def exercise2a():
""" Exercise 2a
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()
biolog.warning("Loading default muscle parameters")
biolog.info(parameters.showParameters())
# Create muscle object
muscle = Muscle.Muscle(parameters)
muscle.l_opt = 0.11
activation = 0.05
stretch=np.arange(-0.09, 0.09, 0.001)
res = isometric_contraction(muscle, stretch, activation)
plt.title('Force-Length when activation is %s' %activation)
plt.title('Force-Length when Lopt is %s' %muscle.l_opt)
plt.ylim(0,1.7*max(res[1]))
# plt.ylim(0,2500)
plt.plot(res[0],res[1])
plt.plot(res[0],res[2])
plt.plot(res[0],res[2]+res[1])
plt.legend(['active force','passive force','total force'])
plt.xlabel('Length(m)')
plt.ylabel('Force(N)')
plt.grid()
plt.show()
""" Example for plotting graphs using matplotlib. """
def exercise2b():
""" Exercise 2b
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(muscle_parameters)
# Run the isotonic_contraction
load=np.arange(0, 300, 10)
res = isotonic_contraction(muscle,load,muscle_parameters=MuscleParameters(),mass_parameters=MassParameters())
plt.plot(res[1],res[0])
plt.title('force-velocity when activation is %s' %res[2])
plt.ylim(0,60)
plt.xlabel('Velocity of the contractile element Vce (m/s)')
plt.ylabel('Force generated by the muscle(N)')
plt.show()
def exercise2b():
""" Exercise 2b
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"""
# Definition of muscles
muscle_parameters = MuscleParameters()
print(muscle_parameters.showParameters())
mass_parameters = MassParameters()
print(mass_parameters.showParameters())
# Create muscle object
muscle = Muscle.Muscle(muscle_parameters)
# Point 2d. Different load values.
biolog.info("Calling for point 2d")
isoK = isotonic_contraction(muscle)
lineV = np.arange(-1, 2500, 1)
zerV = np.zeros(np.size(lineV))
plt.figure("Plot of Force vs Velocity")
plt.plot(isoK[0], isoK[1])
plt.title("Tension vs Normalised Velocity", fontsize=18)
plt.plot(zerV, lineV, linestyle=':', color='red')
plt.xlabel('Normalised Velocity [-]')
plt.ylabel('Total Force of the Muscle [N]')
plt.legend(['Force/Velocity [N]'])
plt.minorticks_on()
plt.grid(which='major', linestyle='-', linewidth='0.5', color='black')
plt.grid(which='minor', linestyle=':', linewidth='0.5', color='black')
save_figure('velociplot')
# plt.plot(isoK[0], isoK[1], 'o', markersize = 5)
# Point 2f. Different muscle activation values.
activations = np.arange(0.5, 1.05, 0.05)
plt.figure(
'Muscle Force vs Normalised velocity for varying activation time')
legend2 = list()
#print(activations)
for i, a in enumerate(activations):
muscle1 = Muscle.Muscle(muscle_parameters)
#print("Activation = {} [s]".format(a))
iso = isotonic_contraction(muscle1, activation=a)
#print("lapin \n {}".format(iso[2]))
legend2.append("Activation = {} [-]".format(a))
plt.plot(iso[0], iso[1]) # plot for active force
plt.xlabel('Normalised Velocity [-]')
plt.ylabel('Total Force [N]')
plt.plot(zerV, lineV, linestyle=':', color='red')
plt.legend(legend2)
plt.grid()
plt.minorticks_on()
plt.grid(which='major', linestyle='-', linewidth='0.5', color='black')
plt.grid(which='minor', linestyle=':', linewidth='0.5', color='black')
save_figure('F_vs_Vel_Activations')
def isotonic_contraction(muscle, load,
muscle_parameters=MuscleParameters(),
mass_parameters=MassParameters()):
""" This function implements the isotonic contraction
of the muscle.
Parameters:
-----------
muscle : <Muscle>
Instance of Muscle class
load : list/array
External load to be applied on the muscle.
It is the mass suspended by the muscle
muscle_parameters : MuscleParameters
Muscle paramters instance
mass_paramters : MassParameters
Mass parameters instance
Since the muscle model is complex and sensitive to integration,
use the following example as a hint to complete your implementation.
