Maximum simulation time
time = np.arange(0., t_max, 0.001*period) # Time vector
act1 = np.zeros((len(time),1))
act2 = np.zeros((len(time),1))
act1[:,0] = stim_amp*(1 + np.sin(2*np.pi*stim_frequency*time))/2
act2[:,0] = stim_amp*(1+ np.sin(2*np.pi*stim_frequency*time + phase_shift))/2
activations = np.hstack((act1, act2))
sim.add_muscle_activations(activations)
sim.initalize_system(x0, time) # Initialize the system state
sim.simulate()
res = sim.results()
# computing the frequency and amplitude
angular_position = res[:,1]
signal_stat = angular_position[int(len(angular_position)/2):len(angular_position)]
index_zeros = np.where(np.diff(np.sign(signal_stat)))[0]
deltas = np.diff(index_zeros)
delta = np.mean(deltas)
period = 2*delta*0.001*period
frequency_pend[j] = 1/period
amplitude_pend[j] = (np.max(signal_stat)-np.min(signal_stat))/2
frequency_pend[0] = 0.0;
# Plotting
plt.figure('2c : effect of amplitude')
plt.subplot(121)
plt.plot(stim_amp_range,frequency_pend)
plt.grid()
plt.xlabel('Stimulation Amplitude')
plt.ylabel('Pendulum Oscillation Frequency [Hz]')
plt.subplot(122)
plt.plot(stim_amp_range,amplitude_pend)
plt.grid()
plt.xlabel('Stimulation Amplitude')
plt.ylabel('Pendulum Oscillation Amplitude [rad]')
plt.savefig('2c_amplitude.png')
plt.show()
def exercise1d():
""" Exercise 1d
Under isotonic conditions external load is kept constant.
A constant stimulation is applied and then suddenly the muscle
is allowed contract. The instantaneous velocity at which the muscle
contracts is of our interest."""
# Defination of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
pylog.warning("Isotonic muscle contraction to be implemented")
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
# Evalute for a single load
load = 100.
# Evalute for a single muscle stimulation
muscle_stimulation = 1.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT,
sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.3
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=load)
# Plotting
plt.figure('Isotonic muscle experiment')
plt.plot(result.time, result.v_ce)
plt.title('Isotonic muscle experiment')
plt.xlabel('Time [s]')
plt.ylabel('Muscle contractilve velocity')
plt.grid()
# Run 1.d
load = np.arange(0,1000,20)
plotVceLoad(load,[0.1,0.5,1])
def exercise2c():
""" Main function to run for Exercise 2c.
Parameters
----------
None
Returns
-------
None
"""
# Define and Setup your pendulum model here
# Check PendulumSystem.py for more details on Pendulum class
pendulum_params = PendulumParameters() # Instantiate pendulum parameters
pendulum_params.L = 0.5 # To change the default length of the pendulum
pendulum_params.m = 1. # To change the default mass of the pendulum
pendulum = PendulumSystem(pendulum_params) # Instantiate Pendulum object
#### CHECK OUT PendulumSystem.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
# Define and Setup your pendulum model here
# Check MuscleSytem.py for more details on MuscleSytem class
M1_param = MuscleParameters() # Instantiate Muscle 1 parameters
M1_param.f_max = 1500 # To change Muscle 1 max force
M2_param = MuscleParameters() # Instantiate Muscle 2 parameters
M2_param.f_max = 1500 # To change Muscle 2 max force
M1 = Muscle(M1_param) # Instantiate Muscle 1 object
M2 = Muscle(M2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
muscles = MuscleSytem(M1, M2) # Instantiate Muscle System with two muscles
pylog.info('Muscle system initialized \n {} \n {}'.format(
M1.parameters.showParameters(), M2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.array([-0.17, 0.0]) # Origin of Muscle 1
m1_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 1
m2_origin = np.array([0.17, 0.0]) # Origin of Muscle 2
m2_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.array([m1_origin, m1_insertion]),
np.array([m2_origin, m2_insertion]))
# Create a system with Pendulum and Muscles using the System Class
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
##### Time #####
t_max = 15 # Maximum simulation time
time = np.arange(0., t_max, 0.005) # Time vector
##### Model Initial Conditions #####
x0_P = np.array([np.pi / 4, 0.]) # Pendulum initial condition
# Muscle Model initial condition
x0_M = np.array([0., M1.L_OPT, 0., M2.L_OPT])
x0 = np.concatenate((x0_P, x0_M)) # System initial conditions
sim = SystemSimulation(sys) # Instantiate Simulation object
plt.figure('Pendulum with different stimulation frequencies')
frequencies = [0.25, 0.5, 0.75, 1.0, 2.0, 3.0, 4.0, 5.0]
for freq in frequencies:
act1 = np.array([np.sin(freq * time)]).T
act2 = np.array([-np.sin(freq * time)]).T
activations = np.hstack((act1, act2))
# Method to add the muscle activations to the simulation
sim.add_muscle_activations(activations)
# Simulate the system for given time
sim.initalize_system(x0, time) # Initialize the system state
# Integrate the system for the above initialized state and time
sim.simulate()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
res = sim.results()
# Plotting the results
plt.plot(res[:, 1], res[:, 2])
plt.title('Pendulum Phase')
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad.s]')
plt.legend((
'0.25',
'0.5',
'0.75',
'1.0',
'2.0',
'3.0',
'4.0',
'5.0',
))
plt.grid()
plt.figure('Pendulum with different stimulation amplitudes')
amplitudes = [0.25, 0.5, 0.75, 1.0, 2.0, 3.0, 4.0, 5.0]
for amp in amplitudes:
act1 = np.array([amp * np.sin(time)]).T
act2 = np.array([amp * (-np.sin(time))]).T
activations = np.hstack((act1, act2))
# Method to add the muscle activations to the simulation
sim.add_muscle_activations(activations)
# Simulate the system for given time
sim.initalize_system(x0, time) # Initialize the system state
# Integrate the system for the above initialized state and time
sim.simulate()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
res = sim.results()
# Plotting the results
plt.plot(res[:, 1], res[:, 2])
plt.title('Pendulum Phase')
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad.s]')
plt.legend((
'0.25',
'0.5',
'0.75',
'1.0',
'2.0',
'3.0',
'4.0',
'5.0',
))
plt.grid()
def exercise1a():
""" Exercise 1a
The goal of this exercise is to understand the relationship
between muscle length and tension.
