def pendulum_integration(state, time, *args):
""" Function for system integration """
pylog.warning("Pendulum equation with spring and damper must be implemented") # _S
pendulum = args[0]
return pendulum.pendulum_system(
state[0], state[1], time, torque=0.0
)[:, 0]
def add_mass(self, mass):
"""Add the mass to the system.
Parameters
----------
mass: <Mass>
Instance of mass model
Example:
--------
>>> from mass import Mass
>>> from system_parameters import MassParameters
>>> mass = Muscle(MassParameters()) #: Default mass
>>> isotonic_system = IsotonicMuscleSystem()
>>> isotonic_system.add_muscle(muscle)
"""
if self.mass is not None:
pylog.warning(
'You have already added the mass model to the system.')
return
else:
if mass.__class__ is not Mass:
pylog.error('Trying to set of type {} to mass'.format(
mass.__class__))
raise TypeError()
else:
pylog.info('Added new mass model to the system')
self.mass = mass
def __init__(self, parameters=None):
super(Mass, self).__init__()
if parameters is None:
pylog.warning('Setting default parameters to mass model.')
self.parameters = MassParameters()
else:
self.parameters = parameters
def isMagic(M):
r = np.size(M, 0)
c = np.size(M, 1)
if (r == c):
magic_num = np.sum(M, 1)[0]
for x in range(0, r - 1):
row_sum = 0
col_sum = 0
udiag_sum = 0
ldiag_sum = 0
for y in range(0, r - 1):
#check rows:
row_sum += M[x, y]
#check columns:
col_sum += M[y, x]
#check upper diagonals:
udiag_sum += M[(x + y) % r, (y) % r]
#check lower diagonals:
ldiag_sum += M[(x + y) % r, (r - y - 1)]
break
if (row_sum != magic_num) or (col_sum != magic_num) or (
udiag_sum != magic_num) or (ldiag_sum != magic_num):
return 'not magic'
break
return 'is magic!'
else:
#return error Not square
pylog.warning('Matrix is not square')
return 'not magic'
def set_frequencies(self, parameters):
"""Set frequencies"""
freqs = np.ones(self.n_oscillators)
freq_body = 0
freq_limb = 0
d_high = 5.0
d_low = 1.0
if self.drive >= d_low and self.drive <= d_high:
freq_body = 0.2 * self.drive + 0.3
d_high = 3.0
if self.drive >= d_low and self.drive <= d_high:
freq_limb = 0.2 * self.drive
freqs[:20] = freq_body
freqs[20:] = freq_limb
self.freqs = freqs
#pylog.warning("Coupling weights must be set")
pylog.warning(self.freqs)
def pendulum_equation(theta, dtheta, time=0, parameters=None, torque=0.):
""" Pendulum equation
with:
- theta: Angle [rad]
- dtheta: Angular velocity [rad/s]
- g: Gravity constant [m/s**2]
- m: Mass [kg]
- L: Length [m]
- d: Damping coefficient []
- torque: External torque [N-m]
"""
if parameters is None:
parameters = PendulumParameters()
pylog.warning(
"Parameters not given, using defaults\n{}".format(parameters))
g, m, L, I, d, sin, dry = (parameters.g, parameters.m, parameters.L,
parameters.I, parameters.d, parameters.sin,
parameters.dry)
if dry:
return -(g / L) * sin(theta) - d * np.sign(dtheta) + torque / m
else:
return -(g / L) * sin(theta) - d * dtheta + torque / m
def add_muscle(self, muscle):
"""Add the muscle to the system.
