def calc(a, b, op='add'):
if op == 'add':
return a + b
elif op == 'sub':
return a - b
else:
pylog.info('valid operations are add and sub')
def exercise2(clargs):
""" Exercise 2 """
pylog.info("Running exercise 2")
# System definition
A = np.array([[1, 4], [-4, -2]])
time_total = 10
time_step = 0.01
x0, time = [0, 1], np.arange(0, time_total, time_step)
# Normal run
integration(x0, time, A, "Normal run")
# Stable point (Optional)
x0 = [0, 0]
integration(x0, time, A, "x0 Fixed point")
# Periodic
A = np.array([[2, 4], [-4, -2]])
x0 = [1, 0]
integration(x0, time, A, "Periodic")
# Plot
if not clargs.save_figures:
plt.show()
def set_nominal_amplitudes(self, parameters):
"""Set nominal amplitudes"""
nominal_amplitudes = np.zeros(self.n_oscillators)
amp_body = 0
amp_limb = 0
d_high = 5.0
d_low = 1.0
if self.drive >= d_low and self.drive <= d_high:
amp_body = 0.065 * self.drive + 0.196
d_high = 3.0
if self.drive >= d_low and self.drive <= d_high:
amp_limb = 0.131 * self.drive + 0.131
gradient = np.linspace(self.amplitude_gradient[0],
self.amplitude_gradient[1], 10)
pylog.info(np.shape(gradient))
gradient_ = np.concatenate((gradient, gradient))
pylog.info(np.shape(gradient_))
nominal_amplitudes[:20] = amp_body * gradient_
nominal_amplitudes[20:] = amp_limb
if (self.turn[1] == 'right' or self.turn[1] == 'Right'):
nominal_amplitudes[
10:20] = nominal_amplitudes[10:20] * self.turn[0]
elif (self.turn[1] == 'left' or self.turn[1] == 'Left'):
nominal_amplitudes[0:10] = nominal_amplitudes[0:10] * self.turn[0]
self.nominal_amplitudes = self.amp_factor * nominal_amplitudes
def run_simulation(world, parameters, timestep, n_iterations, logs):
"""Run simulation"""
# Set parameters
pylog.info((
"Running new simulation:"
"\n - Amplitude: {}"
"\n - Phase lag: {}"
"\n - Turn: {}"
).format(parameters[0], parameters[1], parameters[2]))
# Setup salamander control
salamander = SalamanderCMC(
world,
n_iterations,
logs=logs,
freqs=parameters[0],
amplitudes=parameters[1],
phase_lag=parameters[2],
turn=parameters[3]
)
# Simulation
iteration = 0
while world.step(timestep) != -1:
iteration += 1
if iteration >= n_iterations:
break
salamander.step()
# Log data
pylog.info("Logging simulation data to {}".format(logs))
salamander.log.save_data()
def main():
"""Main function that runs all the exercises."""
pylog.info('Implementing Lab 6 : Exercise 2')
exercise2()
pylog.info('Implementing Lab 6 : Exercise 3')
exercise3()
return
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 main():
"""Main"""
# Duration of each simulation
simulation_duration = 20
# Get supervisor to take over the world
world = Supervisor()
n_joints = 10
timestep = int(world.getBasicTimeStep())
freqs = 1
# Get and control initial state of salamander
reset = RobotResetControl(world, n_joints)
# Simulation example
amplitude = None
phase_lag = None
turn = None
parameter_set = [[freqs, amplitude, phase_lag, turn],
[freqs, amplitude, phase_lag, turn]]
for simulation_i, parameters in enumerate(parameter_set):
reset.reset()
run_simulation(
world,
parameters,
timestep,
int(1000 * simulation_duration / timestep),
logs="./logs/example/simulation_{}.npz".format(simulation_i))
# Pause
world.simulationSetMode(world.SIMULATION_MODE_PAUSE)
pylog.info("Simulations complete")
world.simulationQuit(0)
def validate_muscle_attachment(self, parameters):
"""Validate the muscle attachment positions.
Provided pendulum length and muscle attachments
check if the muscle attachments are valid or not!