Here you will re-create the isometric muscle contraction experiment.
To do so, you will have to keep the muscle at a constant length and
observe the force while stimulating the muscle at a constant activation."""
# Defination of muscles
parameters = MuscleParameters()
pylog.warning("Loading default muscle parameters")
pylog.info(parameters.showParameters())
pylog.info("Use the parameters object to change the muscle parameters")
# Create muscle object
muscle = Muscle(parameters)
pylog.warning("Isometric muscle contraction to be completed")
# Instatiate isometric muscle system
sys = IsometricMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
# Evalute for a single muscle stretch
muscle_stretch = 0.2
# Evalute for a single muscle stimulation
muscle_stimulation = 1.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT]
# x0[0] --> muscle stimulation intial value
# x0[1] --> muscle contracticle length initial value
# Set the time for integration
t_start = 0.0
t_stop = 0.2
time_step = 0.001
time = np.arange(t_start, t_stop, time_step)
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=muscle_stimulation,
muscle_length=muscle_stretch)
# Plotting
plt.figure('Isometric muscle experiment')
plt.plot(result.time, result.tendon_force,label='tendon force')
plt.plot(result.time, result.passive_force,label='passive force')
plt.plot(result.time, result.active_force,label='active force')
plt.plot(result.time, result.l_ce,label='l_ce')
plt.legend()
plt.title('Isometric muscle experiment')
plt.xlabel('Time [s]')
plt.ylabel('Muscle Force')
plt.grid()
# Run 1.a and 1.b - relation between l_ce and active/oassive forces
ms=np.arange(start=0.0,stop=0.32,step=0.005)
plotRelationLceAPForces(muscle_stretch=ms,muscle_stimulation=0.1)
plotRelationLceAPForces(muscle_stretch=ms,muscle_stimulation=0.5)
plotRelationLceAPForces(muscle_stretch=ms,muscle_stimulation=1.)
# Run 1.c
plotRelationLceAPForces(ms,l_opt=0.09)
plotRelationLceAPForces(ms,l_opt=0.13)
def exercise2():
""" Main function to run for Exercise 2.
Parameters
----------
None
Returns
-------
None
"""
# Define and Setup your pendulum model here
# Check PendulumSystem.py for more details on Pendulum class
pendulum_params = PendulumParameters() # Instantiate pendulum parameters
pendulum_params.L = 0.5 # To change the default length of the pendulum
pendulum_params.m = 1. # To change the default mass of the pendulum
pendulum = PendulumSystem(pendulum_params) # Instantiate Pendulum object
#### CHECK OUT PendulumSystem.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
# Define and Setup your pendulum model here
# Check MuscleSytem.py for more details on MuscleSytem class
M1_param = MuscleParameters() # Instantiate Muscle 1 parameters
M1_param.f_max = 1500 # To change Muscle 1 max force
M2_param = MuscleParameters() # Instantiate Muscle 2 parameters
M2_param.f_max = 1500 # To change Muscle 2 max force
M1 = Muscle(M1_param) # Instantiate Muscle 1 object
M2 = Muscle(M2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
muscles = MuscleSytem(M1, M2) # Instantiate Muscle System with two muscles
pylog.info('Muscle system initialized \n {} \n {}'.format(
M1.parameters.showParameters(), M2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.array([-0.17, 0.0]) # Origin of Muscle 1
m1_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 1
m2_origin = np.array([0.17, 0.0]) # Origin of Muscle 2
m2_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.array([m1_origin, m1_insertion]),
np.array([m2_origin, m2_insertion]))
# Create a system with Pendulum and Muscles using the System Class
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
##### Time #####
t_max = 2.5 # Maximum simulation time
time = np.arange(0., t_max, 0.001) # Time vector
##### Model Initial Conditions #####
x0_P = np.array([np.pi / 6, 0.]) # Pendulum initial condition
# Muscle Model initial condition
x0_M = np.array([0., M1.L_OPT, 0., M2.L_OPT])
x0 = np.concatenate((x0_P, x0_M)) # System initial conditions
##### System Simulation #####
# For more details on System Simulation check SystemSimulation.py
# SystemSimulation is used to initialize the system and integrate
# over time
sim = SystemSimulation(sys) # Instantiate Simulation object
# Add muscle activations to the simulation
# Here you can define your muscle activation vectors
# that are time dependent
sin_freq = 1 #hz
ampl_sin = 1
phase_difference_1_2 = np.pi
act1 = np.ones((len(time), 1))
act2 = np.ones((len(time), 1))
for i in range(len(time)):
act1[i, 0] = ampl_sin * (1 + np.sin(2 * np.pi * sin_freq * time[i]))
act2[i, 0] = ampl_sin * (
1 + np.sin(2 * np.pi * sin_freq * time[i] + phase_difference_1_2))