Parameters
----------
muscle: <Muscle>
Instance of muscle model
Example:
--------
>>> from muscle import Muscle
>>> from system_parameters import MuscleParameters
>>> muscle = Muscle(MuscleParameters()) #: Default muscle
>>> isotonic_system = IsotonicMuscleSystem()
>>> isotonic_system.add_muscle(muscle)
"""
if self.muscle is not None:
pylog.warning(
'You have already added the muscle model to the system.')
return
else:
if muscle.__class__ is not Muscle:
pylog.error('Trying to set of type {} to muscle'.format(
muscle.__class__))
raise TypeError()
else:
pylog.info('Added new muscle model to the system')
self.muscle = muscle
def run_network(duration, update=False, drive=0):
"""Run network without Webots and plot results"""
# Simulation setup
timestep = 5e-3
times = np.arange(0, duration, timestep)
n_iterations = len(times)
parameter_set = SimulationParameters(
simulation_duration=100,
drive_mlr=2.5,
phase_lag=2 * np.pi / 10,
)
network = SalamanderNetwork(timestep, parameter_set)
osc_left = np.arange(10)
osc_right = np.arange(10, 20)
osc_legs = np.arange(20, 24)
# Logs
phases_log = np.zeros([n_iterations, len(network.state.phases)])
phases_log[0, :] = network.state.phases
amplitudes_log = np.zeros([n_iterations, len(network.state.amplitudes)])
amplitudes_log[0, :] = network.state.amplitudes
freqs_log = np.zeros([n_iterations, len(network.parameters.freqs)])
freqs_log[0, :] = network.parameters.freqs
outputs_log = np.zeros(
[n_iterations, len(network.get_motor_position_output())])
outputs_log[0, :] = network.get_motor_position_output()
# Run network ODE and log data
tic = time.time()
for i, _ in enumerate(times[1:]):
if update:
network.parameters.update(
SimulationParameters(
drive_mlr=2
# amplitude_gradient=None,
# phase_lag=None
))
network.step()
phases_log[i + 1, :] = network.state.phases
amplitudes_log[i + 1, :] = network.state.amplitudes
outputs_log[i + 1, :] = network.get_motor_position_output()
freqs_log[i + 1, :] = network.parameters.freqs
toc = time.time()
# Network performance
pylog.info("Time to run simulation for {} steps: {} [s]".format(
n_iterations, toc - tic))
# Implement plots of network results
pylog.warning("Implement plots")
#plot_results.main(plot=True)
#plt.plot(phases_log)
plt.close('all')
plt.figure('a')
plt.plot(outputs_log)
plt.figure('b')
plt.plot(amplitudes_log)
def rk4(ode, timestep, time, state, *parameters):
"""ODE solver with Runge-Kutta method"""
k_1 = timestep * ode(time, state, *parameters)
pylog.warning(np.shape(k_1))
k_2 = timestep * ode(time + 0.5 * timestep, state + 0.5 * k_1, *parameters)
k_3 = timestep * ode(time + 0.5 * timestep, state + 0.5 * k_2, *parameters)
k_4 = timestep * ode(time + timestep, state + k_3, *parameters)
return (k_1 + 2 * k_2 + 2 * k_3 + k_4) / 6
def set_parameters(self, freqs, phase_lag):
"""Set parameters of the network"""
# Set coupling weights
pylog.warning("Coupling weights must be set")
# Set desired phases
pylog.warning("Desired phases must be set")
def set_parameters(self, amplitudes, turn):
"""Set parameters of the network"""
# Set convergence rates
pylog.warning("Convergence rates must be set")
# Set desired amplitudes
pylog.warning("Desired amplitudes must be set")
def k2(self, value):
""" Keyword Arguments:
value -- Set the value of spring constant for spring 2[N/rad] """
if (value < 0.0):
pylog.warning('Setting bad spring constant. Should be positive!')
else:
self.parameters['k2'] = value
pylog.info('Changed spring constant of spring 1 to {} [N/rad]'.format(
self.parameters['k2']))
def b2(self, value):
""" Keyword Arguments:
value -- Set the value of damping constant for damper 2. [N-s/rad] """
if (value < 0.0):
pylog.warning('Setting bad damping values. Should be positive!')
