def PID_controler_with_measured_values(self,k_p,k_d,k_i,mass_err,sigma,use_measured_height=False):
# creating the co-axial drone object
Controlled_Drone=CoaxialCopter()
# array for recording the state history
drone_state_history = Controlled_Drone.X
# introducing a small error of the actual mass and the mass for which the path has been calculated
actual_mass = Controlled_Drone.m * mass_err
# creating the control system object
control_system = PIDController_with_ff(k_p,k_d,k_i)
# declaring the initial state of the drone with zero hight and zero velocity
Controlled_Drone.X = np.array([0.0,0.0,0.0,0.0])
Drone_IMU = self.IMU(Controlled_Drone.X[0], 0.95)
observation_hostory = Controlled_Drone.X[0]
# executing the flight
for i in range(1,self.z_path.shape[0]-1):
# condition to use height observation to control the drone or
# use the majically given true state
if use_measured_height:
z_observation= Drone_IMU.measure(Controlled_Drone.X[0],sigma)
u_bar = control_system.control(self.z_path[i],
z_observation,
self.z_dot_path[i],
Controlled_Drone.X[2],
self.z_dot_dot_path[i],
self.dt)
observation_hostory = np.vstack((observation_hostory,z_observation))
else:
u_bar = control_system.control(self.z_path[i],
Controlled_Drone.X[0],
self.z_dot_path[i],
Controlled_Drone.X[2],
self.z_dot_dot_path[i],
self.dt)
observation_hostory = np.vstack((observation_hostory,self.z_path[i]))
Controlled_Drone.set_rotors_angular_velocities(u_bar,0.0)
# calculating the new state vector
drone_state = Controlled_Drone.advance_state(self.dt, actual_mass)
# generating a history of vertical positions for the drone
drone_state_history = np.vstack((drone_state_history, drone_state))
plt.subplot(211)
plt.plot(self.t,self.z_path,linestyle='-',marker='.',color='red')
plt.plot(self.t[1:],drone_state_history[:,0],linestyle='-',color='blue',linewidth=3)
if use_measured_height:
plt.scatter(self.t[1:],observation_hostory[:,0],color='black',marker='.',alpha=0.3)
plt.grid()
if use_measured_height:
plt.title('Change in height (using measured value)').set_fontsize(20)
else:
plt.title('Change in height (ideal case)').set_fontsize(20)
plt.xlabel('$t$ [sec]').set_fontsize(20)
plt.ylabel('$z-z_0$ [$m$]').set_fontsize(20)
plt.xticks(fontsize = 14)
plt.yticks(fontsize = 14)
if use_measured_height:
plt.legend(['Planned path','Executed path','Observed value'],fontsize = 14)
else:
plt.legend(['Planned path','Executed path'],fontsize = 14)
plt.show()
plt.subplot(212)
plt.plot(self.t[1:],abs(self.z_path[1:]-drone_state_history[:,0]),linestyle='-',marker='.',color='blue')
plt.grid()
plt.title('Error value ').set_fontsize(20)
plt.xlabel('$t$ [sec]').set_fontsize(20)
plt.ylabel('||$z_{target} - z_{actual}$|| [$m$]').set_fontsize(20)
plt.xticks(fontsize = 14)
plt.yticks(fontsize = 14)
plt.legend(['Error'],fontsize = 14)
plt.show()
def PID_controler_with_EKF(self,
angle_error,
position_sigma,
motion_sigma,
use_ekf=False):
# Controller parameters
k_p = 20
k_d = 5
k_i = 5
velocity_sigma = position_sigma
Controlled_Drone = self.drone(0.0, 0.0, 1.5)
# array for recording the state history
drone_state_history = Controlled_Drone.X
# creating the control system object
control_system = PIDController_with_ff(k_p, k_d, k_i)
Drone_IMU = self.IMU()
observation_hostory = Controlled_Drone.X[-1]