activations = np.hstack((act1, act2))
# Method to add the muscle activations to the simulation
sim.add_muscle_activations(activations)
# Simulate the system for given time
sim.initalize_system(x0, time) # Initialize the system state
#: If you would like to perturb the pedulum model then you could do
# so by
sim.sys.pendulum_sys.parameters.PERTURBATION = True
# The above line sets the state of the pendulum model to zeros between
# time interval 1.2 < t < 1.25. You can change this and the type of
# perturbation in
# pendulum_system.py::pendulum_system function
# Integrate the system for the above initialized state and time
sim.simulate()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
res = sim.results()
# In order to obtain internal states of the muscle
# you can access the results attribute in the muscle class
muscle1_results = sim.sys.muscle_sys.Muscle1.results
muscle2_results = sim.sys.muscle_sys.Muscle2.results
# Plotting the results
plt.figure('Pendulum')
plt.title('Pendulum Phase')
plt.plot(res[:, 1], res[:, 2])
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad.s]')
plt.grid()
plt.figure('Activations')
plt.title('Sine wave activations for both muscles')
plt.plot(time, act1)
plt.plot(time, act2)
plt.legend(("activation muscle1", "activation muscle2"))
# To animate the model, use the SystemAnimation class
# Pass the res(states) and systems you wish to animate
simulation = SystemAnimation(res, pendulum, muscles)
# To start the animation
if DEFAULT["save_figures"] is False:
simulation.animate()
if not DEFAULT["save_figures"]:
plt.show()
else:
figures = plt.get_figlabels()
pylog.debug("Saving figures:\n{}".format(figures))
for fig in figures:
plt.figure(fig)
save_figure(fig)
plt.close(fig)
def exercise2():
""" Main function to run for Exercise 2.
Parameters
----------
None
Returns
-------
None
"""
# Define and Setup your pendulum model here
# Check PendulumSystem.py for more details on Pendulum class
pendulum_params = PendulumParameters() # Instantiate pendulum parameters
pendulum_params.L = 0.5 # To change the default length of the pendulum
pendulum_params.m = 1. # To change the default mass of the pendulum
pendulum = PendulumSystem(pendulum_params) # Instantiate Pendulum object
#### CHECK OUT PendulumSystem.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
# Define and Setup your pendulum model here
# Check MuscleSytem.py for more details on MuscleSytem class
M1_param = MuscleParameters() # Instantiate Muscle 1 parameters
M1_param.f_max = 1500 # To change Muscle 1 max force
M2_param = MuscleParameters() # Instantiate Muscle 2 parameters
M2_param.f_max = 1500 # To change Muscle 2 max force
M1 = Muscle(M1_param) # Instantiate Muscle 1 object
M2 = Muscle(M2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
muscles = MuscleSytem(M1, M2) # Instantiate Muscle System with two muscles
pylog.info('Muscle system initialized \n {} \n {}'.format(
M1.parameters.showParameters(), M2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.array([-0.17, 0.0]) # Origin of Muscle 1
m1_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 1
m2_origin = np.array([0.17, 0.0]) # Origin of Muscle 2
m2_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.array([m1_origin, m1_insertion]),
np.array([m2_origin, m2_insertion]))
# Create a system with Pendulum and Muscles using the System Class
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
##### Time #####
t_max = 3 # Maximum simulation time
time = np.arange(0., t_max, 0.001) # Time vector
##### Model Initial Conditions #####
x0_P = np.array([0., 0.]) # Pendulum initial condition
# Muscle Model initial condition
x0_M = np.array([0., M1.L_OPT, 0., M2.L_OPT])
x0 = np.concatenate((x0_P, x0_M)) # System initial conditions
##### System Simulation #####
# For more details on System Simulation check SystemSimulation.py
# SystemSimulation is used to initialize the system and integrate
# over time
simsin = SystemSimulation(sys) # Instantiate Simulation object
#simsquare = SystemSimulation(sys)
# Add muscle activations to the simulation
# Here you can define your muscle activation vectors
# that are time dependent
label_test = []
"""" definition of different kinds of activation for each muscle.
Amplitude1 and amplitude2 allows to play with the amplitude of activation on each muscle (RMS value for the sinus activation)
act1 and act2 activates the muscle all the time.
actsin activates with sin(wi) if sin(wi)>0 (no negative activation). The 2 muscles are in opposition of phase.
actsquare does the same with a square signal.
"""
amplitude1 = 1.
amplitude2 = 1.