Parameters
----------
parameters: PendulumParameters
Pendulum parameters
Returns
-------
check : bool
Returns if the muscle attachments are valid or not
"""
check = (parameters.L > abs(self.muscle1_pos[1, 1])) and (
parameters.L > abs(self.muscle2_pos[1, 1])) and (
self.muscle1_pos[1, 0] == 0.0) and (self.muscle2_pos[1, 0]
== 0.0)
if check:
pylog.info('Validated muscle attachments')
return check
pylog.error('Invalid muscle attachment points')
return check
def run_simulation(world, parameters, timestep, n_iterations, logs):
"""Run simulation"""
# Set parameters
pylog.info(
"Running new simulation:\n {}".format("\n ".join([
"{}: {}".format(key, value)
for key, value in parameters.items()
]))
)
# Setup salamander control
salamander = SalamanderCMC(
world,
n_iterations,
logs=logs,
parameters=parameters
)
# Simulation
iteration = 0
while world.step(timestep) != -1:
iteration += 1
if iteration >= n_iterations:
break
salamander.step(parameters)
# Log data
pylog.info("Logging simulation data to {}".format(logs))
salamander.log.save_data()
def s_theta_ref2(self, value):
""" Keyword Arguments:
value -- Set the value of spring 2 reference angle [rad] """
self.parameters['s_theta_ref2'] = value
pylog.info(
'Changed spring 2 reference angle to {} [rad]'.format(
self.parameters['s_theta_ref2']))
def __init__(self, **kwargs):
super(PendulumParameters, self).__init__('Pendulum')
self.parameters = {}
self.units = {}
self.units['g'] = 'N-m/s2'
self.units['m'] = 'kg'
self.units['L'] = 'm'
self.units['I'] = 'kg-m**2'
self.units['sin'] = ''
self.units['PERTURBATION'] = 'bool'
# Initialize parameters
self.parameters = {
'g': 9.81, 'm': 1., 'L': 1., 'I': 0.0, 'sin': np.sin,
'PERTURBATION': False}
# Pendulum parameters
self.g = kwargs.pop("g", 9.81) # Gravity constant
self.m = kwargs.pop("m", 1.) # Mass
self.L = kwargs.pop("L", 1.) # Length
self.sin = kwargs.pop("sin", np.sin) # Sine function
self.PERTURBATION = kwargs.pop("PERTURBATION", False) # Perturbation
pylog.info(self)
return
def run_simulation(world, parameters, timestep, n_iterations, logs):
"""Run simulation"""
# Set parameters
pylog.info("Running new simulation:\n {}".format("\n ".join(
["{}: {}".format(key, value) for key, value in parameters.items()])))
# Setup salamander control
salamander = SalamanderCMC(world,
n_iterations,
logs=logs,
parameters=parameters)
# Simulation
#pos =[]
iteration = 0
while world.step(timestep) != -1:
iteration += 1
if iteration >= n_iterations:
break
salamander.step()
#pos.append(salamander.position_sensors[1])
# plot_results.plot_positions(np.arange(0,n_iterations*timestep, timestep),pos)
# Log data
pylog.info("Logging simulation data to {}".format(logs))
salamander.log.save_data()
def exercise1d(time_param):
""" Plots the v_ce-force relationship by running experiment with multiple weights."""
pylog.info("Exercise 1d")
# Parameters
load_min = 20
load_max = 300
nb_loads = 1000
load = np.linspace(load_min, load_max, num=nb_loads)
muscle_stimulation = 1.
# Experiment
v_ce, tendon_force = isotonic_experiment(
loads=load,
muscle_stimulation=muscle_stimulation,
time_param=time_param)
# Plotting
plt.figure('1_d_isotonic_load_var')
plt.plot(v_ce, tendon_force)
plt.title('Isotonic muscle experiment')
plt.xlabel('Contractile element velocity [m/s]')
plt.ylabel('Tendon force [N]')
plt.axvline(x=0, color="k")
plt.text(0.001, 750, "Equilibrium (v=0)", rotation=-90, color="k")
plt.grid()
def find_ce_stretch_iso(muscle_sys,
ce_stretch,
time_param,
stimulation=1,
error_max=0.01):
"""Finds the total stretch [m] to apply to obtain a certain ce_stretch(relative) in isometric mode"""
stretch = 0
# The stretch is constant for over compression (i.e[0,sth]) hence we wanna monitor this to avoid being
# in a regime where the computations are biased.
minimal_ce_stretch = None
x0 = [0.0, muscle_sys.muscle.L_OPT]
# Running experiments until we find a stretch that matches the conditions on CE
while True:
result = muscle_sys.integrate(x0=x0,
time=time_param.times,
time_step=time_param.t_step,
stimulation=stimulation,
muscle_length=stretch)
if minimal_ce_stretch is None:
minimal_ce_stretch = result.l_ce[
-1] # Monitoring the what the ce_stretch is in over compression
else:
if result.l_ce[-1] > ce_stretch * x0[1] and result.l_ce[
-1] > minimal_ce_stretch:
pylog.info("Reaches l_ce stretch " +
str(result.l_ce[-1] / muscle_sys.muscle.L_OPT) +
" for total stretch of:" + str(stretch))
break
else:
stretch += error_max
return stretch
def exercise1a(time_param):
""" Runs and plot the length-force relationship for a muscle in isometric conditions."""
