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+trailer
+<<
+/Size 322
+/Root 1 0 R
+/Info 3 0 R
+/rgid (PB:266504480_AS:361228867260416@1463135081351)
+/habibi-version (12.208.0)
+/comunity-version (v520.2.0)
+/worker-version (12.208.0)
+/dd (1712067347395)
+/ID [<EC8E7E3BC00095D490D96BCD4B27F643> <EC8E7E3BC00095D490D96BCD4B27F643>]
+>>
+startxref
+416448
+%%EOF
diff --git a/biblio/hopwood-et-al-2024-development-and-evaluation-of-multirotor-flight-dynamic-models-for-estimation-and-control.pdf b/biblio/Hopwood_2024 development-and-evaluation-of-multirotor-flight-dynamic-models-for-estimation-and-control.pdf
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diff --git a/drone/__pycache__/drone_env.cpython-311.pyc b/drone/__pycache__/drone_env.cpython-311.pyc
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diff --git a/drone/__pycache__/rotation.cpython-311.pyc b/drone/__pycache__/rotation.cpython-311.pyc
index 0242eab78cf10c159fbcfa00024125c5ba7a0a73..b622dd345962875e00073b6ccb8c2d8a765b9bd8 100644
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diff --git a/drone/drone_env.py b/drone/drone_env.py
index 87d0fb9f3c0fddb077c935526aae5d30f93e093f..403252031fbc2f16bc8b2af8222a2c9f9647ebca 100644
--- a/drone/drone_env.py
+++ b/drone/drone_env.py
@@ -2,11 +2,9 @@ import numpy as np
 import gymnasium as gym
 from gymnasium.envs.classic_control import utils
 
+from rotation import *
 from drone_model import Drone
-from rotation import quat2eul
 
-deg2rad = np.pi/180
-rad2deg = 1 / deg2rad
 
 class DroneEnv(gym.Env):
 
@@ -16,57 +14,59 @@ class DroneEnv(gym.Env):
         self.tau = 0.02  # seconds between state updates
         
         # Angle at which to fail the episode
-        self.pos_threshold = np.array([2.4, 2.4, 2.4])
-        self.ang_threshold = np.array([15, 15, 15]) * deg2rad
+        self.state = np.zeros(13)
+        self.target = np.zeros(13)
+        self.obs = np.zeros(13)
+        
+        self.pos_threshold = np.array([1., 1., 1.])
+        self.quat_threshold = np.ones(4)
         self.vel_threshold = np.finfo(np.float32).max * np.ones(3)
         self.rot_threshold = np.finfo(np.float32).max * np.ones(3)
 
         high = np.concatenate(
             [
-                self.pos_threshold * 2,
-                self.ang_threshold * 2,
+                self.pos_threshold,
+                self.quat_threshold,
                 self.vel_threshold,
                 self.rot_threshold
             ],
             dtype=np.float32,
         )
+
         self.observation_space = gym.spaces.Box(-high, high, dtype=np.float32)
-        self.action_space = gym.spaces.Box(0, 1, shape=(4,), dtype=np.float32)
-        self.state = np.zeros(13)
-        self.obs = np.zeros(12)
-        self.target = np.zeros(12)
+        self.action_space = gym.spaces.Box(0, 500, shape=(4,), dtype=np.float32)
+
         self.steps_beyond_terminated = None
 
     def observation(self):
-        pos = self.state[0:3]
-        vel = self.state[7:10]
-        rot = self.state[10:13]
-        quat = self.state[3:7]
-        ang = quat2eul(quat)
-        d_pos = pos - self.target[0:3]
-        d_ang = ((ang - self.target[3:6]) + np.pi) % (2*np.pi) - np.pi
-        d_vel = vel - self.target[6:9]
-        d_rot = rot - self.target[9:12]
-        obs = np.concatenate([d_pos, d_ang, d_vel, d_rot])
+        d_pos = self.state[0:3] - self.target[0:3]
+        d_quat = quatmul(quatinv(self.target[3:7]), self.state[3:7])
+        d_vel = self.state[7:10] - self.target[7:10]
+        d_rot = self.state[10:13] - self.target[10:13]
+        obs = np.concatenate([d_pos, d_quat, d_vel, d_rot])
         return obs
 
+    def reward(self):
+        dist_pos = np.linalg.norm(self.obs[0:3])
+        dist_quat = quatdist(self.state[3:7], self.target[3:7])
+        terminated = (dist_pos + dist_quat) > 1
+        reward = 1 - (dist_pos + dist_quat) if not terminated else -1  
+        return reward, terminated
+
     def reset(self, seed=None, options=None):
         super().reset(seed=seed)
         # Note that if you use custom reset bounds, it may lead to out-of-bound
         # state/observations.
-        low, high = utils.maybe_parse_reset_bounds(
-            options, -0.05, 0.05  # default low
-        )  # default high
-        # self.state = self.np_random.uniform(low=low, high=high, size=(13,))
-        self.state = np.array([0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0])
-        self.steps_beyond_terminated = None
+        low, high = utils.maybe_parse_reset_bounds(options, -0.1, 0.1)  
+        self.state = self.target + np.array([0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
         self.obs = self.observation()
         return self.obs, {}
 
     def step(self, action):
-        new_state = self.drone.step(self.state, action, np.zeros(3), self.tau)
-        self.state = new_state
+        self.state = self.drone.step(self.state, action, self.tau)
         self.obs = self.observation()
-        terminated = (self.obs@self.obs < 1)
-        reward = 1 if terminated else 0  # Binary sparse rewards
+        reward, terminated = self.reward()
         return self.obs, reward, terminated, False, {}
+
+    def render(self, mode='human'):
+        pass
diff --git a/drone/drone_model.py b/drone/drone_model.py
index 2fd00d67b64f0236b0a45dcd3292a706b8e32d58..e731d89cc47536d00ad92cc727324504e023d8f1 100644
--- a/drone/drone_model.py
+++ b/drone/drone_model.py
@@ -1,8 +1,8 @@
 import numpy as np
+import yaml
 from scipy.optimize import fsolve
 from scipy.integrate import solve_ivp
-import yaml
-from rotation import quatrot, quatmul
+from rotation import *
 
 class Drone:
 
@@ -18,27 +18,18 @@ class Drone:
         self.PROP_KP = drone['PROP_KP']
         self.PROP_KM = drone['PROP_KM']
 
-    def thrust(self, n):
-        # prop forces computation / notice that negative thrust is not implemented
-        Kp = self.PROP_KP
-        T = Kp * n**2
-        # prop moments computation
-        Km = self.PROP_KM
-        N = np.sign(n) * Km * n**2
-        return T, N
-
-    def u_int(self, n):
-        # position of rotor wrt center of gravity
-        P_R_CG = self.P_R_CG
-        T, N = self.thrust(n)
-        u = np.array([T[0] + T[1] + T[2] + T[3], P_R_CG * (T[3] - T[2]), P_R_CG * (T[0] - T[1]), N[2] + N[3] - N[0] - N[1]])
-        return u
-
-    def dyn(self, x, u, w):
+    def dyn(self, x, n):
 
         G = self.G
         MASS = self.MASS
         INERTIA = self.INERTIA
+        P_R_CG = self.P_R_CG
+        KP = self.PROP_KP
+        KM = self.PROP_KM
+
+        T = KP * n**2
+        N = KM * n**2
+        u = np.array([sum(T), P_R_CG*(T[3]-T[2]), P_R_CG*(T[0]-T[1]), N[2]+N[3]-N[0]-N[1]])
 
         # state demultiplexing
         quat = x[3:7]
@@ -46,14 +37,14 @@ class Drone:
         rot = x[10:13]
 
         # linear velocity derivative
-        dvdt = np.array([0, 0, G]) - 1/MASS * quatrot(quat, np.array([0, 0, u[0]]))
+        dvdt = quatrot(quatinv(quat), np.array([0, 0, -u[0]])) / MASS + np.array([0, 0, G])
 
         # angular velocity derivative
         drdt = np.linalg.inv(INERTIA) @ (u[1:4] - np.cross(rot, INERTIA@rot))
 
         # kinematic equations
-        dpdt = vel + w
-        dqdt = 1/2 * quatmul(quat, np.concatenate([[0], rot]))
+        dpdt = vel
+        dqdt = 0.5 * quatmul(quat, vect2quat(rot))
 
         return np.concatenate([dpdt, dqdt, dvdt, drdt])
 
@@ -64,21 +55,20 @@ class Drone:
         x[9] = vz
 
         def func(n):
-            u = self.u_int(n)
-            dx = self.dyn(x, u, np.zeros(3))
+            dx = self.dyn(x, n)
             return dx[9], dx[10], dx[11], dx[12]
 
         y0 = np.array([100, 100, 100, 100])
         y = fsolve(func, y0)
         return y
 
-    def step(self, x, n, w, dt):
-        func = lambda t, s: self.dyn(s, self.u_int(n), w)
+    def step(self, x, n, dt):
+        func = lambda t, s: self.dyn(s, n)
         sol = solve_ivp(func, (0, dt), x, method='RK45', max_step=0.01)
         return sol.y.T[-1]
 