#declaration of the activations
act1 = np.ones((len(time), 1)) * amplitude1
act2 = np.ones((len(time), 1)) * amplitude2
actsin = np.ones((len(time), 1))
actsin2 = np.ones((len(time), 1))
actsquare = np.ones((len(time), 1))
actsquare2 = np.ones((len(time), 1))
wlist = [0.1, 0.05, 0.01, 0.005]
k = 0
for w in wlist:
#generation of the signals at pulsation w
for i in range(len(actsin)):
if math.sin(w * i) <= 0:
actsin[i] = 0
actsin2[i] = abs(amplitude2 * math.sqrt(2) * math.sin(w * i))
else:
actsin[i] = abs(amplitude1 * math.sqrt(2) * math.sin(w * i))
actsin2[i] = 0
for i in range(len(actsquare)):
if i % (2 * math.pi / w) <= math.pi / w:
actsquare[i] = amplitude1
actsquare2[i] = 0
else:
actsquare[i] = 0
actsquare2[i] = amplitude2
""" uncomment this to plot the activation signals"""
# #Plot of the activation through time
# plt.figure
# plt.plot(actsquare)
# plt.plot(actsin)
# plt.title("Activations wave forms used")
# plt.xlabel("Time (s)")
# plt.ylabel("Activation amplitude (.)")
""" put as parameters the activation you want (act1/2, actsin1/2 or actsquare1/2)"""
activationssin = np.hstack((actsquare, actsquare2))
#activationssquare = np.hstack((actsquare, actsquare2))
# Method to add the muscle activations to the simulation
simsin.add_muscle_activations(activationssin)
#simsquare.add_muscle_activations(activationssquare)
# Simulate the system for given time
simsin.initalize_system(x0, time) # Initialize the system state
#simsquare.initalize_system(x0, time)
#: If you would like to perturb the pedulum model then you could do
# so by
"""perturbation of the signal"""
simsin.sys.pendulum_sys.parameters.PERTURBATION = False
#simsquare.sys.pendulum_sys.parameters.PERTURBATION = True
# The above line sets the state of the pendulum model to zeros between
# time interval 1.2 < t < 1.25. You can change this and the type of
# perturbation in
# pendulum_system.py::pendulum_system function
# Integrate the system for the above initialized state and time
simsin.simulate()
#simsquare.simulate()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
ressin = simsin.results()
#ressquare = simsquare.results()
# In order to obtain internal states of the muscle
# you can access the results attribute in the muscle class
muscle1_results = simsin.sys.muscle_sys.Muscle1.results
muscle2_results = simsin.sys.muscle_sys.Muscle2.results
# Plotting the results
plt.figure('Pendulum')
plt.title('Pendulum Phase')
plt.plot(ressin[:, 1], ressin[:, 2])
label_test.append('w=' + str(wlist[k]))
k = k + 1
#plt.plot(ressquare[:, 1], ressquare[:, 2])
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad.s]')
plt.legend(label_test)
plt.grid()
# To animate the model, use the SystemAnimation class
# Pass the res(states) and systems you wish to animate
simulationsin = SystemAnimation(ressin, pendulum, muscles)
#simulationsquare = SystemAnimation(ressquare, pendulum, muscles)
# To start the animation
if DEFAULT["save_figures"] is False:
simulationsin.animate()
#simulationsquare.animate()
if not DEFAULT["save_figures"]:
plt.show()
else:
figures = plt.get_figlabels()
pylog.debug("Saving figures:\n{}".format(figures))
for fig in figures:
plt.figure(fig)
save_figure(fig)
plt.close(fig)
def main():
# Parameters
muscle_count = 100 # How many muscles to create
min_innervation_ratio = 5
max_innervation_ratio = 2000 # This is a probabalistic set point, not a hard max
min_fiber_count = 1000
max_fiber_count = 1500000
skew = -500000
# Create all the fibers in the body
# We want an aproximately normal distribution of fiber counts across all muscles
# We skew that distribution toward smaller fiber counts as is found in the human body
fiber_counts_by_muscle = norm_in_range(min_fiber_count,
max_fiber_count,
std=3,
count=muscle_count,
round=True,
skew=skew)
fiber_counts_by_muscle = sorted(fiber_counts_by_muscle)
fiber_population_mean = np.mean(fiber_counts_by_muscle) # ~300,000
if plotly and DEBUG:
data = [go.Histogram(x=fiber_counts_by_muscle)]
plotly.offline.plot(data)
##############################################################################
# One muscle
f_count = norm_in_range(min_fiber_count,
max_fiber_count,
3,
round=True,
skew=skew)
f_count = f_count[0]
print "Number of fibers: ", f_count
motor_units = gen_motor_units(f_count, fiber_population_mean,
max_innervation_ratio)
print "Number of Motor Units: ", len(motor_units)
print "Innervation Number: ", f_count / len(motor_units)
m = Muscle(motor_units)
activations = m.get_activations()
print m.get_force()
##############################################################################
# All muscles
muscles = []
for fiber_count in fiber_counts_by_muscle:
# For each muscle we want to group muscle fibers into motor units
# Each motor unit is an int representing the number of fibers the unit innervates
motor_units = gen_motor_units(fiber_count, fiber_population_mean,
max_innervation_ratio)
m = Muscle(motor_units)
muscles.append(m)
# Activate all the muscles
forces = []
for m in muscles:
l = m.get_motor_unit_count()
m.set_activations(np.random.rand(l))
force = m.get_force()