else:
self.parameters['b2'] = value
pylog.info(
'Changed damping constant for damper 2 to {} [N-s/rad]'.format(self.parameters['b2']))
def run_network(duration, update=False, drive=0):
"""Run network without Webots and plot results"""
# Simulation setup
timestep = 5e-3
times = np.arange(0, duration, timestep)
n_iterations = len(times)
parameters = SimulationParameters(
drive=drive,
amplitude_gradient=None,
phase_lag=None,
turn=1.0,
use_drive_saturation=1,
shes_got_legs=1,
cR_body=[0.05, 0.16], #cR1, cR0
cR_limb=[0.131, 0.131], #cR1, cR0
amplitudes_rate=40,
)
network = SalamanderNetwork(timestep, parameters)
osc_left = np.arange(10)
osc_right = np.arange(10, 20)
osc_legs = np.arange(20, 24)
# Logs
phases_log = np.zeros([n_iterations, len(network.state.phases)])
phases_log[0, :] = network.state.phases
amplitudes_log = np.zeros([n_iterations, len(network.state.amplitudes)])
amplitudes_log[0, :] = network.state.amplitudes
freqs_log = np.zeros([n_iterations, len(network.parameters.freqs)])
freqs_log[0, :] = network.parameters.freqs
outputs_log = np.zeros(
[n_iterations, len(network.get_motor_position_output())])
outputs_log[0, :] = network.get_motor_position_output()
# Run network ODE and log data
tic = time.time()
for i, _ in enumerate(times[1:]):
if update:
network.parameters.update(
SimulationParameters(
# amplitude_gradient=None,
# phase_lag=None
))
network.step()
phases_log[i + 1, :] = network.state.phases
amplitudes_log[i + 1, :] = network.state.amplitudes
outputs_log[i + 1, :] = network.get_motor_position_output()
freqs_log[i + 1, :] = network.parameters.freqs
toc = time.time()
# Network performance
pylog.info("Time to run simulation for {} steps: {} [s]".format(
n_iterations, toc - tic))
# Implement plots of network results
pylog.warning("Implement plots")
plot_results.main()
def exercise1(clargs):
""" Exercise 1 """
# Setup
pylog.info("Running exercise 1")
# Setup
time_max = 5 # Maximum simulation time
time_step = 0.2 # Time step for ODE integration in simulation
x0 = np.array([1.]) # Initial state
# Integration methods (Exercises 1.a - 1.d)
pylog.info("Running function integration using different methods")
# Example
pylog.debug("Running example plot for integration (remove)")
example = example_integrate(x0, time_max, time_step)
example.plot_state(figure="Example", label="Example", marker=".")
# Analytical (1.a)
time = np.arange(0, time_max, time_step) # Time vector
x_a = analytic_function(time)
analytical = Result(x_a, time) if x_a is not None else None
# Euler (1.b)
euler = euler_integrate(function, x0, time_max, time_step)
# ODE (1.c)
ode = ode_integrate(function, x0, time_max, time_step)
# ODE Runge-Kutta (1.c)
ode_rk = ode_integrate_rk(function_rk, x0, time_max, time_step)
# Euler with lower time step (1.d)
pylog.warning("Euler with smaller ts must be implemented")
euler_time_step = None
euler_ts_small = (euler_integrate(function, x0, time_max, euler_time_step)
if euler_time_step is not None else None)
# Plot integration results
plot_integration_methods(analytical=analytical,
euler=euler,
ode=ode,
ode_rk=ode_rk,
euler_ts_small=euler_ts_small,
euler_timestep=time_step,
euler_timestep_small=euler_time_step)
# Error analysis (Exercise 1.e)
pylog.warning("Error analysis must be implemented")
# Show plots of all results
if not clargs.save_figures:
plt.show()
return
def exercise_9c(world, timestep, reset):
"""Exercise 9c"""
# Parameters
outfile = TemporaryFile()
