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 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 exercise1():
""" Exercise 1 """
pylog.info("Executing Lab 4 : Exercise 1")
pendulum = PendulumSystem()
pendulum.parameters = PendulumParameters()
pylog.info(
"Find more information about Pendulum Parameters in SystemParameters.py"
)
pylog.info("Executing Lab 4 : Exercise 1")
# Initialize a new pendulum system with default parameters
pendulum = PendulumSystem()
pendulum.parameters = PendulumParameters()
pylog.info(
"Find more information about Pendulum Parameters in SystemParameters.py"
)
# To change a parameter you could so by,
# >>> pendulum.parameters.L = 1.5
# The above line changes the length of the pendulum
# You can instantiate multiple pendulum models with different parameters
# For example,
"""
>>> pendulum_1 = PendulumSystem()
>>> pendulum_1.parameters = PendulumParameters()
>>> pendulum_1.parameters.L = 0.5
>>> parameters_2 = PendulumParameters()
>>> parameters_2.L = 0.5
>>> pendulum_2 = PendulumSystem(paramters=parameters_2)
"""
# Above examples shows how to create two istances of the pendulum
# and changing the different parameters using two different approaches
pylog.warning("Loading default pendulum pendulum.parameters")
pylog.info(pendulum.parameters.showParameters())
# Simulation Parameters
t_start = 0.0
t_stop = 10.0
dt = 0.01
pylog.warning("Using large time step dt={}".format(dt))
time = np.arange(t_start, t_stop, dt)
x0 = [0.5, 0.0]
res = integrate(pendulum_integration, x0, time, args=(pendulum, ))
pylog.info("Instructions for applying pertubations")
# Use pendulum_perturbation method to apply pertubations
# Define the pertubations inside the function pendulum_perturbation
# res = integrate(pendulum_perturbation, x0, time, args=(pendulum,))
res.plot_state("State")
res.plot_phase("Phase")
# To animate the model, use the SystemAnimation class
# Pass the res(states) and systems you wish to animate
simulation1 = SystemAnimation(res, pendulum, handler="Pendulum animation")
simulation2 = SystemAnimation(res,
pendulum,
handler="Pendulum animation 2")
# If you want to disable the parameters in the animation plot
# simulation2 = SystemAnimation(res, pendulum, handler="Pendulum animation 2", show_parameters=False)
# To start the animation, use either simulation.animate() or plt.show()
# simulation.animate()
if DEFAULT["save_figures"] is False:
plt.show()
return
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 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 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
"""
# 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, 0.004) # 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
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)) * 1.
#act2 = np.ones((len(time), 1)) * 0.05
act1 = (np.sin((time/t_max)*10*np.pi)+1)/2
act2 = (np.sin((time/t_max)*10*np.pi + np.pi)+1)/2
act1 = np.reshape(act1, (len(time),1))
act2 = np.reshape(act2, (len(time),1))
activations = np.hstack((act1, act2))
# Plotting the results
plt.figure('Activations')
plt.title('Muscle activations')
plt.plot(time, act1, label = 'Activation muscle 1')
plt.plot(time, act2, label = 'Activation muscle 2')
plt.xlabel('Time [s]')
plt.ylabel('Activation')
plt.legend()
plt.grid()
# Method to add the muscle activations to the simulation
sim.add_muscle_activations(activations)
'''
max_amplitude = np.zeros([10, 10])
i = 0
j = 0
# Simulate the system for given time
for activation_max in np.arange(0, 1, 0.9):
i = 0
for frequency in np.arange(1, 10, 4):
act1 = ((np.sin(
(time / t_max) * frequency * np.pi) + 1) / 2) * activation_max
act2 = ((np.sin((time / t_max) * frequency * np.pi + 1) + 1) /
2) * activation_max
act1 = np.reshape(act1, (len(time), 1))
act2 = np.reshape(act2, (len(time), 1))
activations = np.hstack((act1, act2))
sim.add_muscle_activations(activations)
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
max_amplitude[i, j] = np.max(np.abs(res[:, 1]))
i += 1
# Plotting the results
plt.figure('Pendulum')
plt.title('Pendulum Phase')
plt.plot(res[:, 1],
res[:, 2],
label='activation %.2f - frequency %f' %
(activation_max, frequency))
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad.s]')
plt.grid()
j += 1
plt.figure('Amplitude')
fig, ax1 = plt.subplots(1, 1)
ax1.set_xticklabels(np.array([0, 0, 0.2, 0.4, 0.8, 1]))
ax1.set_yticklabels(np.array([0, 1, 3, 5, 7, 9]))
plt.title('Ampliudes')
plt.imshow(max_amplitude, aspect='equal', origin='lower')
plt.xlabel('Activation')
plt.ylabel('Frequncy')
# 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 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 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 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 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.