forces.append(force)
print sorted(forces)
def system_init():
""" Use this function to create a new default system. """
########## PENDULUM ##########
# Define and Setup your pendulum model here
# Check Pendulum.py for more details on Pendulum class
P_params = PendulumParameters() # Instantiate pendulum parameters
P_params.L = 1.0 # To change the default length of the pendulum
P_params.m = 0.25 # To change the default mass of the pendulum
pendulum = PendulumSystem(P_params) # Instantiate Pendulum object
#### CHECK OUT Pendulum.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
########## MUSCLES ##########
# Define and Setup your muscle model here
# Check MuscleSystem.py for more details on MuscleSystem class
m1_param = MuscleParameters() # Instantiate Muscle 1 parameters
m1_param.f_max = 200. # To change Muscle 1 max force
m1_param.l_opt = 0.4
m1_param.l_slack = 0.45
m2_param = MuscleParameters() # Instantiate Muscle 2 parameters
m2_param.f_max = 200. # To change Muscle 2 max force
m2_param.l_opt = 0.4
m2_param.l_slack = 0.45
m1 = Muscle('m1', m1_param) # Instantiate Muscle 1 object
m2 = Muscle('m2', m2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
# Instantiate Muscle System with two muscles
muscles = MuscleSystem(m1, m2)
pylog.info('Muscle system initialized \n {} \n {}'.format(
m1.parameters.showParameters(), m2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.asarray([0.0, 0.9]) # Origin of Muscle 1
m1_insertion = np.asarray([0.0, 0.15]) # Insertion of Muscle 1
m2_origin = np.asarray([0.0, 0.8]) # Origin of Muscle 2
m2_insertion = np.asarray([0.0, -0.3]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.asarray([m1_origin, m1_insertion]),
np.asarray([m2_origin, m2_insertion]))
########## Network ##########
# The network consists of four neurons
N_params = NetworkParameters() # Instantiate default network parameters
N_params.D = 1 # To change a network parameter
# Similarly to change w -> N_params.w = (4x4) array
N_params.tau = [0.02, 0.02, 0.1, 0.1]
N_params.w = [[0, -5, 5, -5], [-5, 0, -5, 5], [-5, 0, 0, 0], [0, -5, 0, 0]]
N_params.b = [3.0, 3.0, -3.0, -3.0]
N_params.w = np.transpose(N_params.w)
# Create a new neural network with above parameters
neural_network = NeuralSystem(N_params)
pylog.info('Neural system initialized \n {}'.format(
N_params.showParameters()))
########## ADD SYSTEMS ##########
# Create system of Pendulum, Muscles and neural network using SystemClass
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
# Add the neural network to the system
sys.add_neural_system(neural_network)
##### Time #####
t_max = 2.5 # Maximum simulation time
time = np.arange(0., t_max, 0.001) # Time vector
##### Model Initial Conditions #####
x0_P = np.asarray([np.pi / 2, 0.]) # Pendulum initial condition
# Muscle Model initial condition
l_ce_0 = sys.muscle_sys.initialize_muscle_length(np.pi / 2)
x0_M = np.asarray([0.05, l_ce_0[0], 0.05, l_ce_0[1]])
x0_N = np.asarray([-0.5, 1, 0.5, 1]) # Neural Network Initial Conditions
x0 = np.concatenate((x0_P, x0_M, x0_N)) # System initial conditions
##### System Simulation #####
# For more details on System Simulation check SystemSimulation.py
# SystemSimulation is used to initialize the system and integrate
# over time
sim = SystemSimulation(sys) # Instantiate Simulation object
sim.initalize_system(x0, time) # Initialize the system state
return sim
def plotVceLoad(load,ms=[1.]):
# Defination of muscles
muscle_parameters = MuscleParameters()
mass_parameters = MassParameters()
# Create muscle object
muscle = Muscle(muscle_parameters)
# Create mass object
mass = Mass(mass_parameters)
# Instatiate isotonic muscle system
sys = IsotonicMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# Add the mass to the system
sys.add_mass(mass)
# Evalute for a single load
#load = 100.
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT,
sys.muscle.L_OPT + sys.muscle.L_SLACK, 0.0]
# x0[0] - -> activation
# x0[1] - -> contractile length(l_ce)
# x0[2] - -> position of the mass/load
# x0[3] - -> velocity of the mass/load
# Set the time for integration
t_start = 0.0
t_stop = 0.3
time_step = 0.001
time_stabilize = 0.2
time = np.arange(t_start, t_stop, time_step)
plt.figure('Max Velocity-Tension curve')
for s in ms:
muscle_stimulation = s
v = []
for l in load:
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
time_stabilize=time_stabilize,
stimulation=muscle_stimulation,
load=l)
# Find the max or min speed achieved
i = np.argmax(np.abs(result.v_ce))
v.append(-result.v_ce[i])
#if result[i].l_mtc < sys.muscle.L_OPT + sys.muscle.L_SLACK:
for i in range(len(v)):
if i >= 1 and v[i]*v[i-1] <=0:
plt.plot(load[i],v[i],color='green', marker='x', linestyle='dashed',
linewidth=2, markersize=12)
plt.plot(load, v,label='maximal speed\nMuscle stimulation: {}'.format(s))
plt.legend()
plt.title('Isotonic muscle experiment\nMax Velocity-Tension curve')
plt.xlabel('load [kg]')
plt.ylabel('CE speed [m/s]')
#axes = plt.gca()
#axes.set_xlim([0.05,0.2])
#axes.set_ylim([0,1700])
plt.grid()
def exercise3a():
""" Main function to run for Exercise 3.