-    def sim(self, t_span, x0, fctrl, fwind):
-        func = lambda t, s: self.dyn(s, self.u_int(fctrl(t, s, fwind(t, s))), fwind(t, s))
+    def sim(self, t_span, x0, fctrl):
+        func = lambda t, s: self.dyn(s, fctrl(t, s))
         sol = solve_ivp(func, t_span, x0, method='RK45', max_step=0.01)
         return sol
 
diff --git a/drone/main.py b/drone/main.py
index d3e397ada9854c61056f9a64f829ac57837e6548..41ce6317d3bddaac019003a9fd6990c77a280b3e 100644
--- a/drone/main.py
+++ b/drone/main.py
@@ -1,5 +1,6 @@
 import numpy as np
 import matplotlib.pyplot as plt
+
 from drone_model import Drone
 from drone_env import DroneEnv
 
@@ -20,39 +21,24 @@ def uramp(t, t0) :
 
 
 if __name__ == "__main__":
-    drone = Drone()
+    drone_env = DroneEnv()
 
     vh = 0
     vz = 0
-    # cap = 0
-    # omega = 0
-
-    n0 = drone.trim(vh, vz)
+    n0 = drone_env.drone.trim(vh, vz)
     print(n0)
-
-    drone_env = DroneEnv(drone)
-    drone_env.target = np.array([0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0])
-    obs0 = drone_env.reset()[0]
+    
+    drone_env.target = np.array([0, 0, -20, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0])
+    drone_env.reset()
     x0 = drone_env.state
-    print(drone_env.state)
-    obs1 = drone_env.step(n0)[0]
-    print(drone_env.state)
+    print(x0)
 
-    def ctl(t, s, w):
-        # d = (upulse(t, 5, 6))*dx*0.1
-        d = (upulse(t, 1, 1.1)-upulse(t, 1.1, 1.2))*np.linalg.norm(n0)*np.array([0.01, -0.01, 0.0, 0.0])
-        n = n0 + d*0.0
+    def ctl(t, s):
+        dn = (upulse(t, 1, 2) - upulse(t, 2, 3))*np.linalg.norm(n0)*np.array([0.1, 0.1, 0.1, 0.1])
+        n = n0 + dn
         return n
 
-    def pid(t, s, w):
-        n = (10 * s[2])*np.array([1, 1, 1, 1])
-        return n
-
-    def wnd(t, s):
-        w = np.zeros(3)
-        return w 
-
-    sim = drone.sim((0, 20), x0, pid, wnd)
+    sim = drone_env.drone.sim((0, 20), x0, ctl)
 
     fig, axs = plt.subplots(2, 2)
 
diff --git a/drone/rotation.py b/drone/rotation.py
index 563c8f4d59fa06f7533be4b73325cf976578069f..e1975ce35b9a490177956bacc71a42c282756cf1 100644
--- a/drone/rotation.py
+++ b/drone/rotation.py
@@ -1,30 +1,56 @@
 import numpy as np
+from scipy.linalg import expm, logm
 
 deg2rad = np.pi/180
 rad2deg = 1 / deg2rad
 
-
 def hat(x):
     return np.array([[0, -x[2], x[1]], [x[2], 0, -x[0]], [-x[1], x[0], 0]])
 
 def inv_hat(m):
     return np.array([m[2, 1], m[0, 2], m[1, 0]])
 
+
 # (a, n): a = angle, n = vecteur unitaire (axe de rotation)
+
 def quat2axang(q):
-    a = 2 * np.arccos(q[0])
-    n = q[1:4] / np.sqrt(1 - q[0] * q[0])
-    return a, n
+    q = q / sum(q*q)
+    mu = 2 * np.arccos(min(1, q[0]))
+    if (q[0] >= 1) :
+        n = np.zeros(3)
+    else :
+        n = q[1:4] / np.sqrt(1 - q[0]*q[0])
+    return (mu, n)
 
 def dcm2axang(R):
     t = np.trace(R)
-    n = 0.5 * inv_hat(R - R.T)
-    r = np.linalg.norm(n)
-    a = np.arctan2(r, (t - 1) / 2)
-    return a, n / r
+    mu = np.arccos((t - 1) / 2)
+    n = 0.5 * inv_hat(R.T - R) / np.sin(mu)
+    return (mu, n)
+
+
+def axangrot(ax, u):            # left hand rotation du vecteur u d'un angle mu selon l'axe n
+    mu, n = ax
+    v = (1 - np.cos(mu)) * n * np.dot(n, u) + u * np.cos(mu) - np.cross(n, u) * np.sin(mu)
+    return v
 
 
 # Quaternions
+
+def axang2quat(ax):
+    mu, n = ax
+    return np.concatenate([[np.cos(mu / 2)], n * np.sin(mu / 2)])
+    
+def eul2quat(a):
+    qx = np.array([np.cos(a[0]/2), np.sin(a[0]/2), 0, 0])
+    qy = np.array([np.cos(a[1]/2), 0, np.sin(a[1]/2), 0])
+    qz = np.array([np.cos(a[2]/2), 0, 0, np.sin(a[2]/2)])
+    return quatmul(qz, quatmul(qy, qx))
+
+def vect2quat(u):
+    return np.concatenate([[0], u])
+
+
 def quatmat(p):
     m = np.array(
         [
@@ -39,41 +65,36 @@ def quatmat(p):
 def quatmul(p, q):
     return quatmat(p)@q
 
-def quatnorm(q): 
-    return np.dot(q, q)
-
-def quatconj(q):
-    return q * np.array([1, -1, -1, -1])
-
 def quatinv(q):
-    return quatconj(q) / quatnorm(q)
-
-def vect2quat(u):
-    return np.concatenate([[0], u])
+    return np.concatenate([[q[0]], -q[1:4]]) / sum(q*q)
 
 def quatrot(q, u):
-    v = quatmul(quatinv(q), quatmul(vect2quat(u), q))
+    v = quatmul(quatmul(quatinv(q), vect2quat(u)), q)
     return v[1:]
 
+def quatdist(q1, q2):
+    return 2 * np.arccos(min(1,abs(sum(q1*q2))))                 # donne une valeur d'angle entre 0 et PI
 
-def axang2quat(a, n):
-    return np.concatenate([[np.cos(a / 2)], n * np.sin(a / 2)])
-    
-def eul2quat(a):
-    qr = np.array([np.cos(a[0]/2), np.sin(a[0]/2), 0, 0])
-    qp = np.array([np.cos(a[1]/2), 0, np.sin(a[1]/2), 0])
-    qy = np.array([np.cos(a[2]/2), 0, 0, np.sin(a[2]/2)])
-    return quatmul(qy, quatmul(qp, qr))
+def quatdist2(q1, q2):
+    return 1 - abs(sum(q1*q2))                                   # donne une valeur d'angle entre 0 et 1
+
+def quaterr(q1, q2):
+    mu, n = quat2axang(quatmul(quatinv(q2), q1))
+    return mu*n
 
 
 # Matrices de Rotation (DCM)
-def axang2dcm(a, n):
-    dcm = (1 - np.cos(a)) * np.outer(n, n) + np.cos(a) * np.identity(3) - np.sin(a) * hat(n)
+
+def axang2dcm(ax):
+    mu, n = ax
+    dcm = (1 - np.cos(mu)) * np.outer(n, n) + np.cos(mu) * np.identity(3) - np.sin(mu) * hat(n)
     return dcm
 
 def quat2dcm(q):
+    q = q / quatnorm(q)
+    q0 = q[0]
     w = q[1:4]
-    dcm = (2 * np.outer(w, w) + (q[0]**2 - w @ w) * np.identity(3) - 2 * q[0] * hat(w)) / quatnorm(q)
+    dcm = (2 * np.outer(w, w) + (q0**2 - w @ w) * np.identity(3) - 2 * q0 * hat(w)) 
     return dcm
 