pylog.info("Part a")
# Parameters
muscle_stimulation = 1.
ce_stretch_max = 1.5
ce_stretch_min = 0.5
nb_pts = 1000
handles = ["1_a_lce_vs_str", "1_a_lsl_vs_str", "1_a_lmtc_vs_str"]
# Experiment
active_force, passive_force, total_force, l_ce, l_slack, l_mtc = isometric_experiment(
muscle_stimulation,
ce_stretch_max,
ce_stretch_min,
nb_pts,
time_param,
)
# Plotting
plot_isometric_data(active_force,
passive_force,
total_force,
l_ce,
l_slack,
l_mtc,
handle=handles)
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 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 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 evolution_dry(x0, time):
""" Dry friction simulation """
pylog.info("Evolution with dry friction")
parameters = PendulumParameters(d=0.03, dry=True)
pylog.info(parameters)
title = "{} with dry friction (x0={})"
res = integrate(pendulum_system, x0, time, args=(parameters, ))
res.plot_state(title.format("State", x0))
res.plot_phase(title.format("Phase", x0))
def evolution_perturbation(x0, time):
""" Perturbation and no damping simulation """
pylog.info("Evolution with perturbations")
parameters = PendulumParameters(d=0.0)
pylog.info(parameters)
title = "{} with perturbation (x0={})"
res = integrate(pendulum_perturbation, x0, time, args=(parameters, ))
res.plot_state(title.format("State", x0))
res.plot_phase(title.format("Phase", x0))
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 evolution_no_damping(x0, time):
""" No damping simulation """
pylog.info("Evolution with no damping")
parameters = PendulumParameters(d=0.0)
pylog.info(parameters)
title = "{} without damping (x0={})"
res = integrate(pendulum_system, x0, time, args=(parameters, ))
res.plot_state(title.format("State", x0))
res.plot_phase(title.format("Phase", x0))
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 pendulum_perturbation(state, time, *args):
""" Function for system integration with perturbations.
Setup your time based system pertubations within this function.
The pertubation can either be applied to the states or as an
external torque.
"""
pendulum = args[0]
if time > 5 and time < 5.1:
pylog.info("Applying state perturbation to pendulum_system")
state[1] = 2.
return pendulum.pendulum_system(state[0], state[1], time, torque=0.0)[:, 0]
def evolution_cases(time):
""" Normal simulation """
pylog.info("Evolution with basic paramater")
x0_cases = [["Normal", [0.1, 0]], ["Stable", [0.0, 0.0]],
["Unstable", [np.pi, 0.0]], ["Multiple loops", [0.1, 10.0]]]
title = "{} case {} (x0={})"
parameters = PendulumParameters()
for name, x0 in x0_cases:
res = integrate(pendulum_system, x0, time, args=(parameters, ))
res.plot_state(title.format(name, "state", x0))
res.plot_phase(title.format(name, "phase", x0))
def run_simulation(world, parameters, timestep, n_iterations, logs):
"""Run simulation"""
# Set parameters
pylog.info("Running new simulation:\n {}".format("\n ".join(
["{}: {}".format(key, value) for key, value in parameters.items()])))
# Setup salamander control
salamander = SalamanderCMC(world,
n_iterations,
logs=logs,
parameters=parameters)
switch = 1
switch_T = np.inf
switched = False
# Simulation
iteration = 0
while world.step(timestep) != -1:
iteration += 1
if iteration >= n_iterations:
break
"""
if iteration == n_iterations//3:
#salamander.network.parameters.turn = 0.1 #9d1
salamander.network.parameters.drive = -3
salamander.network.parameters.update(salamander.network.parameters.parameters)
if salamander.gps.getValues()[0] > switch and switched == False: #used for 9f
salamander.network.parameters.walk = False
salamander.network.parameters.update(salamander.network.parameters.parameters)
switch_T = iteration
print(switch_T)
switched = True
if salamander.gps.getValues()[0] < switch and switched == True:
salamander.network.parameters.walk = True
salamander.network.parameters.turn = 0
salamander.network.parameters.update(salamander.network.parameters.parameters)
swiched = True
if iteration == switch_T + 600:
print("turning")
salamander.network.parameters.turn = -0.11
salamander.network.parameters.update(salamander.network.parameters.parameters)
elif iteration == switch_T + 3500:
print("straight")
salamander.network.parameters.turn = 0
salamander.network.parameters.update(salamander.network.parameters.parameters)
"""
salamander.step()
# Log data
pylog.info("Logging simulation data to {}".format(logs))
salamander.log.save_data()
def __init__(self, **kwargs):
super(PendulumParameters, self).__init__()
self._mass = 1.0 # Internal parameter : Do NOT use it!
