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flip.py
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import numpy as np
import quadrotor
class quadSys():
def __init__(self):
self.mass = quadrotor.MASS
self.length = quadrotor.LENGTH
self.inertia = quadrotor.INERTIA
self.gravity = quadrotor.GRAVITY
self.delta = quadrotor.DELTA_T
self.numS = quadrotor.NUMBER_STATES
self.numU = quadrotor.NUMBER_CONTROLS
self.horizon = 1000
self.Kn = None
self.z1 = np.zeros((6, 1))
self.z2 = np.matrix([1.5, 0, 3, 0, np.pi, 0]).T
self.z3 = np.matrix([3, 0, 0, 0, 2 * np.pi, 0]).T
self.u = np.array([[self.mass * self.gravity / 2], [self.mass * self.gravity / 2]])
self.prevCost = 1e+20
# Initial Guess
self.uS = np.tile(np.array([[self.mass * self.gravity / 2, self.mass * self.gravity / 2]]).transpose(),
(1, self.horizon))
self.zS = self.get_states(np.array([0., 0., 0., 0., 0., 0.]), self.uS)
self.Q = np.array([[5, 0., 0., 0., 0., 0.],
[0., 2, 0., 0., 0., 0.],
[0., 0., 5, 0., 0., 0.],
[0., 0., 0., 2, 0., 0.],
[0., 0., 0., 0., 2, 0.],
[0., 0., 0., 0., 0., 2]])
self.Q1 = np.array([[10, 0., 0., 0., 0., 0.],
[0., 2, 0., 0., 0., 0.],
[0., 0., 100, 0., 0., 0.],
[0., 0., 0., 2, 0., 0.],
[0., 0., 0., 0., 200, 0.],
[0., 0., 0., 0., 0., 2]])
self.Q2 = np.array([[15.5, 0., 0., 0., 0., 0.],
[0., 2, 0., 0., 0., 0.],
[0., 0., 20.5, 0., 0., 0.],
[0., 0., 0., 2, 0., 0.],
[0., 0., 0., 0., 200, 0.],
[0., 0., 0., 0., 0., 2]])
self.R = np.array([[1, 0.],
[0., 1]])
def get_states(self, x0, u):
xstar = np.tile(np.array([[0., 0., 0., 0., 0., 0.]]).transpose(), (1, self.horizon + 1))
xstar[:, 0] = x0
for i, control in enumerate(u.transpose()):
xstar[:, i + 1] = quadrotor.get_next_state(xstar[:, i], control)
return xstar
def get_next_state(self, z, u):
x = z[0, 0]
vx = z[1, 0]
y = z[2, 0]
vy = z[3, 0]
theta = z[4, 0]
omega = z[5, 0]
dydt = np.zeros([quadrotor.NUMBER_STATES, 1])
dydt[0, 0] = vx
dydt[1, 0] = (-(u[0, 0] + u[1, 0]) * np.sin(theta)) / quadrotor.MASS
dydt[2, 0] = vy
dydt[3, 0] = ((u[0, 0] + u[1, 0]) * np.cos(theta) - quadrotor.MASS * quadrotor.GRAVITY) / quadrotor.MASS
dydt[4, 0] = omega
dydt[5, 0] = (quadrotor.LENGTH * (u[0, 0] - u[1, 0])) / quadrotor.INERTIA
z_next = z + dydt * quadrotor.DELTA_T
return z_next
def get_linearization(self, z, u):
A = np.matrix([[1, self.delta, 0, 0, 0, 0],
[0, 1, 0, 0, -(1 / self.mass) * (u[0, 0] + u[1, 0]) * np.cos(z[4, 0]) * self.delta, 0],
[0, 0, 1, self.delta, 0, 0],
[0, 0, 0, 1, -(1 / self.mass) * (u[0, 0] + u[1, 0]) * np.sin(z[4, 0]) * self.delta, 0],
[0, 0, 0, 0, 1, self.delta], [0, 0, 0, 0, 0, 1]])
B = np.matrix(
[[0, 0], [-np.sin(z[4, 0]) * self.delta / self.mass, -np.sin(z[4, 0]) * self.delta / self.mass], [0, 0],
[np.cos(z[4, 0]) * self.delta / self.mass, np.cos(z[4, 0]) * self.delta / self.mass], [0, 0],
[self.length * self.delta / self.inertia, -self.length * self.delta / self.inertia]])
return A, B
def computeCost(self, z, u, horizonLength):
cost = 0
for i in range(horizonLength - 1):
if 450 <= i <= 550:
cost += (z[:, [i]] - self.z2).T @ self.Q1 @ (z[:, [i]] - self.z2) + (u[:, [i]] - self.u).T @ self.R @ (
u[:, [i]] - self.u)
elif i < 450:
cost += (z[:, [i]] - self.z1).T @ self.Q @ (z[:, [i]] - self.z1) + (u[:, [i]] - self.u).T @ self.R @ (
u[:, [i]] - self.u)