 def eul2dcm(a):
@@ -83,7 +104,34 @@ def eul2dcm(a):
     return Rx @ Ry @ Rz
 
 
+def dcmerr(R1, R2):
+    return inv_hat(logm(R2@R1.T))
+
+def dcmdist(R1, R2):
+    return np.linalg.norm(dcmerr(R1, R2))               # donne une valeur d'angle entre 0 et PI
+
+
+def dcmerr2(R, Rd):
+    return 0.5 * inv_hat(Rd@R.T - R@Rd.T)
+
+def dcmdist2(R, Rd):
+    return np.linalg.norm(np.identity(3) - Rd@R.T)     # donne une valeur ente 0 et 2V2
+
+def dcmdist4(R, Rd):
+    return  0.5 * np.trace(np.identity(3) - Rd@R.T)
+
+
+def dcmdist3(R, Rd):
+    dist = 2 - np.sqrt(1 + np.trace(Rd@R.T))
+    return dist
+
+def dcmerr3(R, Rd):
+    err = inv_hat(Rd@R.T - R@Rd.T) / np.sqrt(1 + np.trace(Rd@R.T))
+    return err
+
+
 # Angles d'Euler (phi, theta, psi) selon axes (x, y, z) : z en premier
+
 def quat2eul(q):
     phi = np.arctan2(2 * (q[0] * q[1] + q[2] * q[3]), q[0]**2 - q[1]**2 - q[2]**2 + q[3]**2)
     theta = -np.arcsin(2 * (q[1] * q[3] - q[0] * q[2]))
@@ -95,3 +143,10 @@ def dcm2eul(R):
     theta = -np.arcsin(R[0, 2])
     psi = np.arctan2(R[0, 1], R[0, 0])
     return np.array([phi, theta, psi])
+
+
+def euldist(e1, e2):                                    # donne une valeur d'angle entre 0 et PI
+    diff = e1 - e2
+    d = np.fmin(np.abs(diff), 2*np.pi - np.abs(diff))
+    r = np.linalg.norm(d) / np.sqrt(3)
+    return r
diff --git a/drone/sac_drone_1.zip b/drone/sac_drone_1.zip
new file mode 100644
index 0000000000000000000000000000000000000000..0bc064fd86920947b8a4cd4b439d915304d6559f
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diff --git a/drone/sac_drone_2.zip b/drone/sac_drone_2.zip
new file mode 100644
index 0000000000000000000000000000000000000000..236a45cbe3831cc656535a543f17bef35793ac81
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diff --git a/drone/train.py b/drone/train.py
new file mode 100644
index 0000000000000000000000000000000000000000..ac0e4024be79613bec2076208e35905444fe3fe4
--- /dev/null
+++ b/drone/train.py
@@ -0,0 +1,16 @@
+import numpy as np
+from stable_baselines3 import SAC
+
+from drone_model import Drone
+from drone_env import DroneEnv
+
+
+if __name__ == "__main__":
+
+    drone_env = DroneEnv()
+    drone_env.target = np.array([0, 0, -20, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0])
+
+    model = SAC("MlpPolicy", drone_env, verbose=1)
+    model.learn(total_timesteps=20000, log_interval=10)
+    model.save("sac_drone_2")
+
diff --git a/mavion/__pycache__/mavion_env.cpython-311.pyc b/mavion/__pycache__/mavion_env.cpython-311.pyc
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diff --git a/mavion/__pycache__/mavion_model.cpython-311.pyc b/mavion/__pycache__/mavion_model.cpython-311.pyc
index 36b589965e84da4a609c7f9fc9026c6e1ee8bafd..c9a43a700b9d5ee72b35d4df6a06b1e5e9bbbceb 100644
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diff --git a/mavion/__pycache__/rotation.cpython-311.pyc b/mavion/__pycache__/rotation.cpython-311.pyc
index 749ea808773963bcc6e585f5880ffabfbb892714..eaa27d5bbdd2317bb12ffb27cbe9374d537808d3 100644
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diff --git a/mavion/__pycache__/rotation.cpython-37.pyc b/mavion/__pycache__/rotation.cpython-37.pyc
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index 0000000000000000000000000000000000000000..b0e233e950a5f28cd4991cfe585f07450814c561
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diff --git a/mavion/main.py b/mavion/main.py
index 69944de72b5b8de5e783ac2eb63419bd0a3c96b2..1c3f68fd57a08a007a6dd6180f5e7d39dc1ca906 100644
--- a/mavion/main.py
+++ b/mavion/main.py
@@ -1,7 +1,9 @@
 import numpy as np
-from rotation import *
+from stable_baselines3 import SAC
 import matplotlib.pyplot as plt
 from mavion_model import Mavion
+from mavion_env import MavionEnv
+from rotation import *
 
 def upulse(t, t0, tf):
     u = 0 if (t<t0 or t>=tf) else 1
@@ -16,39 +18,52 @@ def uramp(t, t0) :
     return u
 
 if __name__ == "__main__":
-    mavion = Mavion()
 
-    vh = 0
+    mav_env = MavionEnv()
+
+    vh = 12
     vz = 0
-    cap = 0
+    cap = 0/rad2deg
     omega = 0
 
-    dx, de, theta = mavion.trim(vh, vz)
+    target = [vh, vz]
+
+    dx, de, theta = mav_env.mavion.trim(target)
     theta = (theta + np.pi) % (2*np.pi) - np.pi
-    print(dx, de, theta*57.3)
+    print(dx, de, theta*rad2deg)
 
-    pos = np.array([0, 0, -10])
+    pos = np.array([0, 0, -20])
     ang = np.array([0, theta, cap])
     vel = np.array([vh * np.cos(cap), vh * np.sin(cap), vz])
     rot = np.array([0, 0, 0])
     quat = eul2quat(ang)
 
     x0 = np.concatenate([pos, quat, vel, rot])
-    print(mavion.equi(x0))
-
-    def ctl(t, s, w):
-        ddx = (upulse(t, 5, 6) - upulse(t, 6, 7))*dx*0.1
-        qt = np.array([1/np.sqrt(2), 0, 1/np.sqrt(2), 0])
-        q = s[3:7]
-        dde = 1.0 * (q - qt)[2]
-        u = np.array([-dx-ddx, dx+ddx, de+dde, de+dde])
+    
+    pos_target = np.array([0, 0, -20])
+    eul_target = np.array([0, 90, 0])*deg2rad
+    quat_target = eul2quat(eul_target)
+    vel_target = np.zeros(3)
+    rot_target = np.zeros(3)
+
+    mav_env.target = np.concatenate([pos_target, quat_target, np.zeros(3), np.zeros(3)])
+    mav_agent = SAC.load("sac_mavion_2", env=mav_env)
+    mav_env.reset()
+    x0 = mav_env.state
+
+    def ctl(t, s):
+        act, _ = mav_agent.predict(s, deterministic=True)
+        # u = act * mav_env.action_range
+        u = np.array([dx, dx, de, de])
         return u
 
     def wnd(t, s):
         w = np.zeros(3)
         return w 
 
-    sim = mavion.sim((0, 60), x0, ctl, wnd)
+    print(x0, ctl(0, x0))
+
+    sim = mav_env.mavion.sim((0, 120), x0, ctl, wnd)
 
     fig, axs = plt.subplots(2, 2)
 
@@ -62,17 +77,17 @@ if __name__ == "__main__":
     quat = sim.y[3:7].T
     ax.plot(sim.t, quat, label=('q0', 'q1', 'q2', 'q3'))
     ax.set_title(label='quaternion')
-    # eul = np.apply_along_axis(quat2eul, 1, sim.y[3:7].T)*57.3
+    # eul = np.apply_along_axis(quat2eul, 1, quat) * rad2deg
     # ax.plot(sim.t, eul, label=('phi', 'theta', 'psi'))
     # ax.set_title(label='euler angles')
     ax.legend()
     ax.grid()
 
     ax = axs[0][1]
-    ax.plot(sim.t, sim.y[7:10].T, label=('u','v','w'))
+    ax.plot(sim.t, sim.y[7:10].T, label=('Vn','Ve','Vv'))
     ax.legend()
     ax.grid()
-    ax.set_title(label='vitesses')
+    ax.set_title(label='vitesses dans le rep. terre')
 
     ax = axs[1][1]
     ax.plot(sim.t, sim.y[10:13].T, label=('p','q','r'))
diff --git a/mavion/mavion.yaml b/mavion/mavion.yaml
index 63ef25c774aa46d725b1d894e07d057ea883ecab..0c8a37764294db108a5e7fae177ee785895b9f10 100644
--- a/mavion/mavion.yaml
+++ b/mavion/mavion.yaml
@@ -22,3 +22,5 @@ ELEVON_MEFFICIENCY : [0, 0.66, 0]
 ELEVON_FEFFICIENCY : [0, 0.33, 0] 
 PROP_KP : 7.84e-06 
 PROP_KM : 2.400e-7     
+MAX_ROTOR_SPD : 850      # rad/s (TBC)
+MAX_FLAP_DEF :  0.5     # rad (TBC)
diff --git a/mavion/mavion_env.py b/mavion/mavion_env.py
index 45996ceb6c66d2e5972e5b53c8c022bbd7375c02..823ed946d17c70c284d8aa1fdb8b28ea85bb7b83 100644
--- a/mavion/mavion_env.py
+++ b/mavion/mavion_env.py
@@ -2,69 +2,69 @@ import numpy as np
 import gymnasium as gym
 from gymnasium.envs.classic_control import utils
 from mavion_model import Mavion
+from rotation import quatinv, quatmul
 
 class MavionEnv(gym.Env):
 
     def __init__(self, mavion=Mavion(), render_mode=None):
 
-        self.tau = 0.02  # seconds between state updates
-        
+        self.mavion = mavion
+        self.tau = 0.2  # seconds between state updates
+
         # Angle at which to fail the episode
-        self.pos_threshold = np.array([2.4, 2.4, 2.4])
-        self.ang_threshold = np.array([15, 15, 15]) * deg2rad
+        self.pos_threshold = np.array([10, 10, 10])
+        self.quat_threshold = np.array([1, 1, 1, 1])
         self.vel_threshold = np.finfo(np.float32).max * np.ones(3)
         self.rot_threshold = np.finfo(np.float32).max * np.ones(3)
 
-        high = np.concatenate(
-            [
-                self.pos_threshold * 2,
-                self.ang_threshold * 2,
+        high = np.concatenate([
+                self.pos_threshold,
+                self.quat_threshold,
                 self.vel_threshold,
                 self.rot_threshold
-            ],
-            dtype=np.float32,
-        )
+            ],dtype=np.float32)
         self.observation_space = gym.spaces.Box(-high, high, dtype=np.float32)
 