Parameters
----------
None
Returns
-------
None
"""
# Define and Setup your pendulum model here
# Check Pendulum.py for more details on Pendulum class
P_params = PendulumParameters() # Instantiate pendulum parameters
P_params.L = 0.5 # To change the default length of the pendulum
P_params.m = 1. # To change the default mass of the pendulum
P_params.PERTURBATION = True
pendulum = PendulumSystem(P_params) # Instantiate Pendulum object
#### CHECK OUT Pendulum.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
# Define and Setup your pendulum model here
# Check MuscleSytem.py for more details on MuscleSytem class
M1_param = MuscleParameters() # Instantiate Muscle 1 parameters
M1_param.f_max = 1500 # To change Muscle 1 max force
M2_param = MuscleParameters() # Instantiate Muscle 2 parameters
M2_param.f_max = 1500 # To change Muscle 2 max force
M1 = Muscle(M1_param) # Instantiate Muscle 1 object
M2 = Muscle(M2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
muscles = MuscleSytem(M1, M2) # Instantiate Muscle System with two muscles
pylog.info('Muscle system initialized \n {} \n {}'.format(
M1.parameters.showParameters(), M2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.array([-0.17, 0.0]) # Origin of Muscle 1
m1_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 1
m2_origin = np.array([0.17, 0.0]) # Origin of Muscle 2
m2_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.array([m1_origin, m1_insertion]),
np.array([m2_origin, m2_insertion]))
##### Neural Network #####
# The network consists of four neurons
N_params = NetworkParameters() # Instantiate default network parameters
N_params.tau = [0.02, 0.02, 0.1, 0.1]
N_params.b = [3.0, 3.0, -3.0, -3.0]
N_params.D = 1.0 # To change a network parameter
N_params.w = np.asarray([[0.0, -5.0, -5.0, 0.0], [-5.0, 0.0, 0.0, -5.0],
[5.0, -5.0, 0.0, 0.0], [-5.0, 5.0, 0.0, 0.0]])
# Similarly to change w -> N_params.w = (4x4) array
print(N_params.w)
############################# Exercise 3A ######################
N_params.w = np.transpose(
np.asarray([[0, -1, 1, -1], [-1, 0, -1, 1], [-1, 0, 0, 0],
[0, -1, 0, 0]])) * 5
print(N_params.w, N_params.D, N_params.tau, N_params.b, N_params.exp)
# Create a new neural network with above parameters
neural_network = NeuralSystem(N_params)
pylog.info('Neural system initialized \n {}'.format(
N_params.showParameters()))
# Create system of Pendulum, Muscles and neural network using SystemClass
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
sys.add_neural_system(
neural_network) # Add the neural network to the system
##### Time #####
t_max = 2. # Maximum simulation time
time = np.arange(0., t_max, 0.001) # Time vector
##### Model Initial Conditions #####
x0_P = np.array([[-0.5, 0], [-0.25, -0.25], [0., 0.],
[0.5, 0]]) # Pendulum initial condition
for i in x0_P:
# Muscle Model initial condition
x0_M = np.array([0., M1.L_OPT, 0., M2.L_OPT])
x0_N = np.array([-1.5, 1, 2.5, 1]) # Neural Network Initial Conditions
x0 = np.concatenate((i, x0_M, x0_N)) # System initial conditions
##### System Simulation #####
# For more details on System Simulation check SystemSimulation.py
# SystemSimulation is used to initialize the system and integrate
# over time
sim = SystemSimulation(sys) # Instantiate Simulation object
# sim.add_external_inputs_to_network(np.ones((len(time), 4)))
# wave_h1 = np.sin(time*3)*2 #makes a sinusoidal wave from 'time'
# wave_h2 = np.sin(time*3 + np.pi)*1 #makes a sinusoidal wave from 'time'
#
# wave_h1[wave_h1<0] = 0 #formality of passing negative values to zero
# wave_h2[wave_h2<0] = 0 #formality of passing negative values to zero
#
# act1 = wave_h1.reshape(len(time), 1) #makes a vertical array like act1
# act2 = wave_h2.reshape(len(time), 1) #makes a vertical array like act1
# column = np.ones((len(time), 1))
# ext_in = np.hstack((act1, column, act2, column))
# sim.add_external_inputs_to_network(ext_in)
sim.initalize_system(x0, time) # Initialize the system state
sim.sys.pendulum_sys.parameters.PERTURBATION = False
# Integrate the system for the above initialized state and time
sim.simulate()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
res = sim.results()
# In order to obtain internal states of the muscle
# you can access the results attribute in the muscle class
muscle1_results = sim.sys.muscle_sys.Muscle1.results
muscle2_results = sim.sys.muscle_sys.Muscle2.results
# Plotting the results: Position(phase) vs time
plt.figure('Pendulum Phase')
plt.title('Pendulum Phase')
plt.plot(res[:, 0], res[:, 1]) #to plot pendulum Position (phase)
# plt.plot(res[:, 0], time) #to plot position
# plt.plot(res[:, 0], res[:, -5:-1]) # to Plot neurons' states
plt.xlabel('time [s]')
plt.ylabel('Position [rad]')
plt.grid()
# Plotting the results: Velocity vs Position (phase)
plt.figure('Pendulum Vel v.s. Phase')
plt.title('Pendulum Vel v.s. Phase')
plt.plot(res[:, 1], res[:, 2]) #to plot Velocity vs Position (phase)
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad.s]')
plt.grid()
# Plotting the results: Velocity vs time
plt.figure('Pendulum Velocity')
plt.title('Pendulum Velocity')
plt.plot(res[:, 0], res[:, 2]) #to plot Velocity vs Position
plt.xlabel('time [s]')
plt.ylabel('Velocity [rad.s]')
plt.grid()
# Plotting the results: Output of the network
plt.figure('Network output')
plt.title('Network output')
plt.plot(res[:, 0], res[:, -1],
label='neuron1') #to plot Velocity vs Position
plt.plot(res[:, 0], res[:, -2], label='neuron2')
plt.plot(res[:, 0], res[:, -3], label='neuron3')
plt.plot(res[:, 0], res[:, -4], label='neuron4')
plt.xlabel('time [s]')
plt.ylabel('Stimulation ')
plt.legend(loc='upper right')
plt.grid()
if DEFAULT["save_figures"] is False:
plt.show()
else:
figures = plt.get_figlabels()
pylog.debug("Saving figures:\n{}".format(figures))
for fig in figures:
plt.figure(fig)
save_figure(fig)
plt.close(fig)
# To animate the model, use the SystemAnimation class
# Pass the res(states) and systems you wish to animate
simulation = SystemAnimation(res, sim.sys.pendulum_sys, sim.sys.muscle_sys,
sim.sys.neural_sys)
# To start the animation
simulation.animate()
def exercise3():
""" Main function to run for Exercise 3.