"""
# Time settings
t_start = 0.0 # Start time
t_stop = 0.2 # Stop time
dt = 0.001 # Time step
time = np.arange(t_start,t_stop,dt)
load = np.array(load)
activation = 0.2
j = 0
res_ = np.ones(len(time))
velocity_ce = np.ones(len(load))
x0 = np.array([-0.0, 0.0])
for load_ in load:
muscle.initializeMuscleLength()
mass_parameters.mass = load_ # load is mass (kg)
state = np.copy(x0)
for time_ in time: # before release, iterate to stable state
res = muscle_integrate(muscle,state[0],activation, dt)
i = 0
# print muscle.force
for time_ in time: # release, integrate for the state equations
mass_res = odeint(mass_integration,state,[time_, time_ + dt],args=(muscle.force, load_, mass_parameters)) # returns the position & velocity at each t
state[0] = mass_res[-1,0] # position of the end of the muscle
state[1] = mass_res[-1,1] # velocity of the end of the muscle
res = muscle_integrate(muscle,state[0],activation,dt)
res_[i] = res['v_CE']
i += 1
if(res['l_MTC'] > muscle_parameters.l_opt + muscle_parameters.l_slack):
velocity_ce[j] = min(res_[:])
else:
velocity_ce[j] = max(res_[:])
j+=1
return load, velocity_ce,activation
def generate_muscle_parameters(self, muscle_name):
"""To create muscle parameters from json file.
Parameters
----------
muscle_name: string
Name of the muscle
"""
param = self.muscle_parameters[muscle_name]
if param is None:
print('Invalid muscle name')
sys.exit(1)
return MuscleParameters(l_slack=param['l_slack'],
l_opt=param['l_opt'],
v_max=param['v_max'],
f_max=param['f_max'],
pennation=param['pennation'],
name=muscle_name)
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 = .5 # To change the default length of the pendulum
P_params.mass = 5. # To change the default mass of the pendulum
pendulum = Pendulum(P_params) # Instantiate Pendulum object
#### CHECK OUT PendulumSystem.py to ADD PERTURBATIONS TO THE MODEL #####
biolog.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
biolog.info('Muscle system initialized \n {} \n {}'.format(
M1.parameters.showParameters(), M2.parameters.showParameters()))
###
########################################## 3a ########################################
#
# # Define a huge mass, such that the pendulum goes up to pi/2 and up t -pi/2
# P_params.mass = 15000.
# # Defines 3 different origins and 3 different insertions for each muscle
# origins1 = [-0.01, -0.05, -0.10, -0.15, -0.2]
# origins2 = map(lambda x: -(x), origins1)
# insertions1 = [-0.15, -0.20, -0.25, -0.30]
# insertions2 = insertions1[:] # Just for visibility
# legendsertion =np.array(['Insertion at -15 cm', 'Insertion at -20 cm', 'Insertion at -25 cm', 'Insertion at -30 cm'])
# legleg = np.array(['Insertion at -15 cm', 'Insertion at -15 cm', 'Insertion at -20 cm', 'Insertion at -20 cm', 'Insertion at -25 cm', 'Insertion at -25 cm', 'Insertion at -30 cm', 'Insertion at -30 cm'])
# cols = ('blue', 'red', 'olive', 'purple')
## length1 = np.array()
#
# for o1,o2 in zip(origins1, origins2):
# fig, (ax1, ax2) = plt.subplots(1,2, sharex = True)
# fig.suptitle('Origin of muscles: o1 = {}, o2 = {}'.format(o1,o2), fontsize='26')
# for i,j in enumerate(insertions1):
# # Define Muscle Attachment points
# m1_origin = np.array([o1, 