-        self.action_space = gym.spaces.Box(0, 1, shape=(4,), dtype=np.float32)
-        
-        self.target = None
-        self.obs = None
-        self.steps_beyond_terminated = None
+        action_max = np.array([1, 1, 1, 1])
+        action_min = np.array([0, 0, -1, -1])
+        self.action_space = gym.spaces.Box(action_min, action_max, dtype=np.float32)
+        self.action_range = np.array([mavion.MAX_ROTOR_SPD, mavion.MAX_ROTOR_SPD, mavion.MAX_FLAP_DEF, mavion.MAX_FLAP_DEF])
 
-        self.mavion = mavion
+        self.state = np.zeros(13)
+        self.target = np.zeros(13)
+        self.obs = np.zeros(13)
 
-    def obs(self):
-        Vh = np.linalg.norm(self.mavion.vel[0:2])
-        Vv = self.mavion.vel[2]
-        Cap = np.arctan2(self.mavion.vel[1], self.mavion.vel[0])
-        phi = self.mavion.ang[0]
-        Turn_rate = self.mavion.G / Vh * np.tan(phi)
-        return np.array([Vh, Vv, Cap, Turn_rate])
-
-    def reset(self, seed=None, options=None):
-        super().reset(seed=seed)
+    def observation(self):
+        obs = np.zeros(13)
+        obs = self.state - self.target
+        obs[3:7] = quatmul(quatinv(self.target[3:7]), self.state[3:7])
+        return obs
 
-        # Note that if you use custom reset bounds, it may lead to out-of-bound
-        # state/observations.
-        low, high = utils.maybe_parse_reset_bounds(
-            options, -0.05, 0.05  # default low
-        )  # default high
-        self.target = np.zeros(12)
-        self.obs = self.np_random.uniform(low=low, high=high, size=(12,))
-        self.state = self.obs + self.target
-        self.steps_beyond_terminated = None
+    def distance(self, s, t):
+        d_pos = np.linalg.norm(t[0:3] - s[0:3]) # distance euclidienne
+        d_quat = 2 * np.arccos(min(1, sum(t[3:7] * s[3:7]))) / np.pi # compris entre 0 et 1
+        d_vel = np.linalg.norm(t[7:10] - s[7:10]) # distance euclidienne
+        d_rot = np.linalg.norm(t[10:13] - s[10:13]) # distance euclidienne
+        return d_pos + d_quat*10 + d_vel*0 + d_rot*0
 
-        return self.obs, {}
+    def reward(self):
+        dist = self.distance(self.state, self.target)
+        terminated = dist > 10
+        reward = 10 - dist if not terminated else -10
+        return reward, terminated
 
     def step(self, action):
-        x = s2q(self.state)
-        u = action
-        w = np.zeros(3)
-        new_state = self.mavion.step(x, u, w, self.tau)
-        self.state = q2s(new_state)
-        terminated = np.array_equal(self.state, self.target)
-        reward = 1 if terminated else 0  # Binary sparse rewards
-        self.obs = self.state - self.target
+        x = self.state
+        u = action * self.action_range
+        self.state  = self.mavion.step(x, u, np.zeros(3), self.tau)
+        self.obs = self.observation()
+        reward, terminated = self.reward()
         return self.obs, reward, terminated, False, {}
 
+    def reset(self, seed=None, options=None):
+        super().reset(seed=seed)
+        low, high = utils.maybe_parse_reset_bounds(options, -1, 1)
+        delta = self.np_random.uniform(low=low, high=high, size=(3,))
+        self.state = self.target + np.concatenate([delta, np.zeros(10)])
+        self.obs = self.observation()
+        return self.obs, {}
diff --git a/mavion/mavion_model.py b/mavion/mavion_model.py
index 11d35c06229d1e4cf38a30cff4ebfe80f4b17152..7ae8eeb1725d8ad404bb71413d8bdeadbef439be 100644
--- a/mavion/mavion_model.py
+++ b/mavion/mavion_model.py
@@ -1,11 +1,11 @@
 import numpy as np
-from rotation import *
 from scipy.optimize import fsolve
 from scipy.integrate import solve_ivp
+from rotation import hat, eul2quat, vect2quat, quatinv, quatmul, quatrot
 import yaml
 
 class Mavion:
-
+    
     def __init__(self, file="mavion.yaml"):
         stream = open(file, "r")
         drone_data = yaml.load(stream, Loader=yaml.Loader)
@@ -28,31 +28,27 @@ class Mavion:
 
         self.ELEVON_MEFFICIENCY = np.array(drone_data['ELEVON_MEFFICIENCY'])
         self.ELEVON_FEFFICIENCY = np.array(drone_data['ELEVON_FEFFICIENCY'])
-        self.PHI_n = drone_data["PHI_n"]
+        self.MAX_ROTOR_SPD = drone_data['MAX_ROTOR_SPD']
+        self.MAX_FLAP_DEF = drone_data['MAX_FLAP_DEF']
 
         # geometric parameters
-        self.P_P1_CG = np.array(drone_data["P_P1_CG"]) * self.CHORD
-        self.P_P2_CG = np.array(drone_data["P_P2_CG"]) * self.CHORD
-        self.P_A1_CG = np.array(drone_data["P_A1_CG"]) * self.CHORD
-        self.P_A2_CG = np.array(drone_data["P_A2_CG"]) * self.CHORD
-
+        self.P_P1_CG = np.array(drone_data["P_P1_CG"]) * np.array([self.CHORD, self.WINGSPAN, 0])
+        self.P_P2_CG = np.array(drone_data["P_P2_CG"]) * np.array([self.CHORD, self.WINGSPAN, 0])
+        self.P_A1_CG = np.array(drone_data["P_A1_CG"]) * np.array([self.CHORD, self.WINGSPAN, 0])
+        self.P_A2_CG = np.array(drone_data["P_A2_CG"]) * np.array([self.CHORD, self.WINGSPAN, 0])
 
+        self.PHI_n = drone_data["PHI_n"]
         self.Cd0 = 0.1
         self.Cy0 = 0.1
         self.dR = -0.1 * self.CHORD
-
         self.PHI_fv = np.diag([self.Cd0, self.Cy0, (2 * np.pi + self.Cd0)])
-
         self.PHI_mv = np.array([[0, 0, 0], 
-            [0, 0, - self.dR * (2 * np.pi + self.Cd0) / self.CHORD], 
+            [0, 0, -self.dR * (2 * np.pi + self.Cd0) / self.CHORD], 
             [0, self.dR * self.Cy0 / self.WINGSPAN, 0]])
+        self.PHI_fw = self.PHI_mv.T
+        self.PHI_mw = 1/2 * np.diag([0.5, 0.5, 0.5])
 
-        self.PHI_mw = 1 / 2 * np.diag([0.5, 0.5, 0.5])
-
-        self.PHI = np.block([[self.PHI_fv, self.PHI_mv.T], [self.PHI_mv, self.PHI_mw]])
 
-
-    
     def thrust(self, dx):
         kp = self.PROP_KP
         km = self.PROP_KM
@@ -62,10 +58,10 @@ class Mavion:
         N = np.sign(dx) * km * dx**2 * np.array([1, 0, 0])
         return np.array([T, N])
 
-    def aero(self, quat, vel, rot, T, de, w):
-
+    def aero(self, vinf, rot, T, de):
         # data extraction from self struct
         PHI_fv = self.PHI_fv
+        PHI_fw = self.PHI_fw
         PHI_mv = self.PHI_mv
         PHI_mw = self.PHI_mw
         PHI_n  = self.PHI_n
@@ -80,48 +76,37 @@ class Mavion:
 
         # derivative data
         Sp = np.pi * Prop_R**2
-
-        # DCM computation
-        D = quat2dcm(quat)
-
-        # freestream velocity computation in body frame
-        vinf = D @ (vel - w)
-
         # computation of total wing section area
         S = Swet + Sdry
-
         # computation of chord matrix
-        B = np.diag([ws, chord, ws])
+        B = np.array([ws, chord, ws])
 
         # eta computation
-        eta = np.sqrt(vinf@vinf + PHI_n * (B@rot)@(B@rot))
+        eta = np.sqrt(vinf@vinf + PHI_n * (B*rot)@(B*rot))
+        qv = 0.5*RHO*S*eta
 
         # Force computation
         # airfoil contribution
-        Fb_a = -1/2*RHO*S*eta * PHI_fv@vinf - 1/2*RHO*S*eta * PHI_mv@B@rot - 1/2*Swet/Sp * PHI_fv@T
+        Fb_a = -qv * (PHI_fv@vinf + PHI_fw@(B*rot)) - 1/2 * Swet/Sp * PHI_fv@T
         # elevon contribution
-        Fb_e = 1/2*RHO*S*eta * PHI_fv@np.cross(de*Thetaf, vinf) \
-                + 1/2*RHO*S*eta * PHI_mv@B@np.cross(de*Thetaf, rot) \
-                + 1/2*Swet/Sp * PHI_fv@np.cross(de*Thetaf, T)
+        Fb_e = qv * (PHI_fv@np.cross(Thetaf*de, vinf) + PHI_fw@(np.cross(Thetaf*de, B*rot)))  + 1/2 * Swet/Sp * PHI_fv@np.cross(Thetaf*de, T)
         Fb = Fb_a + Fb_e
 