Parameters
----------
None
Returns
-------
None
"""
# Define and Setup your pendulum model here
# Check Pendulum.py for more details on Pendulum class
P_params = PendulumParameters() # Instantiate pendulum parameters
P_params.L = 0.5 # To change the default length of the pendulum
P_params.m = 1. # To change the default mass of the pendulum
pendulum = PendulumSystem(P_params) # Instantiate Pendulum object
#### CHECK OUT Pendulum.py to ADD PERTURBATIONS TO THE MODEL #####
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
# Define and Setup your pendulum model here
# Check MuscleSytem.py for more details on MuscleSytem class
M1_param = MuscleParameters() # Instantiate Muscle 1 parameters
M1_param.f_max = 1500 # To change Muscle 1 max force
M2_param = MuscleParameters() # Instantiate Muscle 2 parameters
M2_param.f_max = 1500 # To change Muscle 2 max force
M1 = Muscle(M1_param) # Instantiate Muscle 1 object
M2 = Muscle(M2_param) # Instantiate Muscle 2 object
# Use the MuscleSystem Class to define your muscles in the system
muscles = MuscleSytem(M1, M2) # Instantiate Muscle System with two muscles
pylog.info('Muscle system initialized \n {} \n {}'.format(
M1.parameters.showParameters(), M2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.array([-0.17, 0.0]) # Origin of Muscle 1
m1_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 1
m2_origin = np.array([0.17, 0.0]) # Origin of Muscle 2
m2_insertion = np.array([0.0, -0.17]) # Insertion of Muscle 2
# Attach the muscles
muscles.attach(np.array([m1_origin, m1_insertion]),
np.array([m2_origin, m2_insertion]))
##### Neural Network #####
# The network consists of four neurons
N_params = NetworkParameters() # Instantiate default network parameters
N_params.D = 2. # To change a network parameter
# Similarly to change w -> N_params.w = (4x4) array
# Create a new neural network with above parameters
neural_network = NeuralSystem(N_params)
pylog.info('Neural system initialized \n {}'.format(
N_params.showParameters()))
# Create system of Pendulum, Muscles and neural network using SystemClass
# Check System.py for more details on System class
sys = System() # Instantiate a new system
sys.add_pendulum_system(pendulum) # Add the pendulum model to the system
sys.add_muscle_system(muscles) # Add the muscle model to the system
# Add the neural network to the system
sys.add_neural_system(neural_network)
##### Time #####
t_max = 2.5 # Maximum simulation time
time = np.arange(0., t_max, 0.001) # Time vector
##### Model Initial Conditions #####
x0_P = np.array([0., 0.]) # Pendulum initial condition
# Muscle Model initial condition
x0_M = np.array([0., M1.L_OPT, 0., M2.L_OPT])
x0_N = np.array([-0.5, 1, 0.5, 1]) # Neural Network Initial Conditions
x0 = np.concatenate((x0_P, x0_M, x0_N)) # System initial conditions
##### System Simulation #####
# For more details on System Simulation check SystemSimulation.py
# SystemSimulation is used to initialize the system and integrate
# over time
sim = SystemSimulation(sys) # Instantiate Simulation object
# Add external inputs to neural network
# sim.add_external_inputs_to_network(np.ones((len(time), 4)))
# sim.add_external_inputs_to_network(ext_in)
sim.initalize_system(x0, time) # Initialize the system state
# Integrate the system for the above initialized state and time
sim.simulate()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
res = sim.results()
# Obtain the states of the system after integration
# res is np.array [time, states]
# states vector is in the same order as x0
res = sim.results()
# In order to obtain internal states of the muscle
# you can access the results attribute in the muscle class
muscle1_results = sim.sys.muscle_sys.Muscle1.results
muscle2_results = sim.sys.muscle_sys.Muscle2.results
# Plotting the results
plt.figure('Pendulum')
plt.title('Pendulum Phase')
plt.plot(res[:, 0], res[:, :2])
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad.s]')
plt.grid()
if DEFAULT["save_figures"] is False:
plt.show()
else:
figures = plt.get_figlabels()
pylog.debug("Saving figures:\n{}".format(figures))
for fig in figures:
plt.figure(fig)
save_figure(fig)
plt.close(fig)
# To animate the model, use the SystemAnimation class
# Pass the res(states) and systems you wish to animate
simulation = SystemAnimation(res, sim.sys.pendulum_sys, sim.sys.muscle_sys,
sim.sys.neural_sys)
# To start the animation
simulation.animate()
def exercise1b():
""" Exercise 1a
The goal of this exercise is to understand the relationship
between muscle length and tension.
Here you will re-create the isometric muscle contraction experiment.
To do so, you will have to keep the muscle at a constant length and
observe the force while stimulating the muscle at a constant activation."""