0.0]) # Origin of Muscle 1
# m1_insertion = np.array([0.0, j]) # Insertion of Muscle 1
#
# m2_origin = np.array([o2, 0.0]) # Origin of Muscle 2
# m2_insertion = np.array([0.0, j]) # 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 #####
#
# dt=0.01
# t_max = 1. # Maximum simulation time
# time = np.arange(0., t_max, dt) # Time vector
#
#
#
# ##### Model Initial Conditions #####
# x0_P = np.array([np.pi/2. - 0.00001,0.]) # Pendulum initial condition
#
# # Muscle Model initial condition
# x0_M = np.array([0., M1.l_CE, 0., M2.l_CE])
#
# 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
#
# act1=np.ones((len(time),1))*0.05
# act2=np.ones((len(time),1))*0.05
#
# 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()
#
# # In order to obtain internal paramters of the muscle
# # Check SystemSimulation.py results_muscles() method for more information
# res_muscles = sim.results_muscles()
# length1 = np.array(map(lambda x: np.sqrt(o1**2. + j**2. + 2.*o1*j*np.sin(x)), res[:,1])) # muscle 1 length
# length2 = np.array(map(lambda x: np.sqrt(o2**2. + j**2. + 2.*o2*j*np.sin(x)), res[:,1])) # muscle 2 length
# # moment arm of muscles calculation
# h1lambda = np.array(map(lambda x: np.abs(o1)*np.abs(j)*np.cos(x), res[:,1]))
# h2lambda = np.array(map(lambda x: np.abs(o2)*np.abs(j)*np.cos(x), res[:,1]))
# h1 = h1lambda/length1
# h2 = h2lambda/length2
# # Plotting the result for the current origins
# ax1.plot(res[:, 1], length1)
# ax2.plot(res[:, 1], h1)
# if o1 == -0.1:
# plt.figure('Muscles\' moment arm for insertions at {} and {}'.format(o1, o2))
# if j == -0.15:
# temp = 0.0
# plt.plot(res[:, 1], h1, color=(1.0, temp, 0.0), linestyle = ':')
# plt.plot(res[:, 1], h2, color=(temp, .5, 1.), linestyle = ':')
# elif j == -0.2:
# temp = 0.3
# plt.plot(res[:, 1], h1, color=(1.0, temp, 0.0), linestyle = '--')
# plt.plot(res[:, 1], h2, color=(temp, .5, 1.), linestyle = '--')
# elif j == -0.25:
# temp = 0.7
# plt.plot(res[:, 1], h1, color=(1.0, temp, 0.0), linestyle = '-.')
# plt.plot(res[:, 1], h2, color=(temp, .5, 1.), linestyle = '-.')
# else:
# temp = 1.0
# plt.plot(res[:, 1], h1, color=(1.0, temp, 0.0))
# plt.plot(res[:, 1], h2, color=(temp, .5, 1.))
# plt.legend(legleg)
# plt.xlabel('Pendulum position [rad]', fontsize = '18')
# plt.ylabel('Muscle moment arm [m]', fontsize = '18')
# plt.title('Muscles\' moment arm for insertions at {} and {}.\nRedish = muscle 1 (left), Blueish = muscle 2 (right)'.format(o1, o2), fontsize='26')
# plt.grid('ON')
#
# ax1.legend(legendsertion)
# ax2.legend(legendsertion)
# ax1.set_xlabel('Position [rad]', fontsize='18')
# ax2.set_xlabel('Position [rad]', fontsize='18')
# ax1.set_ylabel('Muscle length [m]', fontsize='18') # Here we computed length 1 but muscle 2 has the same behaviour for identical params
# ax2.set_ylabel('Muscle moment arm [m]', fontsize='18')
# ax1.set_title('Muscle-tendon unit length in terms of pendulum position', fontsize='20')
# ax2.set_title('Muscle\'s moment arm', fontsize='20')
# ax1.grid()
# ax2.grid()
#
######################################## End OF 3a ########################################
##
########################################## 3b ########################################