         # Moment computation
         # airfoil contribution
-        Mb_a = -1/2*RHO*S*eta * B@PHI_mv@vinf - 1/2*RHO*S*eta * B@PHI_mw@B@rot - 1/2*Swet/Sp * B@PHI_mv@T
+        Mb_a = -qv * B*(PHI_mv@vinf + PHI_mw@(B*rot)) - 1/2 * Swet/Sp * B*(PHI_mv@T)
         # elevon contribution
-        Mb_e = 1/2*RHO*S*eta * B@PHI_mv@np.cross(de*Thetam, vinf) \
-                + 1/2*RHO*S*eta * B@PHI_mw@B@np.cross(de*Thetam, rot) \
-                + 1/2*Swet/Sp * B@PHI_mv@np.cross(de*Thetam, T)
+        Mb_e = qv * B*(PHI_mv@np.cross(Thetam*de, vinf) + PHI_mw@(np.cross(Thetam*de, B*rot))) + 1/2 * Swet/Sp * B*(PHI_mv@np.cross(Thetam*de, T))
         Mb = Mb_a + Mb_e
 
         return np.array([Fb, Mb])
 
+
     def dyn(self, x, u, w):
 
         G = self.G
         MASS = self.MASS
         INERTIA = self.INERTIA
-
         # position of propellers wrt center of gravity
         P_P1_CG = self.P_P1_CG
         P_P2_CG = self.P_P2_CG
@@ -133,66 +118,79 @@ class Mavion:
         INERTIA_PROP_N = self.INERTIA_PROP_N
 
         # state demultiplexing
-        quat = x[3:7]
-        vel = x[7:10]
-        rot = x[10:13]
-
-        # linear velocity derivative
-        D = quat2dcm(quat)
-
-        [T1, N1] = self.thrust(u[0])
+        quat = x[3:7]        # quaternion de passage de ned (ref terrestre) à frd (ref avion) = q_frd/ned   
+        vel = x[7:10]        # vitesse par rapport au sol exprimée dans le repere terre (ned)
+        rot = x[10:13]       # vitesse de rotation dans le repere avion (body / frd)
+        
+        [T1, N1] = self.thrust(-u[0])       
         [T2, N2] = self.thrust(u[1])
-        [F1, M1] = self.aero(quat, vel, rot, T1, u[2], w)
-        [F2, M2] = self.aero(quat, vel, rot, T2, u[3], w)
-
-        Fb = T1 + T2 + F1 + F2
-        dvdt = np.array([0, 0, G]) + 1/MASS * D.T@Fb
+        tau1 = N1 - (rot[0] - u[0]) * (INERTIA_PROP_X - INERTIA_PROP_N) * np.array([0, rot[2], -rot[1]])
+        tau2 = N2 - (rot[0] + u[1]) * (INERTIA_PROP_X - INERTIA_PROP_N) * np.array([0, rot[2], -rot[1]])
 
-        # angular velocity derivative
-        Ma = M1 + M2 + np.cross(P_A1_CG, F1) + np.cross(P_A2_CG, F2)
+        vrel = quatrot(quat, vel - w)       # vitesse aéro exprimée dans le repere avion (frd)
+        [F1, M1] = self.aero(vrel, rot, T1, u[2])
+        [F2, M2] = self.aero(vrel, rot, T2, u[3])
 
-        tau1 = N1 - (rot[0] + u[0]) * (INERTIA_PROP_X - INERTIA_PROP_N) * np.array([0, rot[2], -rot[1]])
-        tau2 = N2 - (rot[0] + u[1]) * (INERTIA_PROP_X - INERTIA_PROP_N) * np.array([0, rot[2], -rot[1]])
-        Mg = tau1 + tau2 + np.cross(P_P1_CG, T1) + np.cross(P_P2_CG, T2)
-        
-        Mb = Ma + Mg
-        drdt = np.linalg.inv(INERTIA) @ (Mb - np.cross(rot, INERTIA@rot))
+        Fb = T1 + F1 + T2 + F2
+        Mb = M1 + tau1 + np.cross(P_A1_CG, F1) + np.cross(P_P1_CG, T1) + M2 + tau2 + np.cross(P_A2_CG, F2) + np.cross(P_P2_CG, T2) 
 
-        # kinematic equations
         dpdt = vel
-        dqdt = 1/2 * quatmul(quat, np.concatenate([[0], rot]))
+        dqdt = 0.5 * quatmul(quat, vect2quat(rot))
+        dvdt = quatrot(quatinv(quat), Fb) / MASS + np.array([0, 0, G]) # exprimée dans le repere terrestre (ned)
+        drdt = np.linalg.inv(INERTIA) @ (Mb - hat(rot)@(INERTIA@rot))
 
         return np.concatenate([dpdt, dqdt, dvdt, drdt])
 
-    def equi(self, x):
-        vel = x[7:10]
-        vh = np.linalg.norm(vel[0:2])
-        vz = vel[2]
-        cap = np.arctan2(vel[1], vel[0])
-        return np.array([vh, vz, cap])
-
-    def trim(self, vh, vz):
+    def trim(self, target):
+        vh, vz = target
         x = np.zeros(13)
         x[7] = vh
         x[9] = vz
 
         def func(y):
             dx, de, theta = y
-            x[3:7] = np.array([np.cos(theta/2), 0, np.sin(theta/2), 0])
-            u = np.array([-dx, dx, de, de])
+            x[3:7] = eul2quat([0, theta, 0])
+            u = np.array([dx, dx, de, de])
             dq_dt = self.dyn(x, u, np.zeros(3))
-            return dq_dt[7], dq_dt[9], dq_dt[11] 
+            return dq_dt[7], dq_dt[9], dq_dt[11] # (v_north, vz, q)
 
         y0 = np.array([100, 0, 0])
         y = fsolve(func, y0)
         return y  # vh, vz, tangage
 
+    def trim_turn(self, target):
+        v, omega = target
+        vel = np.array([v, 0, 0])
+        rot = np.array([0, 0, omega])
+        v_dot = hat(rot)@vel
+        print(v_dot)
+        
+        x = np.zeros(13)
+        x[7:10] = vel
+
+        def func(y):
+            dx1, dx2, de1, de2, theta, phi = y
+            x[3:7] = eul2quat([phi, theta, 0])
+            x[10:13] = quatrot(x[3:7], rot)
+            u = np.array([dx1, dx2, de1, de2])
+            dq_dt = self.dyn(x, u, np.zeros(3)) 
+            dv = dq_dt[7:10] - v_dot
+            dr = dq_dt[10:13] 
+            return np.concatenate([dv, dr])
+
+        y0 = np.array([100, 100, 0, 0, 0, 0])
+        y = fsolve(func, y0)
+        return y
+
     def step(self, x, u, w, dt):
         func = lambda t, s: self.dyn(s, u, w)
         sol = solve_ivp(func, (0, dt), x, method='RK45', max_step=0.01)
         return sol.y.T[-1]
 
     def sim(self, t_span, x0, fctrl, fwind):
-        func = lambda t, s: self.dyn(s, fctrl(t, s, fwind(t, s)), fwind(t, s))
-        sol = solve_ivp(func, t_span, x0, method='RK45', max_step=0.01)
+        func = lambda t, s: self.dyn(s, fctrl(t, s), fwind(t, s))
+        def hit_ground(t, s): return -s[2]
+        hit_ground.terminal = True
+        hit_ground.direction = -1
+        sol = solve_ivp(func, t_span, x0, method='RK45', max_step=0.01, events=hit_ground)
         return sol
diff --git a/mavion/rotation.py b/mavion/rotation.py
index 5e5ea07dd985e50ded4ba4fde7d1436aea7698c4..3abefb3b010dc216f787d43652bd4ff57db694f9 100644
--- a/mavion/rotation.py
+++ b/mavion/rotation.py
@@ -1,4 +1,8 @@
 import numpy as np
+from scipy.linalg import expm, logm
+
+deg2rad = np.pi / 180
+rad2deg = 1 / deg2rad
 
 def hat(x):
     return np.array([[0, -x[2], x[1]], [x[2], 0, -x[0]], [-x[1], x[0], 0]])
@@ -6,70 +10,83 @@ def hat(x):
 def inv_hat(m):
     return np.array([m[2, 1], m[0, 2], m[1, 0]])
 
+
 # (a, n): a = angle, n = vecteur unitaire (axe de rotation)
+
 def quat2axang(q):
-    a = 2 * np.arccos(q[0])
-    n = q[1:4] / np.sqrt(1 - q[0] * q[0])
-    return a, n
+    q = q / sum(q*q)
+    mu = 2 * np.arccos(min(1, q[0]))
+    if (q[0] >= 1) :
+        n = np.zeros(3)
+    else :
+        n = q[1:4] / np.sqrt(1 - q[0]*q[0])
+    return (mu, n)
 
 def dcm2axang(R):
     t = np.trace(R)
-    n = 0.5 * inv_hat(R - R.T)
-    r = np.linalg.norm(n)
-    a = np.arctan2(r, (t - 1) / 2)
-    return a, n / r
-
+    mu = np.arccos((t - 1) / 2)
+    n = 0.5 * inv_hat(R.T - R) / np.sin(mu)
+    return (mu, n)
 