parameter_set = [
[
SimulationParameters(
simulation_duration=20,
drive=4.5,
amplitude_gradient=[head, tail],
phase_lag=2 * np.pi / 10,
# ...
) for head in np.linspace(0.1, 1.5, 15)
] for tail in np.linspace(0.1, 1.5, 15)
]
# for amplitudes in ...
pylog.warning(np.shape(parameter_set))
head = np.linspace(0.1, 1.5, 15)
tail = np.linspace(0.1, 1.5, 15)
pylog.warning(head)
energy = np.zeros((len(head), len(tail)))
for i in range(0, len(head)):
for j in range(0, len(tail)):
reset.reset()
parameters = parameter_set[i][j]
run_simulation(
world,
parameters,
timestep,
int(1000 * parameters.simulation_duration / timestep),
logs="./logs/simulation9c_more_head{}_tail{}.npz".format(
head[i], tail[j]))
data = np.load("logs/simulation9c_more_head{}_tail{}.npz".format(
head[i], tail[j]))
velocity = np.diff(data["joints"][:, :, 0], axis=0) / timestep
velocity = np.insert(velocity, 0, 0, axis=0)
torque = data["joints"][:, :, 2]
energy[i, j] = np.mean(np.trapz(velocity * torque, dx=timestep))
np.save(outfile, energy)
outfile.seek(0) #for when you want to open it again
plt.imshow(energy, extent=[0.1, 1, 0.1, 1])
plt.xlabel('head factor')
plt.ylabel('tail factor')
plt.title('Energy estimation')
plt.colorbar()
plt.show()
def pendulum_system(self, time, theta, dtheta, torque):
""" Pendulum System.
Accessor method adding pertrubtions."""
# YOU CAN ADD PERTURBATIONS TO THE PENDULUM MODEL HERE
if self.parameters.PERTURBATION is True:
if 1.2 < time < 1.25:
pylog.warning('Perturbing the pendulum')
torque += 100
return np.array([
[dtheta],
[self.pendulum_equation(theta, dtheta, torque)] # d2theta
])[:, 0]
def add_muscle(self, muscle):
if self.muscle is not None:
pylog.warning(
'You have already added the muscle model to the system.')
return
else:
if muscle.__class__ is not Muscle:
pylog.error('Trying to set of type {} to muscle'.format(
muscle.__class__))
raise TypeError()
else:
pylog.info('Added new muscle model to the system')
self.muscle = muscle
def add_pendulum_system(self, system):
"""Add the pendulum system.
Parameters
----------
system: Pendulum
Pendulum system
"""
if self.systems_list.count('pendulum') == 1:
pylog.warning(
'You have already added the pendulum model to the system.')
return
else:
pylog.info('Added pedulum model to the system')
self.systems_list.append('pendulum')
self.pendulum_sys = system
def add_muscle_system(self, system):
"""Add the muscle system.
Parameters
----------
system: MuscleSystem
Muscle system
"""
if self.systems_list.count('muscle') == 1:
pylog.warning(
'You have already added the muscle model to the system.')
return
else:
pylog.info('Added muscle model to the system')
self.systems_list.append('muscle')
self.muscle_sys = system
def add_neural_system(self, system):
"""Add the neural network system.
Parameters
----------
system: NeuralSystem
Neural Network system
"""
if self.systems_list.count('neural') == 1:
pylog.warning(
'You have already added the neural model to the system.')