# Defination of muscles
parameters = MuscleParameters()
pylog.warning("Loading default muscle parameters")
pylog.info(parameters.showParameters())
pylog.info("Use the parameters object to change the muscle parameters")
# Create muscle object
muscle = Muscle(parameters)
pylog.warning("Isometric muscle contraction to be completed")
# Instatiate isometric muscle system
sys = IsometricMuscleSystem()
# Add the muscle to the system
sys.add_muscle(muscle)
# You can still access the muscle inside the system by doing
# >>> sys.muscle.L_OPT # To get the muscle optimal length
stimulations = np.arange(.0, 1.0, .02)
stretches = np.arange(.12, .36, .05) #default length is 0.24
allStretches = []
allStims = []
allActForces = []
allPassForces = []
allNetForces = []
for stretch in stretches:
# Evalute for a single muscle stretch
muscle_active_forces = []
muscle_passive_forces = []
total_force = []
l_ce = []
for stimulation in stimulations:
# Evalute for a single muscle stimulation
muscle_stimulation = stimulation
# Set the initial condition
x0 = [0.0, sys.muscle.L_OPT]
# x0[0] --> muscle stimulation intial value
# x0[1] --> muscle contracticle length initial value
# Set the time for integration
t_start = 0.0
t_stop = 0.3
time_step = 0.001
time = np.arange(t_start, t_stop, time_step)
# Run the integration
result = sys.integrate(x0=x0,
time=time,
time_step=time_step,
stimulation=muscle_stimulation,
muscle_length=stretch)
muscle_active_forces.append(result.active_force[-1])
muscle_passive_forces.append(result.passive_force[-1])
total_force.append(result.active_force[-1] +
result.passive_force[-1])
l_ce.append(result.l_ce[-1])
allStretches.append(stretch)
allStims.append(stimulation)
allActForces.append(result.active_force[-1])
allPassForces.append(result.passive_force[-1])
allNetForces.append(total_force[-1])
# # Plotting results of individual trials to verify steady state assumption
# plt.figure('Force over time with different stimulations and lengths %.2f' %stretch)
# plt.plot(time, result.active_force, label='Active: Stim = %.2f'%stimulation + ' L = %.2f'%stretch)
# plt.plot(time, result.passive_force, label='Passive: Stim = %.2f'%stimulation + ' L = %.2f'%stretch)
# plt.plot(time, result.active_force+result.passive_force, label='Net: Stim = %.2f'%stimulation + ' L = %.2f'%stretch)
# plt.title('Force over time with different stimulations and lengths')
# plt.xlabel('Time [s]')
# plt.ylabel('Active Muscle Force [N]')
# plt.legend(loc='upper right')
# plt.grid()
# Plotting
plt.figure('Isometric Muscle: Stimulation vs Force')
plt.subplot(3, 1, 1)
plt.plot(stimulations,
muscle_active_forces,
label='L_mtu = %.2f' % stretch)
plt.title('Isometric Muscle: Stimulation vs Force')
plt.xlabel('Stimulation')
plt.ylabel('Active Force [N]')
plt.legend(loc='upper right')
plt.grid()
plt.subplot(3, 1, 2)
plt.plot(stimulations,
muscle_passive_forces,
label='L_mtu = %.2f' % stretch)
plt.xlabel('Stimulation')
plt.ylabel('Passive Force [N]')
plt.legend(loc='upper right')
plt.grid()
plt.subplot(3, 1, 3)
plt.plot(stimulations, total_force, label='L_mtu = %.2f' % stretch)
plt.xlabel('Stimulation')
plt.ylabel('Total Force [N]')
plt.legend(loc='upper right')
plt.grid()
allActForces = np.array(allActForces).reshape(
(stretches.size, stimulations.size))
allPassForces = np.array(allPassForces).reshape(
(stretches.size, stimulations.size))
allNetForces = np.array(allNetForces).reshape(
(stretches.size, stimulations.size))
stimulations, stretches = np.meshgrid(stimulations, stretches)
fig1b = plt.figure('1b. Stim vs Active Force Surface Plot')
ax = fig1b.gca(projection='3d')
ax = fig1b.add_subplot(111, projection='3d')
ax.plot_surface(stimulations,
stretches,
allActForces,
cmap=cm.coolwarm,
linewidth=0.5,
antialiased=False)
ax.set_xlabel('Stimulation')
ax.set_ylabel('Muscle Length (m)')
ax.set_zlabel('Active Force (N)')
plt.title('Stimulation vs Active Force')
fig1b = plt.figure('1b. Stim vs Passive Force Surface Plot')
ax = fig1b.gca(projection='3d')
ax = fig1b.add_subplot(111, projection='3d')
ax.plot_surface(stimulations,
stretches,
allPassForces,
cmap=cm.coolwarm,
linewidth=0.5,
antialiased=False)
ax.set_xlabel('Stimulation')
ax.set_ylabel('Muscle Length (m)')
ax.set_zlabel('Passive Force (N)')
plt.title('Stimulation vs Passive Force')
fig1b = plt.figure('1b. Stim vs Total Force Surface Plot')
ax = fig1b.gca(projection='3d')
ax = fig1b.add_subplot(111, projection='3d')
ax.plot_surface(stimulations,
stretches,
allNetForces,
cmap=cm.coolwarm,
linewidth=0.5,
antialiased=False)
ax.set_xlabel('Stimulation')
ax.set_ylabel('Muscle Length (m)')
ax.set_zlabel('Net Force (N)')
plt.title('Stimulation vs Total Force')