-# Quaternions
-def quatmat(p):
-    m = np.array(
-        [
-            [p[0], -p[1], -p[2], -p[3]],
-            [p[1],  p[0], -p[3],  p[2]], 
-            [p[2],  p[3],  p[0], -p[1]], 
-            [p[3], -p[2],  p[1],  p[0]]
-        ]
-    )
-    return m
 
-def quatmul(p, q):
-    return quatmat(p)@q
+def axangrot(ax, u):            # left hand rotation du vecteur u d'un angle mu selon l'axe n
+    mu, n = ax
+    v = (1 - np.cos(mu)) * n * np.dot(n, u) + u * np.cos(mu) - np.cross(n, u) * np.sin(mu)
+    return v
 
-def quatnorm(q): 
-    return np.dot(q, q)
 
-def quatconj(q):
-    return q * np.array([1, -1, -1, -1])
+# Quaternions
 
-def quatinv(q):
-    return quatconj(q) / quatnorm(q)
+def axang2quat(ax):
+    mu, n = ax
+    return np.concatenate([[np.cos(mu/2)], n * np.sin(mu/2)])
+    
+def eul2quat(a):
+    qx = np.array([np.cos(a[0]/2), np.sin(a[0]/2), 0, 0])       # roll angle : phi
+    qy = np.array([np.cos(a[1]/2), 0, np.sin(a[1]/2), 0])       # pitch angle : theta
+    qz = np.array([np.cos(a[2]/2), 0, 0, np.sin(a[2]/2)])       # yaw angle : psi
+    return quatmul(qz, quatmul(qy, qx))
 
 def vect2quat(u):
     return np.concatenate([[0], u])
 
-def quatrot(u, q):
-    v = quatmul(quatinv(q), quatmul(vect2quat(u), q))
+def quatmul(p, q):
+    m = np.array([[p[0], -p[1], -p[2], -p[3]],
+                  [p[1],  p[0], -p[3],  p[2]],
+                  [p[2],  p[3],  p[0], -p[1]], 
+                  [p[3], -p[2],  p[1],  p[0]]])
+    return m@q
+
+def quatinv(q):
+    return np.concatenate([[q[0]], -q[1:4]]) / sum(q*q)
+
+def quatrot(q, u):
+    v = quatmul(quatmul(quatinv(q), vect2quat(u)), q)
     return v[1:]
 
+def quatdist(q1, q2):
+    return 2 * np.arccos(min(1,abs(sum(q1*q2))))                 # donne une valeur d'angle entre 0 et PI
 
-def axang2quat(a, n):
-    return np.concatenate([[np.cos(a / 2)], n * np.sin(a / 2)])
-    
-def eul2quat(a):
-    qr = np.array([np.cos(a[0]/2), np.sin(a[0]/2), 0, 0])
-    qp = np.array([np.cos(a[1]/2), 0, np.sin(a[1]/2), 0])
-    qy = np.array([np.cos(a[2]/2), 0, 0, np.sin(a[2]/2)])
-    return quatmul(qy, quatmul(qp, qr))
+def quatdist2(q1, q2):
+    return 1 - abs(sum(q1*q2))                                   # donne une valeur d'angle entre 0 et 1
+
+def quaterr(q1, q2):
+    mu, n = quat2axang(quatmul(quatinv(q2), q1))
+    return mu*n
 
 
 # Matrices de Rotation (DCM)
-def axang2dcm(a, n):
-    dcm = (1 - np.cos(a)) * np.outer(n, n) + np.cos(a) * np.identity(3) - np.sin(a) * hat(n)
+
+def axang2dcm(ax):
+    mu, n = ax
+    dcm = (1 - np.cos(mu)) * np.outer(n, n) + np.cos(mu) * np.identity(3) - np.sin(mu) * hat(n)
     return dcm
 
 def quat2dcm(q):
+    q = q / quatnorm(q)
+    q0 = q[0]
     w = q[1:4]
-    dcm = (2 * np.outer(w, w) + (q[0]**2 - w @ w) * np.identity(3) - 2 * q[0] * hat(w)) / quatnorm(q)
+    dcm = (2 * np.outer(w, w) + (q0**2 - w @ w) * np.identity(3) - 2 * q0 * hat(w)) 
     return dcm
 
 def eul2dcm(a):
@@ -79,10 +96,37 @@ def eul2dcm(a):
     return Rx @ Ry @ Rz
 
 
+def dcmerr(R1, R2):
+    return inv_hat(logm(R2@R1.T))
+
+def dcmdist(R1, R2):
+    return np.linalg.norm(dcmerr(R1, R2))               # donne une valeur d'angle entre 0 et PI
+
+
+def dcmerr2(R, Rd):
+    return 0.5 * inv_hat(Rd@R.T - R@Rd.T)
+
+def dcmdist2(R, Rd):
+    return np.linalg.norm(np.identity(3) - Rd@R.T)     # donne une valeur ente 0 et 2V2
+
+def dcmdist4(R, Rd):
+    return  0.5 * np.trace(np.identity(3) - Rd@R.T)
+
+
+def dcmdist3(R, Rd):
+    dist = 2 - np.sqrt(1 + np.trace(Rd@R.T))
+    return dist
+
+def dcmerr3(R, Rd):
+    err = inv_hat(Rd@R.T - R@Rd.T) / np.sqrt(1 + np.trace(Rd@R.T))
+    return err
+
+
 # Angles d'Euler (phi, theta, psi) selon axes (x, y, z) : z en premier
+
 def quat2eul(q):
     phi = np.arctan2(2 * (q[0] * q[1] + q[2] * q[3]), q[0]**2 - q[1]**2 - q[2]**2 + q[3]**2)
-    theta = -np.arcsin(2 * (q[1] * q[3] - q[0] * q[2]))
+    theta = -np.arcsin(min(1, 2 * (q[1] * q[3] - q[0] * q[2])))
     psi = np.arctan2(2 * (q[0] * q[3] + q[1] * q[2]), q[0]**2 + q[1]**2 - q[2]**2 - q[3]**2)
     return np.array([phi, theta, psi])
     