return
else:
pylog.info('Added neural network to the system')
self.systems_list.append('neural')
self.neural_sys = system
def exercise5():
""" Lab 3 - Exrecise 5 """
# Fixed parameters of the neural network
tau = [0.05, 0.05]
D = 1
# Additional parameters
b = [0, 0]
w = [[1, 0], [0, 1]]
# All system parameters packed in object for integration
params = LeakyIntegratorParameters(tau, D, b, w)
# Initial conditions
y_0 = [[0, 0]] # Values of the membrane potentials of the two neurons
dt = 1e-4
t_max = 30 # Set total simulation time
# Integration (make sure to implement)
two_coupled_li_neurons(y_0, t_max, dt, params, "Case1")
# Two stable fixed points and one saddle node
pylog.warning("Implement two stable fixed points and one saddle node")
tau = [1, 1]
D = 1
b = [-3.4, -2.5]
w = [[5.25, -1], [1, 5.25]]
# All system parameters packed in object for integration
params = LeakyIntegratorParameters(tau, D, b, w)
y_0 = [[0, 0]] # Values of the membrane potentials of the two neurons
two_coupled_li_neurons(y_0, t_max, dt, params, "Case2")
# Limit cycle
"""
pylog.warning("Implement limit cycle")
"""
tau = [0.1, 0.1]
D = 1
b = [-2.75, -1.75]
w = [[4.5, -1], [1, 4.5]]
# All system parameters packed in object for integration
params = LeakyIntegratorParameters(tau, D, b, w)
y_0 = [[0, 0]] # Values of the membrane potentials of the two neurons
two_coupled_li_neurons(y_0, t_max, dt, params, "Case3")
pylog.warning(u"Implement Poincare analysis of limit cycle")
# Limit cycle (small), one stable fixed point and one saddle node
pylog.warning("Implement a system with:"
"\n- One limit cycle (small)"
"\n- One stable fixed point"
"\n- One saddle node")
pylog.warning(u"Implement Poincare analysis of limit cycle")
if DEFAULT["save_figures"] is False:
plt.show()
return
def ode_integrate(fun, x0, time_max, time_step):
""" Integrate function using Euler method
- fun: Function df/dt = f(x, t) to integrate
- x0: Initial state
- time_tot: Total time to simulate [s]
- time_step: Time step [s]
Use odeint from the scipy library for integration
Make sure to then use the Result class similarly to the example_integrate
found above (i.e. Result(x, time))
"""
time = np.arange(0, time_max, time_step)
# COMPLETE CODE
pylog.warning("ODE integration must be implemented")
return None
def euler_integrate(fun, x0, time_max, time_step):
""" Integrate function using Euler method
- fun: Function df/dt = f(x, t) to integrate
- x0: Initial state
- time_tot: Total time to simulate [s]
- time_step: Time step [s]
For loop in Python:
>>> a = [0, 0, 0] # Same as [0 for _ in range(3)] (List comprehension)
>>> for i in range(3):
... a[i] = i
>>> print(a)
[0, 1, 2]
Creating a matrix of zeros in python:
>>> state = np.zeros([3, 2])
>>> print(state)
[[0. 0.]
[0. 0.]
[0. 0.]]
For loop for a state in python
>>> state = np.zeros([3, 2])
>>> state[0, 0], state[0, 1] = 1, 2
>>> for i, time in enumerate([0, 0.1, 0.2]):
... state[i, 0] += time
... state[i, 1] -= time
>>> print(state)
[[ 1. 2. ]
[ 0.1 -0.1]
[ 0.2 -0.2]]
Make sure to use the Result class similarly to the example_integrate
found above (i.e. Result(x, time))
"""
time = np.arange(0, time_max, time_step)
x = np.zeros([len(time), len(x0)])
# COMPLETE CODE
pylog.warning("Euler integration must be implemented")
return None
def exercise5():
""" Lab 3 - Exrecise 5 """
# Fixed parameters of the neural network
tau = [0.1, 0.1]
D = 1
# Additional parameters
b = [-2.75, -1.75]
w = [[4.5, -1], [1, 4.5]]
# All system parameters packed in object for integration
params = LeakyIntegratorParameters(tau, D, b, w)
# Initial conditions
# SET THE INITIAL CONDITIONS
y_0 = [[0, 0]] # Values of the membrane potentials of the two neurons
# Integration time parameters
# Force integration to return values at small steps for
# better detecting Poincare maps crossings
dt = 1e-4
t_max = 30 # Set total simulation time
# Integration (make sure to implement)
two_coupled_li_neurons(y_0, t_max, dt, params, "Case1")
# Two stable fixed points and one saddle node
pylog.warning("Implement two stable fixed points and one saddle node")
# Limit cycle
pylog.warning("Implement limit cycle")
pylog.warning("Implement Poincare analysis of limit cycle")
# Limit cycle (small), one stable fixed point and one saddle node
pylog.warning("Implement a system with:"
"\n- One limit cycle (small)"
"\n- One stable fixed point"
"\n- One saddle node")
pylog.warning(u"Implement Poincare analysis of limit cycle")
if DEFAULT["save_figures"] is False:
plt.show()
return
def save_figure(figure, name=None):
""" Save figure """
if os.path.isdir(DEFAULT["save_folder"]):
path = DEFAULT["save_folder"]
else:
pylog.warning(
"The DEFAULT save directory does not exist. Switching to current directory"
)
path = os.getcwd()
if DEFAULT["save_figures"]:
for extension in DEFAULT["save_extensions"]:
fig = figure.replace(" ", "_").replace(".", "dot")
if name is None:
name = "{}.{}".format(fig, extension)
else:
name = "{}.{}".format(name, extension)
plt.savefig(path + name, bbox_inches='tight')
pylog.debug("Saving figure {}...".format(name))
def name(self, animal_name):
"""
Parameters
----------
animal_name : <str>
Name of the animal.