#
# # Define a huge mass, such that the pendulum goes up to pi/2 and up t -pi/2
# P_params.mass = 1500.
# # Defines 3 different origins and 3 different insertions for each muscle
# origins1 = [-0.01, -0.05, -0.10, -0.15, -0.2]
# origins2 = map(lambda x: -(x), origins1)
# insertions1 = [-0.15, -0.20, -0.25, -0.30]
# insertions2 = insertions1[:] # Just for visibility
# legendsertion =np.array(['Insertion at -15 cm', 'Insertion at -20 cm', 'Insertion at -25 cm', 'Insertion at -30 cm'])
# legleg = np.array(['Insertion at -15 cm', 'Insertion at -15 cm', 'Insertion at -20 cm', 'Insertion at -20 cm', 'Insertion at -25 cm', 'Insertion at -25 cm', 'Insertion at -30 cm', 'Insertion at -30 cm'])
# cols = ('blue', 'red', 'olive', 'purple')
## length1 = np.array()
#
# for o1,o2 in zip(origins1, origins2):
# fig, (ax1, ax2) = plt.subplots(1,2, sharex = True)
# fig.suptitle('Origin of muscles - passive: o1 = {}, o2 = {}'.format(o1,o2), fontsize='26')
# for i,j in enumerate(insertions1):
# # Define Muscle Attachment points
# m1_origin = np.array([o1, 0.0]) # Origin of Muscle 1
# m1_insertion = np.array([0.0, j]) # Insertion of Muscle 1
#
# m2_origin = np.array([o2, 0.0]) # Origin of Muscle 2
# m2_insertion = np.array([0.0, j]) # 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 #####
#
# dt=0.01
# t_max = 1. # Maximum simulation time
# time = np.arange(0., t_max, dt) # Time vector
#
#
#
# ##### Model Initial Conditions #####
# x0_P = np.array([np.pi/2. - 0.00001,0.]) # Pendulum initial condition
#
# # Muscle Model initial condition
# x0_M = np.array([0., M1.l_CE, 0., M2.l_CE])
#
# 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
#
# act1=np.ones((len(time),1))*0.00 # Passive muscles, unactivated.
# act2=np.ones((len(time),1))*0.00
#
# 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()
#
# # In order to obtain internal paramters of the muscle
# # Check SystemSimulation.py results_muscles() method for more information
# res_muscles = sim.results_muscles()
# length1 = np.array(map(lambda x: np.sqrt(o1**2. + j**2. + 2.*o1*j*np.sin(x)), res[:,1])) # muscle 1 length
# length2 = np.array(map(lambda x: np.sqrt(o2**2. + j**2. + 2.*o2*j*np.sin(x)), res[:,1])) # muscle 2 length
# # moment arm of muscles calculation
# h1lambda = np.array(map(lambda x: np.abs(o1)*np.abs(j)*np.cos(x), res[:,1]))
# h2lambda = np.array(map(lambda x: np.abs(o2)*np.abs(j)*np.cos(x), res[:,1]))
# h1 = h1lambda/length1
# h2 = h2lambda/length2
# # Plotting the result for the current origins
# ax1.plot(res[:, 1], length1)
# ax2.plot(res[:, 1], h1)
# if o1 == -0.1:
# plt.figure('Muscles\' moment arm for insertions at {} and {} - passive'.format(o1, o2))
# if j == -0.15:
# temp = 0.0
# plt.plot(res[:, 1], h1, color=(1.0, temp, 0.0), linestyle = ':')
# plt.plot(res[:, 1], h2, color=(temp, .5, 1.), linestyle = ':')
# elif j == -0.2:
# temp = 0.3
# plt.plot(res[:, 1], h1, color=(1.0, temp, 0.0), linestyle = '--')
# plt.plot(res[:, 1], h2, color=(temp, .5, 1.), linestyle = '--')
# elif j == -0.25:
# temp = 0.7
# plt.plot(res[:, 1], h1, color=(1.0, temp, 0.0), linestyle = '-.')
# plt.plot(res[:, 1], h2, color=(temp, .5, 1.), linestyle = '-.')
# else:
# temp = 1.0
# plt.plot(res[:, 1], h1, color=(1.0, temp, 0.0))
# plt.plot(res[:, 1], h2, color=(temp, .5, 1.))
# plt.legend(legleg)
# plt.xlabel('Pendulum position [rad]', fontsize = '18')
# plt.ylabel('Muscle moment arm [m]', fontsize = '18')
# plt.title('Muscles\' moment arm for insertions at {} and {} - passive.\nRedish = muscle 1 (left), Blueish = muscle 2 (right)'.format(o1, o2), fontsize='26')
# plt.grid('ON')
#
# ax1.legend(legendsertion)
# ax2.legend(legendsertion)
# ax1.set_xlabel('Position [rad]', fontsize='18')
# ax2.set_xlabel('Position [rad]', fontsize='18')
# ax1.set_ylabel('Muscle length [m]', fontsize='18') # Here we computed length 1 but muscle 2 has the same behaviour for identical params
# ax2.set_ylabel('Muscle moment arm [m]', fontsize='18')
# ax1.set_title('Muscle-tendon unit length in terms of pendulum position', fontsize='20')
# ax2.set_title('Muscle\'s moment arm', fontsize='20')
# ax1.grid()
# ax2.grid()
#
######################################## End OF 3b ########################################