self._length = 1.0 # Internal parameter : Do NOT use it!
self.g = kwargs.pop("g", 9.81) # Gravity constant
self.I = None # Inertia be set automatically when mass and length are set
self.m = kwargs.pop("m", 1.) # Mass
self.L = kwargs.pop("L", 1.) # Length
self.d = kwargs.pop("d", 0.3) # damping
self.sin = kwargs.pop("sin", np.sin) # Sine function
self.dry = kwargs.pop("dry", False) # Use dry friction (True or False)
pylog.info(self)
def plot_integration_methods(**kwargs):
""" Plot integration methods results """
pylog.info("Plotting integration results")
# Results
analytical = kwargs.pop("analytical", None)
euler = kwargs.pop("euler", None)
ode = kwargs.pop("ode", None)
ode_rk = kwargs.pop("ode_rk", None)
euler_ts_small = kwargs.pop("euler_ts_small", None)
# Figures
fig_all = kwargs.pop("figure", "Integration methods".replace(" ", "_"))
fig_ts = "Integration methods smaller ts".replace(" ", "_")
fig_euler = "Euler integration".replace(" ", "_")
d = "."
# Time steps information
et_val = kwargs.pop("euler_timestep", None)
ets_val = kwargs.pop("euler_timestep_small", None)
et = " (ts={})".format(et_val) if et_val is not None else ""
ets = " (ts={})".format(ets_val) if ets_val is not None else ""
# Analytical
if analytical is not None:
analytical.plot_state(figure=fig_euler, label="Analytical", marker=d)
# Euler
if euler is not None:
euler.plot_state(figure=fig_euler, label="Euler" + et, marker=d)
# ODE
ls = " "
ode_plot = False
if ode is not None:
if ode_plot is False:
analytical.plot_state(figure=fig_all, label="Analytical", marker=d)
euler.plot_state(figure=fig_all, label="Euler" + et, marker=d)
ode_plot = True
ode.plot_state(figure=fig_all, label="LSODA", linestyle=ls, marker="x")
# ODE Runge-Kutta
if ode_rk is not None:
if ode_plot is False:
analytical.plot_state(figure=fig_all, label="Analytical", marker=d)
euler.plot_state(figure=fig_all, label="Euler" + et, marker=d)
ode_rk.plot_state(figure=fig_all, label="RK", linestyle=ls, marker=d)
# Euler with lower time step
if euler_ts_small is not None:
euler_ts_small.plot_state(figure=fig_ts, label="Euler" + ets)
analytical.plot_state(figure=fig_ts, label="Analytical", marker=d)
def isotonic_experiment(muscle_stimulation, loads,
time_param=TimeParameters()):
# Muscle
muscle_parameters = MuscleParameters()
muscle = Muscle(muscle_parameters)
# Initial conditions
x0 = [0] * StatesIsotonic.NB_STATES.value
x0[StatesIsotonic.STIMULATION.value] = 0.
x0[StatesIsotonic.L_CE.value] = muscle.L_OPT
x0[StatesIsotonic.LOAD_POS.value] = muscle.L_OPT + muscle.L_SLACK
x0[StatesIsotonic.LOAD_SPEED.value] = 0.
# Containers
v_ce = []
tendon_force = []
# Integration
pylog.info("Running the experiments (this might take a while)...")
for load in loads:
# New load definition
mass_parameters = MassParameters()
mass_parameters.mass = load
mass = Mass(mass_parameters)
# System definition
sys = IsotonicMuscleSystem()
sys.add_muscle(muscle)
sys.add_mass(mass)
result = sys.integrate(x0=x0,
time=time_param.times,
time_step=time_param.t_step,
time_stabilize=time_param.t_stabilize,
stimulation=muscle_stimulation,
load=load)
# Result processing
if result.l_mtc[-1] > x0[StatesIsotonic.LOAD_POS.value]:
# Extension
index = result.v_ce.argmax()
v_ce.append(result.v_ce.max())
tendon_force.append(result.tendon_force[index])
else:
# Contraction
index = result.v_ce.argmin()
v_ce.append(result.v_ce.min())
tendon_force.append(result.tendon_force[index])
return v_ce, tendon_force