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 exercise3():
""" Main function to run for Exercise 3.
Parameters
----------
None
Returns
-------
None
"""
'''
# Create system
sim = system_init()
# Add external inputs to neural network
sim.add_external_inputs_to_network(np.ones((len(sim.time), 4)))
# 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()
# 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()
'''
######################################################
# initialization
########## PENDULUM ##########
P_params = PendulumParameters()
P_params.L = 1.0
P_params.m = 0.25
pendulum = PendulumSystem(P_params)
pylog.info('Pendulum model initialized \n {}'.format(
pendulum.parameters.showParameters()))
########## MUSCLES ##########
m1_param = MuscleParameters()
m1_param.f_max = 200.
m1_param.l_opt = 0.4
m1_param.l_slack = 0.45
m2_param = MuscleParameters()
m2_param.f_max = 200.
m2_param.l_opt = 0.4
m2_param.l_slack = 0.45
m1 = Muscle('m1', m1_param)
m2 = Muscle('m2', m2_param)
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])
m1_insertion = np.asarray([0.0, 0.15])
m2_origin = np.asarray([0.0, 0.8])
m2_insertion = np.asarray([0.0, -0.3])
muscles.attach(np.asarray([m1_origin, m1_insertion]),
np.asarray([m2_origin, m2_insertion]))
##### Time #####
t_max = 2.5
time = np.arange(0., t_max, 0.001)
###########################################################
###########################################################
###########################################################
###########################################################
###########################################################
### code for 3a
pylog.info("3a")
d = 1.
tau = np.array([0.02, 0.02, 0.1, 0.1])
b = np.array([3., 3., -3., -3.])
w = np.zeros((4, 4))
w[0, 1] = w[0, 3] = w[1, 0] = w[1, 2] = -5
w[0, 2] = w[1, 3] = 5
w[2, 0] = w[3, 1] = -5
w = w.T
N_params = NetworkParameters()
N_params.D = d
N_params.tau = tau
N_params.b = b
N_params.w = w
neural_network = NeuralSystem(N_params)
sys = System()
sys.add_pendulum_system(pendulum)
sys.add_muscle_system(muscles)
sys.add_neural_system(neural_network)
x0_P = np.asarray([np.pi / 2, 0.])
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])
x0 = np.concatenate((x0_P, x0_M, x0_N))
sim = SystemSimulation(sys)
sim.initalize_system(x0, time)
sim.simulate()
res = sim.results()
positions = res[:, 1]
vels = res[:, 2]
plt.figure('3a. Activation with time ')
plt.title('Activation with time')
plt.plot(res[:, 0], res[:, 3], label="Activation 1")
plt.plot(res[:, 0], res[:, 5], label="Activation 2")
plt.xlabel('Time [s]')
plt.ylabel('Activation')
plt.legend()
plt.grid()
plt.show()
# Plotting the results
plt.figure('3a. Pendulum state with time')
plt.title('Pendulum state with time')
plt.plot(res[:, 0], positions)
plt.xlabel('Time [s]')
plt.ylabel('Position [rad]')
plt.grid()
plt.show()
# Plotting the results
plt.figure('3a. Pendulum phase plot')
plt.title('Pendulum phase plot')
plt.plot(positions, vels)
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad/s]')
plt.grid()
plt.show()
###########################################################
###########################################################
###########################################################
###########################################################
###########################################################
### code for 3b
pylog.info("3b")
all_positions = []
all_vels = []
all_time = []
all_act_1 = []
all_act_2 = []
external_drives = np.array([0, 0.2, 0.5, 1., 2., 5.])