@@ -91,3 +135,10 @@ def dcm2eul(R):
     theta = -np.arcsin(R[0, 2])
     psi = np.arctan2(R[0, 1], R[0, 0])
     return np.array([phi, theta, psi])
+
+
+def euldist(e1, e2):                                    # donne une valeur d'angle entre 0 et PI
+    diff = e1 - e2
+    d = np.fmin(np.abs(diff), 2*np.pi - np.abs(diff))
+    r = np.linalg.norm(d) / np.sqrt(3)
+    return r
diff --git a/mavion/sac_mavion_1.zip b/mavion/sac_mavion_1.zip
new file mode 100644
index 0000000000000000000000000000000000000000..4d25e94e558f54e45f722480de5d474d8983513c
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diff --git a/mavion/sac_mavion_2.zip b/mavion/sac_mavion_2.zip
new file mode 100644
index 0000000000000000000000000000000000000000..fa3aa447a44d1f0f7f3a5d2d041cb1c769016369
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diff --git a/mavion/train.py b/mavion/train.py
new file mode 100644
index 0000000000000000000000000000000000000000..a2a72cf5c5c76728bb19f195c62fce3b6517641a
--- /dev/null
+++ b/mavion/train.py
@@ -0,0 +1,24 @@
+import numpy as np
+from stable_baselines3 import SAC
+from mavion_env import MavionEnv
+from rotation import *
+
+
+if __name__ == "__main__":
+
+    pos_target = np.array([0, 0, -20])
+    eul_target = np.array([0, 90, 0])*deg2rad
+    quat_target = eul2quat(eul_target)
+    vel_target = np.zeros(3)
+    rot_target = np.zeros(3)
+
+    env = MavionEnv()
+    env.target = np.concatenate([pos_target, quat_target, np.zeros(3), np.zeros(3)])
+    print(env.target)
+    obs = env.reset()
+    print(env.state)
+    print(obs)
+
+    model = SAC("MlpPolicy", env, verbose=1)
+    model.learn(total_timesteps=20000, log_interval=10)
+    model.save("sac_mavion_2")
diff --git a/mavion/trim_turn.py b/mavion/trim_turn.py
new file mode 100644
index 0000000000000000000000000000000000000000..5def2e0d861f495ab5079fe185b780835f00bbb3
--- /dev/null
+++ b/mavion/trim_turn.py
@@ -0,0 +1,33 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from mavion_model import Mavion
+
+rad2deg = 180/np.pi
+
+
+if __name__ == "__main__":
+
+    mavion = Mavion()
+
+    vit = np.arange(0, 30, 1)
+    rot = np.arange(0, 1, 0.1)
+
+    for v in vit:
+        dx, de, theta = mavion.trim([v, 0])
+        theta = (theta + np.pi) % (2*np.pi) - np.pi
+        print(dx, de, theta*rad2deg)
+        print("------------------------------------")
+
+        for om in rot :
+            phi = np.arctan(v*om/9.81)
+            print(phi*rad2deg)
+
+            dx1, dx2, de1, de2, theta, phi = mavion.trim_turn([v, om])
+            print(dx1, dx2, de1, de2)
+            theta = (theta + np.pi) % (2*np.pi) - np.pi
+            phi = (phi + np.pi/2) % (np.pi) - np.pi/2
+            print(theta*rad2deg, phi*rad2deg)
+
+
+
+        
\ No newline at end of file
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diff --git a/mitmav/main.py b/mitmav/main.py
new file mode 100644
index 0000000000000000000000000000000000000000..e5d1dc517836bb18525b9f7ac41b0037fb7e472d
--- /dev/null
+++ b/mitmav/main.py
@@ -0,0 +1,79 @@
+import numpy as np
+from rotation import *
+import matplotlib.pyplot as plt
+from model import Mav
+
+def upulse(t, t0, tf):
+    u = 0 if (t<t0 or t>=tf) else 1
+    return u
+
+def ustep(t, t0) :
+    u = 0 if t<t0 else 1
+    return u
+
+def uramp(t, t0) :
+    u = 0 if t<t0 else (t - t0)
+    return u
+
+if __name__ == "__main__":
+    uav = Mav()
+
+    vh = 0
+    vz = 0
+    cap = 0
+    omega = 0
+
+    dx, de, theta = uav.trim(vh, vz)
+    theta = (theta + np.pi) % (2*np.pi) - np.pi
+    print(dx, de, theta*57.3)
+
+    pos = np.array([0, 0, -10])
+    ang = np.array([0, theta, cap])
+    vel = np.array([vh * np.cos(cap), vh * np.sin(cap), vz])
+    rot = np.array([0, 0, 0])
+    quat = eul2quat(ang)
+
+    # x0 = np.concatenate([pos, quat, vel, rot])
+    x0 = np.concatenate([pos, quat, vel, rot])
+    u0 = np.array([-dx, dx, de, de])
+
+    def ctl(t, s):
+        ddx = (upulse(t, 5, 6) - upulse(t, 6, 7))*dx*0.0
+        qt = np.array([1/np.sqrt(2), 0, 1/np.sqrt(2), 0])
+        q = s[3:7]
+        dde = 0.0 * (q - qt)[2]
+        u = u0 + np.array([ddx, ddx, dde, dde])
+        return u
+
+    sim = uav.sim((0, 60), x0, ctl)
+
+    fig, axs = plt.subplots(2, 2)
+
+    ax = axs[0][0]
+    ax.plot(sim.t, sim.y[0:3].T, label=('x','y','z'))
+    ax.legend()
+    ax.grid()
+    ax.set_title(label='positions')
+
+    ax = axs[1][0]
+    quat = sim.y[3:7].T
+    # ax.plot(sim.t, quat, label=('q0', 'q1', 'q2', 'q3'))
+    # ax.set_title(label='quaternion')
+    eul = np.apply_along_axis(quat2eul, 1, quat) * rad2deg
+    ax.plot(sim.t, eul, label=('phi', 'theta', 'psi'))
+    ax.set_title(label='euler angles')
+    ax.legend()
+    ax.grid()
+
+    ax = axs[0][1]
+    ax.plot(sim.t, sim.y[7:10].T, label=('u','v','w'))
+    ax.legend()
+    ax.grid()
+    ax.set_title(label='vitesses')
+
+    ax = axs[1][1]
+    ax.plot(sim.t, sim.y[10:13].T, label=('p','q','r'))
+    ax.legend()
+    ax.grid()
+    ax.set_title(label='rotations')
+    plt.show()
diff --git a/mitmav/mav.yaml b/mitmav/mav.yaml
new file mode 100644
index 0000000000000000000000000000000000000000..8efe7addddab46630311bfbbb7e1b82513223f1c
--- /dev/null
+++ b/mitmav/mav.yaml
@@ -0,0 +1,15 @@
+---
+NAME : "MIT_MAV"
+
+WINGSPAN : 0.55
+ASPECT_RATIO : 4.3
+CHORD : 0.125
+MASS :  0.68
+INERTIA : [0.0036, 0.0036, 0.0072]
+PROP_DIAM : 0.13
+MAX_ROTOR_SPD : 2500  # rad/s
+MAX_FLAP_DEF :  1     # rad
+AERO : [0.29, 0.0, 2.23, 0, 0.18, 1.25, -0.025] # CL_V(kg/m) CD_V(kg/m) CL_T CD_T CLdelta_V(kg/m) CLdelta_T Cmu_T(m)
+PROP : [1.6e-6, 1.78e-8] # CT(kg.m/rad^2) CN(kg.m^2/rad^2)
+PACG : [-0.02, 0.12, 0]
+PPCG : [0.03, 0.12, 0]
diff --git a/mitmav/model.py b/mitmav/model.py
new file mode 100644
index 0000000000000000000000000000000000000000..07432182d925c9a03584be5e8049dd0f95606678
--- /dev/null
+++ b/mitmav/model.py
@@ -0,0 +1,122 @@
+import numpy as np
+from rotation import *
+from scipy.optimize import fsolve
+from scipy.integrate import solve_ivp
+import yaml
+
+class Mav:
+
+    def __init__(self, file="mav.yaml"):
+        stream = open(file, "r")
+        data = yaml.load(stream, Loader=yaml.Loader)
+
+        self.NAME = data['NAME']
+        self.MASS = data['MASS']
+        self.INERTIA = data["INERTIA"]
+        self.WINGSPAN = data['WINGSPAN']
+        self.AERO = data["AERO"]
+        self.PACG = data["PACG"]
+        self.a0 = 0
+        self.PROP = data["PROP"]
+        self.PPCG = data["PPCG"]
+        self.aT = -5*np.pi/180
+
+
+    def motor_thrust(self, dx):
+        CT, CN  = self.PROP
+        # prop forces computation
+        T = CT * dx**2
+        # prop moments computation
+        N = -np.sign(dx) * CN * dx**2
+        return T, N
+
+    def force(self, vel, u):
+        # coeff AERO : CL_V(kg/m) CD_V(kg/m) CL_T CD_T CLdelta_V(kg/m) CLdelta_T Cmu_T(m)
+        CL_V, CD_V, CL_T, CD_T, CLdelta_V, CLdelta_T, Cmu_T = self.AERO
+
+        a_bar = self.a0 + self.aT
+        V = np.linalg.norm(vel)
+        dx1, dx2 = u[0:2]
+        de1, de2 = u[2:4]
+
+        # Force computation
+        # thrust contribution
+        T1, N1 = self.motor_thrust(dx1)
+        T2, N2 = self.motor_thrust(dx2)
+        f_T1 = np.array([np.cos(a_bar)*(1 - CD_T)*T1, 0, np.sin(a_bar)*(CL_T - 1)*T1]) 
+        f_T2 = np.array([np.cos(a_bar)*(1 - CD_T)*T2, 0, np.sin(a_bar)*(CL_T - 1)*T2])
+        f_thrust =f_T1 + f_T2
+        # elevon contribution
+        f_de1 = -np.array([0, 0, (np.cos(a_bar)*CLdelta_T*T1 + CLdelta_V*V*vel[0])*de1])
+        f_de2 = -np.array([0, 0, (np.cos(a_bar)*CLdelta_T*T2 + CLdelta_V*V*vel[0])*de2])
+        f_delta = f_de1 + f_de2
+        # wing contribution
+        f_wing = -np.array([CD_V*V*vel[0], 0, CL_V*V*vel[2]])
+        f_tot = f_thrust + f_delta + f_wing
+
+        # Moment computation
+        # torque contribution
+        m_torque = np.array([np.cos(self.aT), 0, -np.sin(self.aT)]) * (N1 + N2)
+        # thrust/airfoil contribution
+        R = np.array([[np.cos(self.a0), 0 , -np.sin(self.a0)], [0, 1, 0], [np.sin(self.a0), 0 , np.cos(self.a0)]])
+        M = R@(f_T1 - f_T2)