######################################## Part 3c,d,e,f ##########################################
LC = True # Limit Cycle ON => LC True, Limit Cyle OFF => LC False
if LC == True:
P_params.mass = 10.
else:
P_params.mass = 100.
# For point 3f, we changed max forces up here (line 55 and 57)
# 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 #####
dt = 0.01
t_max = 5. # Maximum simulation time
time = np.arange(0., t_max, dt) # Time vector
##### Model Initial Conditions #####
x0_P = np.array([2 * np.pi / 6., 0.]) # Pendulum initial condition
# Muscle Model initial condition
x0_M = np.array([0., M1.l_CE, 0., M2.l_CE])
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
act1 = np.arange(0., t_max, dt)
act2 = np.arange(0., t_max, dt)
if LC == True:
act1 = (np.sin(2. * np.pi / t_max * 5. * act1) +
1.) * .5 # acts = time
act2 = (
-np.sin(2. * np.pi / t_max * 5. * act2) + 1.
) * .5 # by increasing frequency, we don't let the time to gravity to make its office and contribute to the system's equilibrium, so the amplitude of the pendulum diminues.
act1 = act1.reshape(len(act1), 1)
act2 = act2.reshape(len(act2), 1)
else:
act1 = np.ones((len(time), 1)) * 0.25
act2 = np.ones((len(time), 1)) * 0.25
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()
# In order to obtain internal paramters of the muscle
# Check SystemSimulation.py results_muscles() method for more information
res_muscles = sim.results_muscles()
# Plotting the results
plt.figure('Pendulum')
# plt.title('Pendulum Phase')
plt.title('Limit cycle behaviour for a max force of {} N'.format(M1.F_max),
fontsize='22')
# plt.plot(res[:, 1], res[:, 2])
plt.plot(time, res[:, 1])
# plt.xlabel('Position [rad]')
# plt.ylabel('Velocity [rad.s]')
plt.xlabel('Time [s]')
plt.ylabel('Pendulum position [rad]')
plt.grid()
# Plotting activation
legact = ("Muscle 1 - left", "Muscle 2 - right")
plt.figure('Activations')
# plt.title('Pendulum Phase')
plt.title('Muscle activation patterns', fontsize='22')
# plt.plot(res[:, 1], res[:, 2])
plt.plot(time, act1, color='red')
plt.plot(time, act2, color='green')
# plt.xlabel('Position [rad]')
# plt.ylabel('Velocity [rad.s]')
plt.xlabel('Time [s]')
plt.ylabel('Activation [-]')
plt.legend(legact)
plt.grid()
if DEFAULT["save_figures"] is False:
plt.show()
else:
figures = plt.get_figlabels()
biolog.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, pendulum, muscles)
# To start the animation
simulation.animate()
def exercise4():
""" 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.mass = 1. # To change the default mass of the pendulum
pendulum = Pendulum(P_params) # Instantiate Pendulum object
#### CHECK OUT Pendulum.py to ADD PERTURBATIONS TO THE MODEL #####
biolog.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
biolog.info('Muscle system initialized \n {} \n {}'.format(
M1.parameters.showParameters(),
M2.parameters.showParameters()))
# Define Muscle Attachment points
m1_origin = np.array([-0.10, 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, -0.10]) # 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 = 1. # To change a network parameter
# Similarly to change w -> N_params.w = (4x4) array
N_params.w=[[.0,-5.,-5.0,0.],
[-5.,0.,.0,-5.0],
[3.0,-1.0,.0,.0],
[-1.0,3.,.0,.0]]
N_params.b=[3.0,3.0,-3.0,-3.]