for temp_drive in external_drives:
sim = SystemSimulation(sys)
sim.initalize_system(x0, time)
sim.add_external_inputs_to_network(
np.ones((len(sim.time), 4)) * temp_drive)
sim.simulate()
res = sim.results()
all_time = all_time + [res[:, 0]]
all_positions = all_positions + [res[:, 1]]
all_vels = all_vels + [res[:, 2]]
all_act_1 = all_act_1 + [res[:, 3]]
all_act_2 = all_act_2 + [res[:, 5]]
plt.figure('3a. Activation with time by different external drives')
plt.title('Activation with time by different external drives')
for i in range(len(external_drives)):
plt.plot(all_time[i], all_act_1[i])
plt.plot(all_time[i], all_act_2[i])
plt.xlabel('Time [s]')
plt.ylabel('Activation')
temp_legends = [
'external drive: ' + format((temp_drive), '.2f')
for temp_drive in external_drives
]
plt.legend(temp_legends)
plt.grid()
plt.show()
plt.figure('3b. Pendulum state with time by different external drives')
plt.title('Pendulum state with time by different external drives')
for i in range(len(external_drives)):
plt.plot(all_time[i], all_positions[i])
plt.xlabel('Time [s]')
plt.ylabel('Position [rad]')
temp_legends = [
'external drive: ' + format((temp_drive), '.2f')
for temp_drive in external_drives
]
plt.legend(temp_legends)
plt.grid()
plt.show()
plt.figure('3a. Pendulum phase plot by different external drives')
plt.title('Pendulum phase plot by different external drives')
for i in range(len(external_drives)):
plt.plot(all_positions[i], all_vels[i])
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad/s]')
temp_legends = [
'external drive: ' + format((temp_drive), '.2f')
for temp_drive in external_drives
]
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,
sim.sys.neural_sys)
if DEFAULT["save_figures"] is False:
# 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 exercise1():
""" Exercise 1 """
pylog.info("Executing Lab 4 : Exercise 1")
pendulum = PendulumSystem()
pendulum.parameters = PendulumParameters()
pylog.info(
"Find more information about Pendulum Parameters in SystemParameters.py")
pylog.info("Executing Lab 4 : Exercise 1")
# Initialize a new pendulum system with default parameters
pendulum = PendulumSystem()
pendulum.parameters = PendulumParameters()
pylog.info(
"Find more information about Pendulum Parameters in SystemParameters.py")
# To change a parameter you could so by,
# >>> pendulum.parameters.L = 1.5
# The above line changes the length of the pendulum
# You can instantiate multiple pendulum models with different parameters
# For example,
"""
>>> pendulum_1 = PendulumSystem()
>>> pendulum_1.parameters = PendulumParameters()
>>> pendulum_1.parameters.L = 0.5
>>> parameters_2 = PendulumParameters()
>>> parameters_2.L = 0.5
>>> pendulum_2 = PendulumSystem(paramters=parameters_2)
"""
# Above examples shows how to create two istances of the pendulum
# and changing the different parameters using two different approaches
pendulum.parameters.k1 = 50
pendulum.parameters.k2 = 50
pendulum.parameters.s_theta_ref1 = 1.0
pendulum.parameters.s_theta_ref2 = 1.0
pendulum.parameters.b1 = 0.5
pendulum.parameters.b2 = 0.5
pylog.warning("Loading default pendulum pendulum.parameters")
pylog.info(pendulum.parameters.showParameters())
# Simulation Parameters
t_start = 0.0
t_stop = 10.0
dt = 0.01
pylog.warning("Using large time step dt={}".format(dt))
time = np.arange(t_start, t_stop, dt)
x0 = [0.5, 0.0]
res = integrate(pendulum_integration, x0, time, args=(pendulum,))
pylog.info("Instructions for applying pertubations")
# Use pendulum_perturbation method to apply pertubations
# Define the pertubations inside the function pendulum_perturbation
# res = integrate(pendulum_perturbation, x0, time, args=(pendulum,))
res.plot_state("State")
res.plot_phase("Phase")
x0 = [0.5, 0.1]
pendulum_limit_cycle(x0, time, pendulum)
pendulum_spring_constant(x0, time, pendulum)
pendulum_spring_reference(x0, time, pendulum)
pendulum_spring_damper(x0, time, pendulum)
pendulum_set_position(x0, time, pendulum)
if DEFAULT["save_figures"] is False:
plt.show()
return
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 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
"""
'''
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()
'''
###########################################################
###########################################################
###########################################################
###########################################################
###########################################################
### 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()
###########################################################
###########################################################
###########################################################
###########################################################
###########################################################
### 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 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 exercise2():
""" Main function to run for Exercise 2.