mu = np.array([[Controlled_Drone.X[0]], [Controlled_Drone.X[1]],
[Controlled_Drone.X[2]]])
sigma_cov = np.matmul(
np.identity(3),
np.array([angle_error, velocity_sigma, position_sigma]))
EKFfilter = self.EKF(motion_sigma, angle_error, velocity_sigma,
position_sigma, self.dt)
EKFfilter.initial_values(mu, sigma_cov)
EKF_history = mu[2]
sigma_cov_history = sigma_cov[1]
z_observation = Drone_IMU.measure(
Controlled_Drone.X[-1] / np.cos(Controlled_Drone.X[0]),
position_sigma)
# executing the flight
for i in range(1, self.z_path.shape[0] - 1):
if use_ekf:
z_EKF = mu[2]
v_EKF = mu[1]
u_bar = control_system.control(self.z_path[i], z_EKF,
self.z_dot_path[i], v_EKF,
self.z_dot_dot_path[i], self.dt)
else:
u_bar = control_system.control(
self.z_path[i],
z_observation * np.cos(Controlled_Drone.X[0]),
self.z_dot_path[i], Controlled_Drone.X[1],
self.z_dot_dot_path[i], self.dt)
observation_hostory = np.vstack(
(observation_hostory, z_observation))
#u_bar=u_bar + np.random.normal(0.0, motion_sigma)
u_bar = u_bar + np.random.normal(0.0, motion_sigma)
# calculating the new state vector
#u_bar = max(-1/np.sqrt(2),u_bar)
#u_bar = min(1/np.sqrt(2),u_bar)
u_bar = -u_bar
u_bar = max(-1 / np.sqrt(2), u_bar)
u_bar = min(1 / np.sqrt(2), u_bar)
phi_new = float(np.arcsin(u_bar))
drone_state = Controlled_Drone.advance_state(phi_new, self.dt)
# generating a history of vertical positions for the drone
drone_state_history = np.vstack((drone_state_history, drone_state))
#################
mu_bar, sigma_bar = EKFfilter.predict(phi_new)
z_observation = Drone_IMU.measure(
Controlled_Drone.X[2] / np.cos(Controlled_Drone.X[0]),
position_sigma)
mu, sigma_cov = EKFfilter.update(z_observation)
#################
# generating a history of vertical positions for the drone
EKF_history = np.vstack((EKF_history, mu[-1]))
sigma_cov_history = np.vstack((sigma_cov_history, sigma_cov[1, 1]))
plt.subplot(211)
plt.plot(self.t,
self.z_path,
linestyle='-',
marker='.',
color='red',
label='Planned path')
if use_ekf:
plt.plot(self.t[1:],
EKF_history[:, 0],
linestyle='-',
color='green',
linewidth=3,
label='Estimated position')
plt.plot(self.t[1:],
drone_state_history[:, -1],
linestyle='-',
color='blue',
linewidth=3,
label='Executed path')
plt.scatter(self.t[1:],
observation_hostory[:, 0],
color='black',
marker='.',
alpha=0.3,
label='Observed value')
plt.grid()
if use_ekf:
plt.title(
'Change in position (using estimated value)').set_fontsize(20)
else:
plt.title(
'Change in position (using measured value)').set_fontsize(20)
plt.xlabel('$t$ [sec]').set_fontsize(20)
plt.ylabel('$y$ [$m$]').set_fontsize(20)
plt.xticks(fontsize=14)
plt.yticks(fontsize=14)
plt.legend(fontsize=14)
plt.show()
plt.subplot(212)
plt.plot(self.t[1:],
abs(self.z_path[1:] - drone_state_history[:, -1]),
linestyle='-',
marker='.',
color='blue')
plt.grid()
plt.title('Error value ').set_fontsize(20)
plt.xlabel('$t$ [sec]').set_fontsize(20)
plt.ylabel('||$y_{target} - y_{actual}$|| [$m$]').set_fontsize(20)
plt.xticks(fontsize=14)
plt.yticks(fontsize=14)
plt.legend(['Error'], fontsize=14)
plt.show()
def PID_controler_with_KF(self, position_sigma, motion_sigma, use_kf=False):
# Controller parameters
k_p = 20
k_d = 5
k_i = 5
mass_err = 1.0
velocity_sigma = position_sigma # velocity uncertainty
# creating the co-axial drone object
Controlled_Drone=CoaxialCopter()