N_params.tau=[.02,.02,.1,.1]
biolog.info(N_params.showParameters())
# Create a new neural network with above parameters
neural_network = NeuralSystem(N_params)
# 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 = 20. # 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_CE, 0., M2.l_CE])
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
heaviside=np.heaviside(time - np.mean(time),0.5)
h4=np.zeros((len(time),4))
h4[:,0]=heaviside
h4[:,1]=heaviside
h4[:,2]=heaviside
h4[:,3]=heaviside
sim.add_external_inputs_to_network(h4) # Activates the external drive to its max (1)
# 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()
# In order to obtain internal paramters of the muscle
# Check SystemSimulation.py results_muscles() method for more information
res_muscles = sim.results_muscles()
# Plotting the results
plt.figure('Pendulum')
plt.title('Pendulum Phase',fontsize = '18')
plt.plot(res[:, 1], res[:, 2])
plt.xlabel('Position [rad]',fontsize = '16')
plt.ylabel('Velocity [rad/s]', fontsize = '16')
plt.grid()
if DEFAULT["save_figures"] is False:
plt.show()
else:
figures = plt.get_figlabels()
biolog.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, pendulum, muscles, neural_network)
# To start the animation
simulation.animate()
# Plotting the results
plt.figure('Time & Phase')
plt.subplot(2,1,1)
plt.plot(res[:,0],res[:,1])
# plt.xlabel('Time [s]')
plt.grid()
plt.ylabel('Pos. [rad]',fontsize = '16')
plt.title('Position',fontsize = '18')
plt.subplot(2,1,2)
plt.title('Velocity',fontsize = '18')
plt.plot(res[:,0],res[:,2])
plt.xlabel('Time [s]',fontsize = '16')
plt.ylabel('Vel [rad/s]',fontsize = '16')
plt.grid()
plt.show()
def exercise2a():
""" Exercise 2a
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."""
font1 = {'family': 'normal', 'weight': 'bold', 'size': 18}
font2 = {'family': 'normal', 'weight': 'normal', 'size': 12}
# Definition of muscles
parameters = MuscleParameters()
biolog.warning("Loading default muscle parameters")
biolog.info(parameters.showParameters())
# Create muscle object
muscle = Muscle.Muscle(parameters)
# Isometric contraction, varying the activation between [0-1]
isoM = isometric_contraction(muscle)
legend1 = ("Passive Force", "Active Force", "Total Force")
plt.figure('Forces vs Length')
plt.title("Force-Length relationship")
plt.plot(isoM[0], isoM[1])
plt.plot(isoM[0], isoM[2])
plt.plot(isoM[0], isoM[3])
plt.xlabel('Total length of the contractile element [m]')
plt.ylabel('Force [N]')
plt.legend(legend1)
plt.grid()
save_figure('F_vs_length')