cost += (z[:, [horizonLength - 1]] - self.z1).T @ self.Q @ (z[:, [horizonLength - 1]] - self.z1)
else:
cost += (z[:, [i]] - self.z3).T @ self.Q2 @ (z[:, [i]] - self.z3) + (u[:, [i]] - self.u).T @ self.R @ (
u[:, [i]] - self.u)
cost += (z[:, [horizonLength - 1]] - self.z1).T @ self.Q @ (z[:, [horizonLength - 1]] - self.z1)
return cost
def getQuadraticApproximation(self, zS, uS, horizonLength):
listOfA = []
listOfB = []
listOfq = []
listOfr = []
for i in range(horizonLength - 1):
a, b = self.get_linearization(zS[:, [i]], uS[:, [i]])
listOfA.append(a)
listOfB.append(b)
if 450 <= i <= 550:
q, r = self.Q1 @ (zS[:, [i]] - self.z2), self.R @ (uS[:, [i]] - self.u)
elif i < 450:
q, r = self.Q @ (zS[:, [i]] - self.z1), self.R @ (uS[:, [i]] - self.u)
else:
q, r = self.Q2 @ (zS[:, [i]] - self.z3), self.R @ (uS[:, [i]] - self.u)
listOfq.append(q)
listOfr.append(r)
q = self.Q @ (zS[:, [-1]] - self.z1)
listOfq.append(q)
return listOfA, listOfB, listOfq, listOfr
def lineSearch(self, K_gains, k_feedforward):
alpha = 1
while alpha > 0.01:
z0 = np.zeros((6, 1))
for i in range(self.horizon - 1):
if i != 0:
z = np.column_stack((z, zTemp))
uTemp = self.uS[:, [i]] + K_gains[i] @ (zTemp - self.zS[:, [i]]) + alpha * k_feedforward[i]
u = np.column_stack((u, uTemp))
zTemp = self.get_next_state(zTemp, uTemp)
else:
zTemp = np.zeros((6, 1))
uTemp = self.uS[:, [i]] + K_gains[i] @ (zTemp - self.zS[:, [i]]) + alpha * k_feedforward[i]
z = zTemp
u = uTemp
zTemp = self.get_next_state(zTemp, uTemp)
zTemp = zTemp.reshape([6, 1])
z = np.column_stack((z, zTemp))
cost = self.computeCost(z, u, horizonLength=1000)
if cost < self.prevCost:
self.prevCost = cost
self.zS = z
self.uS = u
return True
else:
alpha *= 0.5
return False
def full_flip_controller(self, state, i):
return self.uS[:, [i]].reshape([2, ])
def ilrq(self):
n = 0
while True:
n = n + 1
K_gains = []
k_feedforward = []
listOfA, listOfB, listOfq, listOfr = self.getQuadraticApproximation(self.zS, self.uS, self.horizon)
Pn = self.Q2
pn = listOfq[-1]
for i in range(self.horizon - 1):
q = listOfq[self.horizon - 2 - i]
A = listOfA[self.horizon - 2 - i]
B = listOfB[self.horizon - 2 - i]
r = listOfr[self.horizon - 2 - i]
if 450 <= i <= 550:
Kn = -np.linalg.inv(self.R + B.transpose() @ Pn @ B) @ B.transpose() @ Pn @ A
P = self.Q1 + A.transpose() @ Pn @ A + A.transpose() @ Pn @ B @ Kn
kn = -np.linalg.inv(self.R + B.transpose() @ Pn @ B) @ (B.transpose() @ pn + r)
p = q + A.transpose() @ pn + A.transpose() @ Pn @ B @ kn
elif i < 450:
Kn = -np.linalg.inv(self.R + B.transpose() @ Pn @ B) @ B.transpose() @ Pn @ A
P = self.Q2 + A.transpose() @ Pn @ A + A.transpose() @ Pn @ B @ Kn
kn = -np.linalg.inv(self.R + B.transpose() @ Pn @ B) @ (B.transpose() @ pn + r)
p = q + A.transpose() @ pn + A.transpose() @ Pn @ B @ kn
else:
Kn = -np.linalg.inv(self.R + B.transpose() @ Pn @ B) @ B.transpose() @ Pn @ A
P = self.Q + A.transpose() @ Pn @ A + A.transpose() @ Pn @ B @ Kn
kn = -np.linalg.inv(self.R + B.transpose() @ Pn @ B) @ (B.transpose() @ pn + r)
p = q + A.transpose() @ pn + A.transpose() @ Pn @ B @ kn
Pn = P
pn = p
K_gains.append(Kn)
k_feedforward.append(kn[:, 0])
K_gains = K_gains[::-1]
k_feedforward = k_feedforward[::-1]
if self.lineSearch(K_gains, k_feedforward):
pass
else:
break
if n == 15:
break