# array for recording the state history
drone_state_history = Controlled_Drone.X
# introducing a small error of the actual mass and the mass for which the path has been calculated
actual_mass = Controlled_Drone.m * mass_err
# creating the control system object
control_system = PIDController_with_ff(k_p,k_d,k_i)
# declaring the initial state of the drone with zero hight and zero velocity
Controlled_Drone.X = np.array([0.0,0.0,0.0,0.0])
Drone_IMU = self.IMU()
observation_hostory = Controlled_Drone.X[0]
mu = np.array([[Controlled_Drone.X[1]],[Controlled_Drone.X[0]]])
sigma_cov = np.matmul(np.identity(2), np.array([velocity_sigma,position_sigma]))
EKFfilter=self.KF(motion_sigma,velocity_sigma,position_sigma,self.dt)
EKFfilter.initial_values(mu, sigma_cov)
EKF_history = mu[1,0]
sigma_cov_history = sigma_cov[1]
# executing the flight
for i in range(1,self.z_path.shape[0]-1):
# condition to use height observation to control the drone or
# use the magically given true state
z_observation= Drone_IMU.measure(Controlled_Drone.X[0],position_sigma)
if use_kf:
z_EKF=mu[1,0]
v_EKF=mu[0,0]
u_bar = control_system.control(self.z_path[i],
z_EKF,
self.z_dot_path[i],
v_EKF,
self.z_dot_dot_path[i],
self.dt)
else:
u_bar = control_system.control(self.z_path[i],
z_observation,
self.z_dot_path[i],
Controlled_Drone.X[2],
self.z_dot_dot_path[i],
self.dt)
observation_hostory = np.vstack((observation_hostory,z_observation))
u_bar=u_bar + np.random.normal(0.0, motion_sigma)
Controlled_Drone.set_rotors_angular_velocities(u_bar,0.0)
# calculating the new state vector
drone_state = Controlled_Drone.advance_state(self.dt, actual_mass)
# generating a history of vertical positions for the drone
drone_state_history = np.vstack((drone_state_history, drone_state))
#################
mu_bar, sigma_bar = EKFfilter.predict(u_bar)
z_observation= Drone_IMU.measure(drone_state[0],position_sigma)
mu, sigma_cov = EKFfilter.update(z_observation)
#################
# generating a history of vertical positions for the drone
EKF_history= np.vstack((EKF_history,mu_bar[1,0]))
sigma_cov_history = np.vstack((sigma_cov_history,sigma_cov[1,1]))
plt.subplot(211)
plt.plot(self.t,self.z_path,linestyle='-',marker='.',color='red',label = 'Planned path')
if use_kf:
plt.plot(self.t[1:],EKF_history[:,0],linestyle='-',color='green',linewidth=3,label = 'Estimated path')
plt.plot(self.t[1:],drone_state_history[:,0],linestyle='-',color='blue',linewidth=3, label = 'Executed path')
plt.scatter(self.t[1:],observation_hostory[:,0],color='black',marker='.',alpha=0.3, label = 'Observed value')
plt.grid()
if use_kf:
plt.title('Change in height (using estimated value)').set_fontsize(20)
else:
plt.title('Change in height (using measured value)').set_fontsize(20)
plt.xlabel('$t$ [sec]').set_fontsize(20)
plt.ylabel('$z-z_0$ [$m$]').set_fontsize(20)
plt.xticks(fontsize = 14)
plt.yticks(fontsize = 14)
plt.legend(fontsize = 14)
plt.show()
plt.subplot(212)
plt.plot(self.t[1:],abs(self.z_path[1:]-drone_state_history[:,0]),linestyle='-',marker='.',color='blue')
plt.grid()
plt.title('Error value ').set_fontsize(20)
plt.xlabel('$t$ [sec]').set_fontsize(20)
plt.ylabel('||$z_{target} - z_{actual}$|| [$m$]').set_fontsize(20)
plt.xticks(fontsize = 14)
plt.yticks(fontsize = 14)
plt.legend(['Error'],fontsize = 14)
plt.show()