# Stabilisation has been verified for integrating the muscle for 0.2s. However, to be sure, we integrated it for 0.25s
# plt.figure("Stab??")
# plt.plot(isoM[4],isoM[5])
# Effect of varying l_opt (fiber length) NOT SURE)
muscleS = Muscle.Muscle(parameters) # 'short' muscle
muscleS.l_opt = 0.05 # short fiber length
muscleL = Muscle.Muscle(parameters) # 'long' muscle
muscleL.l_opt = 0.25 # long fiber length
muscleXL = Muscle.Muscle(parameters) # 'extra long' muscle
muscleXL.l_opt = 0.50 # extra long fiber length
isoS = isometric_contraction(muscleS,
stretch=np.arange(-0.25, 0.25, 0.001),
activation=0.25)
isoL = isometric_contraction(muscleL,
stretch=np.arange(-0.25, 0.25, 0.001),
activation=0.25)
isoXL = isometric_contraction(muscleXL,
stretch=np.arange(-0.25, 0.25, 0.001),
activation=0.25)
legendS = ("Short fibers: {} [m], \n max_total_length: {} [m]".format(
muscleS.l_opt, np.max(isoS[0])),
"Long fibers: {} [m], \n max_total_length: {} [m]".format(
muscleL.l_opt, np.max(isoL[0])),
"Extra Long fibers: {} [m], \n max_total_length: {} [m]".format(
muscleXL.l_opt, np.max(isoXL[0])))
plt.figure(
'Short, Long and Extra Long muscle fibers (l_opt) active force vs length'
)
plt.title(
"Stretching of -25% to +25% and activation of 25% for each muscle type"
)
plt.plot((isoS[0]) / (np.max(isoS[0])) * 100,
isoS[2]) # we plot the percentage of total length
plt.plot((isoL[0]) / (np.max(isoL[0])) * 100, isoL[2])
plt.plot((isoXL[0]) / (np.max(isoXL[0])) * 100, isoXL[2])
plt.xlabel(
'Percentage of maximal total length (l_CE + stretching) of the contractile element [m]'
)
plt.ylabel('Active Force [N]')
plt.legend(legendS)
plt.grid()
plt.minorticks_on()
plt.grid(which='major', linestyle='-', linewidth='0.5', color='black')
plt.grid(which='minor', linestyle=':', linewidth='0.5', color='black')
save_figure('short_vs_long_vs_xtraLong')
legendSx = ("Short fibers: {} [m], \n max_total_length: {} [m]".format(
muscleS.l_opt, np.max(isoS[0])),
"Long fibers: {} [m], \n max_total_length: {} [m]".format(
muscleL.l_opt, np.max(isoL[0])))
plt.figure('Short and Long muscle fibers (l_opt) active force vs length')
plt.plot(isoS[0], isoS[2])
plt.plot(isoL[0], isoL[2])
plt.xlabel('Length (l_CE + stretching) of the contractile element [m]')
plt.ylabel('Active Force [N]')
plt.legend(legendSx)
plt.grid()
plt.minorticks_on()
plt.grid(which='major', linestyle='-', linewidth='0.5', color='black')
plt.grid(which='minor', linestyle=':', linewidth='0.5', color='black')
save_figure('short_vs_Long')
# Effect of varying activation (stimulation)
activations = np.arange(0.0, 1.05, 0.05)
max_F_Diff = np.zeros(
np.size(activations)
) # vectors to assess the evolution of the difference of the maximas of passive and active force
ratio = np.zeros(
np.size(activations)
) # to implement the total_force/total_length ratio for every activation value
plt.figure('Active force vs Length with varying activation time')
legend2 = list()
#print(activations)
for i, a in enumerate(activations):
muscle1 = Muscle.Muscle(parameters)
#print("Activation = {} [s]".format(a))
iso = isometric_contraction(muscle1, activation=a)
#print("lapin \n {}".format(iso[2]))
legend2.append("Activation = {} [-]".format(a))
plt.plot(iso[0], iso[2]) # plot for active force
# plt.plot(iso[0],iso[3]) # plot for total force
max_F_Diff[i] = np.abs(np.max(iso[1]) - np.max(iso[2]))
ratio[i] = ((np.mean(iso[3])) / (np.mean(iso[0]))) / 1000
plt.xlabel('Total length of the contractile element [m]')
plt.ylabel('Force [N]')
plt.legend(legend2)
plt.grid()
save_figure('F_vs_length')
# Force difference figure
plt.figure(
'Difference between the max of the passive and the active force')
plt.plot(activations,
max_F_Diff,
color='black',
marker='v',
linestyle='dashed',
linewidth=1,
markersize=5)
plt.xlabel('Activation value [s]')
plt.ylabel('Force Difference [N]')
plt.legend(['$\Delta$'])
plt.minorticks_on()
plt.grid(which='major', linestyle='-', linewidth='0.5', color='red')
plt.grid(which='minor', linestyle=':', linewidth='0.5', color='black')
save_figure('delta_plot')
# Force/length ratio
plt.figure(
'Ratio between the total force (active + passive) and the total length of the contractile element'
)
plt.plot(activations,
ratio,
color='black',
marker='v',
linestyle='dashed',
linewidth=1,
markersize=5)
plt.xlabel('Activation value [-]')
plt.ylabel('(Total_force/total_length)/1000 [N]/[m]')
plt.legend(['$Ratio$'])
plt.minorticks_on()
plt.grid(which='major', linestyle='-', linewidth='0.5', color='red')
plt.grid(which='minor', linestyle=':', linewidth='0.5', color='black')
save_figure('ratio_plot')
biolog.info("Isometric muscle contraction implemented")
""" Example for plotting graphs using matplotlib. """
def isotonic_contraction(muscle,
load=np.arange(1., 330., 10),
muscle_parameters=MuscleParameters(),
mass_parameters=MassParameters(),
activation=1.0):
""" This function implements the isotonic contraction
of the muscle.
