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Quadrotor.py
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from cmath import cos, sin
import numpy as np
import scipy.integrate
import math
from scipy.spatial.transform import Rotation
from numpy.linalg import inv
class Quadrotor_linear():
def __init__(self):
"""
Define model parameters and state space for linear quadrotor dynamics
"""
self.mass = 0.90 # kg
self.Ixx = 30*1.43e-5 # kg*m^2
self.Iyy = 30*1.43e-5 # kg*m^2
self.Izz = 30*2.89e-5 # kg*m^2
self.arm_length = 0.046 # meters
g = 9.81 # m/s^2
L = self.arm_length
self.to_TM = np.array([[1, 1, 1, 1],
[ 0, L, 0, -L],
[-L, 0, L, 0]])
self.t_step = 0.1
"""
Continuous state space without considering yawing(assuming yaw angle is 0 for all the time)
state = [x y z dx dy dz phi theta phi_dot theta_dot]
dot_state = [dx dy dz ddx ddy ddz phi_dot theta_dot phi_ddot theta_ddot]
u = [F1 F2 F3 F4]
"""
# x y z dx dy dz phi theta phi_dot theta_dot
self.A_c = np.array([[0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], #dx
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], #dy
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], #dz
[0, 0, 0, 0, 0, 0, 0, g, 0, 0 ], #ddx
[0, 0, 0, 0, 0, 0, -g, 0, 0, 0 ], #ddy
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], #ddz
[0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], #phi_dot
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ], #theta_dot
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], #phi_ddot
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]]) #theta_ddot
self.B_c = np.array([[0, 0, 0], #dx
[0, 0, 0], #dy
[0, 0, 0], #dz
[0, 0, 0], #ddx
[0, 0, 0], #ddy
[1/self.mass, 0, 0], #ddz
[0, 0, 0], #phi_dot
[0, 0, 0], #theta_dot
[0, 1/self.Ixx, 0], #phi_ddot
[0, 0, 1/self.Iyy] #theta_ddot
]) @ self.to_TM
self.C_c = np.identity(10)
self.D_c = np.zeros((1,4))
# Discretization state space
self.A = np.eye(10) + self.A_c * self.t_step
self.B = self.B_c * self.t_step
self.C = self.C_c
self.D = self.D_c
def next_x(self, x, u):
return self.A.dot(x).reshape(-1,1) + self.B.dot(u)
def disturbed_next_x(self,x,u,real_d,Bd):
return self.A @ x.reshape(-1,1) + self.B @ u.reshape(-1,1) + Bd @ real_d.reshape(-1,1)
def disturbed_output(self,x,real_d, Cd, sigma_noise):
return self.C @ x.reshape(-1,1) + Cd @ real_d.reshape(-1,1) + np.random.normal(loc=np.zeros((1,10)),scale=sigma_noise).reshape(10,1)
def from_nonlinear(self, quadrotor):
linearized_state = np.zeros(10).reshape(-1,1)
linearized_state[:8] = quadrotor.state[:8].reshape(-1,1)
linearized_state[8:] = quadrotor.state[9:11].reshape(-1,1)
return linearized_state
### Non linear quadrotor model. Wasnt used in the end ###
class Quadrotor():
"""
Quadrotor forward dynamics model.
"""
def __init__(self):
self.mass = 0.030 # kg
self.Ixx = 1.43e-5 # kg*m^2
self.Iyy = 1.43e-5 # kg*m^2
self.Izz = 2.89e-5 # kg*m^2
self.arm_length = 0.046 # meters
#TODO: change force limit
self.cmd_rotor_forces_min = -0.7 # N
self.cmd_rotor_forces_max = 0.7 # N
self.k_thrust = 2.3e-08 # N/(rad/s)**2
self.k_drag = 7.8e-11 # Nm/(rad/s)**2
self.inertia = np.diag(np.array([self.Ixx, self.Iyy, self.Izz])) # kg*m^2
self.g = 9.81 # m/s^2
# Precomputes
k = self.k_drag/self.k_thrust
L = self.arm_length
self.to_TM = np.array([[1, 1, 1, 1],
[ 0, L, 0, -L],
[-L, 0, L, 0],
[ k, -k, k, -k]])
self.inv_inertia = np.linalg.inv(self.inertia)
#self.weight = np.array([0, 0, -self.mass*self.g])
self.weight = np.array([0, 0, 0])
self.t_step = 0.05
# self.inv_inertia = inv(self.inertia)
# self.weight = np.array([0, 0, 0])
# self.t_step = 0.05
def reset(self, position=[0, 0, 0], yaw =0, pitch=0, roll=0):
'''
state is a 12 dimensional vector
postion*3 velocity*3 attitude(rpy)*3 angular velocity*3
state = [x y z dx dy dz psi theta phi p q r]
dot_state = [dx dy dz ddx ddy ddz dqw dqx dqy dqz dr dp dq]
'''
s = np.zeros(12)
s[0] = position[0]
s[1] = position[1]
s[2] = position[2]
s[6] = pitch
s[7] = roll
s[8] = yaw
self.state = s
return self.state
def step(self, cmd_rotor_forces):
'''
Considering the max and min of rotor forces
action is a 4 dimensional vector: conmmand rotor forces
action = [F1, F2, F3, F4]
'''
rotor_thrusts = np.clip(cmd_rotor_forces, self.cmd_rotor_forces_min, self.cmd_rotor_forces_max)
TM = self.to_TM @ cmd_rotor_forces
T = TM[0]
M = TM[1:4].flatten()
# Form autonomous ODE for constant inputs and integrate one time step.
def s_dot_fn(t, s):
return self._s_dot_fn(t, s, T, M)
'''
The next state can be obtained through integration （Runge-Kutta）
'''
s = self.state
sol = scipy.integrate.solve_ivp(s_dot_fn, (0, self.t_step), s, first_step=self.t_step)
self.state = sol['y'][:,-1]
return self.state
def _s_dot_fn(self, t, s, u1, u2):
"""
Compute derivative of state for quadrotor given fixed control inputs as
an autonomous ODE.
"""
state = self.state
x_dot = state[3:6]
v_dot = np.array([u1[0]/self.mass * (cos(state[8]) * sin(state[7]) + cos(state[7]) * sin(state[6]) * sin(state[8])),
u1[0]/self.mass * (sin(state[8]) * sin(state[7]) - cos(state[8]) * cos(state[7]) * sin(state[6])),
u1[0]/self.mass * (cos(state[6]) * cos(state[7]))])
q_dot = state[9:]
q_dot_hat = Quadrotor.hat_map(q_dot)
w_dot = self.inv_inertia @ (u2 - q_dot_hat @ (self.inertia @ q_dot))
# Pack into vector of derivatives.
s_dot = np.zeros((12,))
s_dot[0:3] = x_dot
s_dot[3:6] = v_dot
s_dot[6:9] = q_dot
s_dot[9:] = w_dot
return s_dot
@classmethod
def hat_map(cls, s):
"""
Given vector s in R^3, return associate skew symmetric matrix S in R^3x3
"""
return np.array([[0, -s[2], s[1]],
[s[2], 0, -s[0]],
[-s[1], s[0], 0]])