+        m_wing = np.array([-self.PPCG[1] * M[2], Cmu_T * (T1 + T2), self.PPCG[1] * M[0]])
+
+        # elevon contribution
+        m_delta = np.array([self.PACG[1] * np.cos(self.a0) * (f_de2[2] - f_de1[2]), 
+                            self.PACG[0] * (f_de1[2] + f_de2[2]),
+                            self.PACG[1] * np.sin(self.a0) * (f_de2[2] - f_de1[2])])
+
+        m_tot = m_torque + m_wing + m_delta
+
+        return f_tot, m_tot
+
+
+    def dyn(self, x, u):
+        G = 9.81
+        MASS = self.MASS
+        INERTIA = np.diag(self.INERTIA)
+
+        # state demultiplexing
+        quat = x[3:7]
+        vel = x[7:10]
+        rot = x[10:13]
+
+        Fb, Mb = self.force(vel, u)
+        dvdt = np.array([0, 0, G]) + 1/MASS * quatrot(Fb, quatinv(quat))
+        drdt = np.linalg.inv(INERTIA) @ (Mb - np.cross(rot, INERTIA@rot))
+
+        # kinematic equations
+        dpdt = vel
+        dqdt = 1/2 * quatmul(quat, np.concatenate([[0], rot]))
+
+        return np.concatenate([dpdt, dqdt, dvdt, drdt])
+
+    def trim(self, vh, vz):
+        x = np.zeros(13)
+        x[7] = vh
+        x[9] = vz
+
+        def func(y):
+            dx, de, theta = y
+            x[3:7] = np.array([np.cos(theta/2), 0, np.sin(theta/2), 0])
+            u = np.array([-dx, dx, de, de])
+            dq_dt = self.dyn(x, u)
+            return dq_dt[7], dq_dt[9], dq_dt[11] 
+
+        y0 = np.array([1000, 0, 0])
+        y = fsolve(func, y0)
+        return y  # vh, vz, tangage
+
+    def step(self, x, u, dt):
+        func = lambda t, s: self.dyn(s, u)
+        sol = solve_ivp(func, (0, dt), x, method='RK45', max_step=0.01)
+        return sol.y.T[-1]
+
+    def sim(self, t_span, x0, fctrl):
+        func = lambda t, s: self.dyn(s, fctrl(t, s))
+        def hit_ground(t, s): return -s[2]
+        hit_ground.terminal = True
+        hit_ground.direction = -1
+        sol = solve_ivp(func, t_span, x0, method='RK45', max_step=0.01, events=hit_ground)
+        return sol
diff --git a/rotations/__pycache__/rotation.cpython-311.pyc b/rotations/__pycache__/rotation.cpython-311.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..2090f23909c568355dc6146ec87126ac0c5a4398
Binary files /dev/null and b/rotations/__pycache__/rotation.cpython-311.pyc differ
diff --git a/rotations/quaternion.ipynb b/rotations/quaternion.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..e507316de09ea0ace61fac55cbad1b41a53d6670
--- /dev/null
+++ b/rotations/quaternion.ipynb
@@ -0,0 +1,92 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from rotation import *"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "49.032470775389854\n",
+      "[ 18.95712447 -44.53259522   7.85229806]\n",
+      "49.03247077538984\n",
+      "[ 18.95712447 -44.53259522   7.85229806]\n"
+     ]
+    }
+   ],
+   "source": [
+    "eul_target = [0, 90, 180]\n",
+    "eul = [20, 45, 180]\n",
+    "\n",
+    "ang_target = np.array(eul_target) * deg2rad \n",
+    "ang = np.array(eul) * deg2rad \n",
+    "\n",
+    "quat_target = eul2quat(ang_target)\n",
+    "quat = eul2quat(ang)\n",
+    "print(quatdist(quat, quat_target) * rad2deg)\n",
+    "print(quaterr(quat, quat_target) * rad2deg)\n",
+    "\n",
+    "R_target = eul2dcm(ang_target)\n",
+    "R = eul2dcm(ang)\n",
+    "print(dcmdist(R, R_target) * rad2deg)\n",
+    "print(dcmerr(R, R_target) * rad2deg)\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(5, 5, 5)"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "u = np.array([0,1,2])\n",
+    "\n",
+    "u@u, sum(u*u), np.inner(u,u)\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "base",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/rotations/rotation.py b/rotations/rotation.py
new file mode 100644
index 0000000000000000000000000000000000000000..e1975ce35b9a490177956bacc71a42c282756cf1
--- /dev/null
+++ b/rotations/rotation.py
@@ -0,0 +1,152 @@
+import numpy as np
+from scipy.linalg import expm, logm
+
+deg2rad = np.pi/180
+rad2deg = 1 / deg2rad
+
+def hat(x):
+    return np.array([[0, -x[2], x[1]], [x[2], 0, -x[0]], [-x[1], x[0], 0]])
+
+def inv_hat(m):
+    return np.array([m[2, 1], m[0, 2], m[1, 0]])
+
+
+# (a, n): a = angle, n = vecteur unitaire (axe de rotation)
+
+def quat2axang(q):
+    q = q / sum(q*q)
+    mu = 2 * np.arccos(min(1, q[0]))
+    if (q[0] >= 1) :
+        n = np.zeros(3)
+    else :
+        n = q[1:4] / np.sqrt(1 - q[0]*q[0])
+    return (mu, n)
+
+def dcm2axang(R):
+    t = np.trace(R)
+    mu = np.arccos((t - 1) / 2)
+    n = 0.5 * inv_hat(R.T - R) / np.sin(mu)
+    return (mu, n)
+
+
+def axangrot(ax, u):            # left hand rotation du vecteur u d'un angle mu selon l'axe n
+    mu, n = ax
+    v = (1 - np.cos(mu)) * n * np.dot(n, u) + u * np.cos(mu) - np.cross(n, u) * np.sin(mu)
+    return v
+
+
+# Quaternions
+
+def axang2quat(ax):
+    mu, n = ax
+    return np.concatenate([[np.cos(mu / 2)], n * np.sin(mu / 2)])
+    
+def eul2quat(a):
+    qx = np.array([np.cos(a[0]/2), np.sin(a[0]/2), 0, 0])
+    qy = np.array([np.cos(a[1]/2), 0, np.sin(a[1]/2), 0])
+    qz = np.array([np.cos(a[2]/2), 0, 0, np.sin(a[2]/2)])
+    return quatmul(qz, quatmul(qy, qx))
+
+def vect2quat(u):
+    return np.concatenate([[0], u])
+
+
+def quatmat(p):
+    m = np.array(
+        [
+            [p[0], -p[1], -p[2], -p[3]],
+            [p[1],  p[0], -p[3],  p[2]], 
+            [p[2],  p[3],  p[0], -p[1]], 
+            [p[3], -p[2],  p[1],  p[0]]
+        ]
+    )
+    return m
+
+def quatmul(p, q):
+    return quatmat(p)@q
+
+def quatinv(q):
+    return np.concatenate([[q[0]], -q[1:4]]) / sum(q*q)
+
+def quatrot(q, u):
+    v = quatmul(quatmul(quatinv(q), vect2quat(u)), q)
+    return v[1:]
+
+def quatdist(q1, q2):
+    return 2 * np.arccos(min(1,abs(sum(q1*q2))))                 # donne une valeur d'angle entre 0 et PI
+
+def quatdist2(q1, q2):
+    return 1 - abs(sum(q1*q2))                                   # donne une valeur d'angle entre 0 et 1
+
+def quaterr(q1, q2):
+    mu, n = quat2axang(quatmul(quatinv(q2), q1))
+    return mu*n
+
+
+# Matrices de Rotation (DCM)
+
+def axang2dcm(ax):
+    mu, n = ax
+    dcm = (1 - np.cos(mu)) * np.outer(n, n) + np.cos(mu) * np.identity(3) - np.sin(mu) * hat(n)
+    return dcm
+
+def quat2dcm(q):
+    q = q / quatnorm(q)
+    q0 = q[0]
+    w = q[1:4]
+    dcm = (2 * np.outer(w, w) + (q0**2 - w @ w) * np.identity(3) - 2 * q0 * hat(w)) 
+    return dcm
+
+def eul2dcm(a):
+    Rx = np.array([[1, 0, 0], [0, np.cos(a[0]), np.sin(a[0])], [0, -np.sin(a[0]), np.cos(a[0])]])
+    Ry = np.array([[np.cos(a[1]), 0, -np.sin(a[1])], [0, 1, 0], [np.sin(a[1]), 0, np.cos(a[1])]])
+    Rz = np.array([[np.cos(a[2]), np.sin(a[2]), 0], [-np.sin(a[2]), np.cos(a[2]), 0], [0, 0, 1]])               
+    return Rx @ Ry @ Rz
+
+
+def dcmerr(R1, R2):
+    return inv_hat(logm(R2@R1.T))
+
+def dcmdist(R1, R2):
+    return np.linalg.norm(dcmerr(R1, R2))               # donne une valeur d'angle entre 0 et PI
+
+
+def dcmerr2(R, Rd):
+    return 0.5 * inv_hat(Rd@R.T - R@Rd.T)
+
+def dcmdist2(R, Rd):
+    return np.linalg.norm(np.identity(3) - Rd@R.T)     # donne une valeur ente 0 et 2V2
+
+def dcmdist4(R, Rd):
+    return  0.5 * np.trace(np.identity(3) - Rd@R.T)
+
+
+def dcmdist3(R, Rd):
+    dist = 2 - np.sqrt(1 + np.trace(Rd@R.T))
+    return dist
+
+def dcmerr3(R, Rd):
+    err = inv_hat(Rd@R.T - R@Rd.T) / np.sqrt(1 + np.trace(Rd@R.T))
+    return err
+
+
+# Angles d'Euler (phi, theta, psi) selon axes (x, y, z) : z en premier
+
+def quat2eul(q):
+    phi = np.arctan2(2 * (q[0] * q[1] + q[2] * q[3]), q[0]**2 - q[1]**2 - q[2]**2 + q[3]**2)
+    theta = -np.arcsin(2 * (q[1] * q[3] - q[0] * q[2]))
+    psi = np.arctan2(2 * (q[0] * q[3] + q[1] * q[2]), q[0]**2 + q[1]**2 - q[2]**2 - q[3]**2)
+    return np.array([phi, theta, psi])
+    
+def dcm2eul(R):
+    phi = np.arctan2(R[1, 2], R[2, 2])
+    theta = -np.arcsin(R[0, 2])
+    psi = np.arctan2(R[0, 1], R[0, 0])
+    return np.array([phi, theta, psi])
+
+
+def euldist(e1, e2):                                    # donne une valeur d'angle entre 0 et PI
+    diff = e1 - e2
+    d = np.fmin(np.abs(diff), 2*np.pi - np.abs(diff))
+    r = np.linalg.norm(d) / np.sqrt(3)
+    return r