Parameters
----------
None
Returns
-------
None
"""
#----------------# Exercise 2a #----------------#
theta = np.linspace(-np.pi/4, np.pi/4,num=50)
h1=[]
a1= 1
a2a1=np.linspace(0.5,2,num=4)
plt.figure('2a_Muscle_Length_vs_Theta')
plt.title('Muscle Length vs Theta')
plt.xlabel('Position [rad]')
plt.ylabel('Muscle length [m]')
plt.grid()
plt.figure('2a_Moment_arm_vs_Theta')
plt.title('Moment arm vs Theta')
plt.xlabel('Position [rad]')
plt.ylabel('Moment arm [m]')
plt.grid()
for i in range(0,len(a2a1)):
a2=a2a1[i]*a1
L1=(np.sqrt(a1**2+a2**2+2*a1*a2*np.sin(theta)))
h1=((a1*a2*np.cos(theta))/L1)
plt.figure('2a_Muscle_Length_vs_Theta')
plt.plot(theta,L1,label=('a2/a1 = %.1f' %(a2a1[i])))
plt.figure('2a_Moment_arm_vs_Theta')
plt.plot(theta,h1,label=('a2/a1= %.1f' %(a2a1[i])))
plt.figure('2a_Muscle_Length_vs_Theta')
plt.legend()
plt.figure('2a_Moment_arm_vs_Theta')
plt.legend()
#----------------# Exercise 2a finished #----------------#
# 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 = 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
activationFunction = ['sin','square']
for idx, act in enumerate(activationFunction):
#----------------# Exercise 2c #----------------#
w = np.linspace(0.2,4,4)
# w = 0.5
# a = np.linspace(0.1,1,4)
plt.figure('2c_LimitCycle_'+str(act))
# plt.figure('2c_LimitCycle_Amplitude_'+str(act))
plt.title('Pendulum Phase')
plt.figure('2c_Amplitude_'+str(act))
# plt.figure('2c_Amplitude_Amplitude_'+str(act))
plt.title('Amplitude vs. Frequency')
# plt.title('Amplitude vs. Stimulation Amplitude')
for i in range(0,len(w)):
# for i in range(0,len(a)):
# plt.figure('2c_LimitCycle_Amplitude_'+str(act))
plt.figure('2c_LimitCycle_'+str(act))
print('Running simulation %d out of %d'%(i+1,len(w)))
# print('Running simulation %d out of %d'%(i+1,len(a)))
if act == 'sin':
sinAct = np.sin(2*np.pi*w[i]*time).reshape(len(time),1)
# sinAct = a[i]*np.sin(2*np.pi*w*time).reshape(len(time),1)
else:
sinAct = signal.square(2*np.pi*w[i]*time).reshape(len(time),1)
# sinAct = a[i]*signal.square(2*np.pi*w*time).reshape(len(time),1)
sinFlex = sinAct.copy()
sinFlex[sinAct<0] = 0
sinExt = sinAct.copy()
sinExt[sinAct>0] = 0
sinExt = abs(sinExt)
sinAct1 = np.ones((len(time),1))
sinAct2 = np.ones((len(time),1))
sinAct1 = sinFlex
sinAct2 = sinExt
sinActivations = np.hstack((sinAct1,sinAct2))
# Method to add the muscle activations to the simulation
sim.add_muscle_activations(sinActivations)
# 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.plot(res[:, 1], res[:, 2], label='Act. $%s(2\cdot{}\\pi\cdot{}%.1f\cdot{}t)$'%(act,w[i]))
# plt.plot(res[:, 1], res[:, 2], label='Act. $%.1f\cdot{}%s(2\cdot{}\\pi\cdot{}0.5\cdot{}t)$'%(a[i],act))
plt.figure('2c_Amplitude_'+str(act))
plt.plot(time,res[:, 1], label='Frequency = %.1f'%(w[i]))
# plt.figure('2c_Amplitude_Amplitude_'+str(act))
# plt.plot(time,res[:, 1], label='Amplitude = %.1f'%(a[i]))
plt.figure('2c_LimitCycle_'+str(act))
# plt.figure('2c_LimitCycle_Amplitude_'+str(act))
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad/s]')
plt.grid()
plt.legend()
plt.figure('2c_Amplitude_'+str(act))
# plt.figure('2c_Amplitude_Amplitude_'+str(act))
plt.xlabel('Time [s]')
plt.ylabel('Amplitude [rad]')
plt.grid()
plt.legend()
#----------------# Exercise 2c finished #----------------#
#----------------# Exercise 2b #----------------#
w = 0.5
if act == 'sin':
sinAct = np.sin(2*np.pi*w*time).reshape(len(time),1)
else:
sinAct = signal.square(2*np.pi*w*time).reshape(len(time),1)
sinFlex = sinAct.copy()
sinFlex[sinAct<0] = 0
sinExt = sinAct.copy()
sinExt[sinAct>0] = 0
sinExt = abs(sinExt)
sinAct1 = np.ones((len(time),1))
sinAct2 = np.ones((len(time),1))
sinAct1 = sinFlex
sinAct2 = sinExt
activations = np.hstack((sinAct1,sinAct2))
# 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('2b_LimitCycle_'+str(act))
plt.title('Pendulum Phase')
plt.plot(res[:, 1], res[:, 2], label='Act. $%s(2\cdot{}\\pi\cdot{}%.1f\cdot{}t)$, Pert. ($t=3.2,\\theta = 1, \dot{\\theta} = -0.5$)' %(act,w))
plt.xlabel('Position [rad]')
plt.ylabel('Velocity [rad/s]')
plt.grid()
plt.legend()
plt.figure('2b_ActivationFunction_'+str(act))
plt.title('Activation Function')
plt.plot(time, sinAct1, label='Flexor')
plt.plot(time, sinAct2, label='Extensor')
plt.xlabel('Time [s]')
plt.ylabel('Activation')
plt.grid()
plt.legend()
#----------------# Exercise 2b finished #----------------#
# 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)
plt.show