If it is not a string then a warning is thrown
Returns
-------
out : None
"""
# Check if animal is a string or not
if not isinstance(animal_name, str):
pylog.warning(
'You don\'t really know how to name your animals! ')
# This also works and is useful for dealing with inheritance:
if not isinstance(animal_name, str):
pylog.warning(
'You don\'t really know how to name your animals! (isinstance)')
self._name = animal_name
def ode_integrate_rk(fun_rk, x0, time_max, time_step):
""" Integrate function using Euler method
- fun: Function df/dt = f(x, t) to integrate
- x0: Initial state
- time_tot: Total time to simulate [s]
- time_step: Time step [s]
For Runge-Kutta, use:
solver = ode(fun)
solver.set_integrator('dopri5')
solver.set_initial_value(x0, time[0])
xi = solver.integrate(ti)
Note that solver.integrate(ti) only integrates for one time step at time ti
(where ti is the current time), so you will need to use a for loop
Make sure to use the Result class similarly to the example_integrate
found above (i.e. Result(x, time))
"""
time = np.arange(0, time_max, time_step)
# COMPLETE CODE
pylog.warning("ODE integration with RK must be implemented")
return None
def exercise3(clargs):
""" Exercise 3 """
parameters = PendulumParameters() # Checkout pendulum.py for more info
pylog.info(parameters)
# Simulation parameters
time = np.arange(0, 30, 0.01) # Simulation time
x0 = [0.1, 0.0] # Initial state
# To use/modify pendulum parameters (See PendulumParameters documentation):
# parameters.g = 9.81 # Gravity constant
# parameters.m = 1. # Mass
# parameters.L = 1. # Length
# parameters.I = 1. # Inertia (Automatically computed!)
# parameters.d = 0.3 # damping
# parameters.sin = np.sin # Sine function
# parameters.dry = False # Use dry friction (True or False)
# Example of system integration (Similar to lab1)
# (NOTE: pendulum_equation must be imlpemented first)
pylog.debug("Running integration example")
res = integrate(pendulum_system, x0, time, args=(parameters,))
res.plot_state("State")
res.plot_phase("Phase")
# Evolutions
# Write code here (You can add functions for the different cases)
pylog.warning(
"Evolution of pendulum in normal conditions must be implemented"
)
pylog.warning(
"Evolution of pendulum without damping must be implemented"
)
pylog.warning(
"Evolution of pendulum with perturbations must be implemented"
)
pylog.warning(
"Evolution of pendulum with dry friction must be implemented"
)
# Show plots of all results
if not clargs.save_figures:
plt.show()
def exercise2(clargs):
""" Exercise 2 """
pylog.info("Running exercise 2")
# System definition
pylog.warning("Proper matrix A must be implemented")
A = np.array([[1, 0], [0, 1]])
time_total = 10
time_step = 0.01
x0, time = [0, 1], np.arange(0, time_total, time_step)
# Normal run
pylog.warning("System integration must be implemented")
# integration(x0, time, A, "example")
# Stable point (Optional)
pylog.warning("Stable point integration must be implemented")
# Periodic
pylog.warning("Periodic system must be implemented")
# Plot
if not clargs.save_figures:
plt.show()