Parameters:
-----------
muscle : <Muscle>
Instance of Muscle class
load : list/array
External load to be applied on the muscle.
It is the mass suspended by the muscle
muscle_parameters : MuscleParameters
Muscle paramters instance
mass_paramters : MassParameters
Mass parameters instance
Since the muscle model is complex and sensitive to integration,
use the following example as a hint to complete your implementation.
Example:
--------
>>> for load_ in load:
>>> # Iterate over the different muscle load values
>>> mass_parameters.mass = load_ # Set the mass applied on the muscle
>>> state = np.copy(x0) # Reset the state for next iteration
>>> for time_ in time:
>>> # Integrate for 0.2 seconds
>>> # Integration before the quick release
>>> res = muscle_integrate(muscle, state[0], activation=1.0, dt)
>>> for time_ in time:
>>> # Quick Release experiment
>>> # Integrate the mass system by applying the muscle force on to it for a time step dt
>>> mass_res = odeint(mass_integration, state, [
>>> time_, time_ + dt], args=(muscle.force, load_, mass_parameters))
>>> state[0] = mass_res[-1, 0] # Update state with final postion of mass
>>> state[1] = mass_res[-1, 1] # Update state with final position of velocity
>>> # Now update the muscle model with new position of mass
>>> res = muscle_integrate(muscle, state[0], 1.0, dt)
>>> # Save the relevant data
>>> res_[id] = res['v_CE']
>>> if(res['l_MTC'] > muscle_parameters.l_opt + muscle_parameters.l_slack):
>>> velocity_ce[idx] = min(res_[:])
>>> else:
>>> velocity_ce[idx] = max(res_[:])
"""
load = np.array(load)
biolog.info('Exercise 2b isotonic contraction running')
# Time settings
t_start = 0.0 # Start time
t_stop = 0.1 # Stop time
dt = 0.001 # Time step
timesteps = np.arange(t_start, t_stop, dt)
timecharge = np.arange(0.0, 2.5, dt)
x0 = np.array([0.0, 0.0]) # Initial state of the muscle
# Empty vectors for further isotonic representations
F = np.zeros(np.size(load)) # force
V = np.zeros(np.size(
load)) # will contain contractile element's velocity for each loads
temp = np.zeros(np.size(timesteps))
for k, l in enumerate(load):
mass_parameters.mass = l # Set the mass applied on the muscle
state = np.copy(x0) # reset the state for next iteration
print("The current load is: {}\n\n{}\n\n".format(
mass_parameters.mass, "pump-it"))
for t in timecharge:
effect = muscle_integrate(muscle, state[0], activation, dt=dt)
# print(effect['activeForce'])
for j, t in enumerate(timesteps):
mass_res = odeint(mass_integration,
state, [t, t + dt],
args=(muscle.force, mass_parameters))
state[0] = mass_res[-1,
0] # Update state with final postion of mass
state[1] = mass_res[
-1, 1] # Update state with final position of velocity
effect = muscle_integrate(muscle, state[0], activation, dt)
temp[j] = effect['v_CE']
# print(effect['force'])
# print("The velocity is : {}".format(temp[j]))
# print("LMTC TAMERE: {}".format(effect['l_MTC']))
# print("\n\n {} \n\n {}".format(effect['l_MTC'],(effect['l_MTC'] > muscle_parameters.l_opt + muscle_parameters.l_slack)))
if (effect['l_MTC'] >
muscle_parameters.l_opt + muscle_parameters.l_slack):
V[k] = min(temp[:])
else:
V[k] = max(temp[:])
F[k] = effect['force']
# print(V)
# print(k,F)
return V, F # V = isoK[0], F = isoK[1]