release grid based_sweep_coverage_path_planner.py

Author: AtsushiSakai

PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py

@@ -13,14 +13,17 @@
 import scipy.linalg as la
 
 sys.path.append("../../PathPlanning/CubicSpline/")
-import cubic_spline_planner
 
+try:
+    import cubic_spline_planner
+except ImportError:
+    raise
 
-# LQR parameter
-Q = np.eye(5)
-R = np.eye(2)
+# === Parameters =====
 
-# parameters
+# LQR parameter
+lqr_Q = np.eye(5)
+lqr_R = np.eye(2)
 dt = 0.1  # time tick[s]
 L = 0.5  # Wheel base of the vehicle [m]
 max_steer = np.deg2rad(45.0)  # maximum steering angle[rad]
@@ -56,23 +59,23 @@ def pi_2_pi(angle):
     return (angle + math.pi) % (2 * math.pi) - math.pi
 
 
-def solve_DARE(A, B, Q, R):
+def solve_dare(A, B, Q, R):
     """
     solve a discrete time_Algebraic Riccati equation (DARE)
     """
-    X = Q
-    Xn = Q
-    maxiter = 150
+    x = Q
+    x_next = Q
+    max_iter = 150
     eps = 0.01
 
-    for i in range(maxiter):
-        Xn = A.T @ X @ A - A.T @ X @ B @ \
-            la.inv(R + B.T @ X @ B) @ B.T @ X @ A + Q
-        if (abs(Xn - X)).max() < eps:
+    for i in range(max_iter):
+        x_next = A.T @ x @ A - A.T @ x @ B @ \
+                 la.inv(R + B.T @ x @ B) @ B.T @ x @ A + Q
+        if (abs(x_next - x)).max() < eps:
             break
-        X = Xn
+        x = x_next
 
-    return Xn
+    return x_next
 
 
 def dlqr(A, B, Q, R):
@@ -83,17 +86,17 @@ def dlqr(A, B, Q, R):
     """
 
     # first, try to solve the ricatti equation
-    X = solve_DARE(A, B, Q, R)
+    X = solve_dare(A, B, Q, R)
 
     # compute the LQR gain
     K = la.inv(B.T @ X @ B + R) @ (B.T @ X @ A)
 
-    eigs = la.eig(A - B @ K)
+    eig_result = la.eig(A - B @ K)
 
-    return K, X, eigs[0]
+    return K, X, eig_result[0]
 
 
-def lqr_steering_control(state, cx, cy, cyaw, ck, pe, pth_e, sp):
+def lqr_speed_steering_control(state, cx, cy, cyaw, ck, pe, pth_e, sp, Q, R):
     ind, e = calc_nearest_index(state, cx, cy, cyaw)
 
     tv = sp[ind]
@@ -102,42 +105,59 @@ def lqr_steering_control(state, cx, cy, cyaw, ck, pe, pth_e, sp):
     v = state.v
     th_e = pi_2_pi(state.yaw - cyaw[ind])
 
+    # A = [1.0, dt, 0.0, 0.0, 0.0
+    #      0.0, 0.0, v, 0.0, 0.0]
+    #      0.0, 0.0, 1.0, dt, 0.0]
+    #      0.0, 0.0, 0.0, 0.0, 0.0]
+    #      0.0, 0.0, 0.0, 0.0, 1.0]
     A = np.zeros((5, 5))
     A[0, 0] = 1.0
     A[0, 1] = dt
     A[1, 2] = v
     A[2, 2] = 1.0
     A[2, 3] = dt
     A[4, 4] = 1.0
-    # print(A)
 
+    # B = [0.0, 0.0
+    #     0.0, 0.0
+    #     0.0, 0.0
+    #     v/L, 0.0
+    #     0.0, dt]
     B = np.zeros((5, 2))
     B[3, 0] = v / L
     B[4, 1] = dt
 
     K, _, _ = dlqr(A, B, Q, R)
 
+    # state vector
+    # x = [e, dot_e, th_e, dot_th_e, delta_v]
+    # e: lateral distance to the path
+    # dot_e: derivative of e
+    # th_e: angle difference to the path
+    # dot_th_e: derivative of th_e
+    # delta_v: difference between current speed and target speed
     x = np.zeros((5, 1))
-
     x[0, 0] = e
     x[1, 0] = (e - pe) / dt
     x[2, 0] = th_e
     x[3, 0] = (th_e - pth_e) / dt
     x[4, 0] = v - tv
 
+    # input vector
+    # u = [delta, accel]
+    # delta: steering angle
+    # accel: acceleration
     ustar = -K @ x
 
     # calc steering input
-
-    ff = math.atan2(L * k, 1)
-    fb = pi_2_pi(ustar[0, 0])
+    ff = math.atan2(L * k, 1)  # feedforward steering angle
+    fb = pi_2_pi(ustar[0, 0])  # feedback steering angle
+    delta = ff + fb
 
     # calc accel input
-    ai = ustar[1, 0]
-
-    delta = ff + fb
+    accel = ustar[1, 0]
 
-    return delta, ind, e, th_e, ai
+    return delta, ind, e, th_e, accel
 
 
 def calc_nearest_index(state, cx, cy, cyaw):
@@ -162,7 +182,7 @@ def calc_nearest_index(state, cx, cy, cyaw):
     return ind, mind
 
 
-def closed_loop_prediction(cx, cy, cyaw, ck, speed_profile, goal):
+def do_simulation(cx, cy, cyaw, ck, speed_profile, goal):
     T = 500.0  # max simulation time
     goal_dis = 0.3
     stop_speed = 0.05
@@ -179,8 +199,8 @@ def closed_loop_prediction(cx, cy, cyaw, ck, speed_profile, goal):
     e, e_th = 0.0, 0.0
 
     while T >= time:
-        dl, target_ind, e, e_th, ai = lqr_steering_control(
-            state, cx, cy, cyaw, ck, e, e_th, speed_profile)
+        dl, target_ind, e, e_th, ai = lqr_speed_steering_control(
+            state, cx, cy, cyaw, ck, e, e_th, speed_profile, lqr_Q, lqr_R)
 
         state = update(state, ai, dl)
 
@@ -216,13 +236,13 @@ def closed_loop_prediction(cx, cy, cyaw, ck, speed_profile, goal):
     return t, x, y, yaw, v
 
 
-def calc_speed_profile(cx, cy, cyaw, target_speed):
-    speed_profile = [target_speed] * len(cx)
+def calc_speed_profile(cyaw, target_speed):
+    speed_profile = [target_speed] * len(cyaw)
 
     direction = 1.0
 
     # Set stop point
-    for i in range(len(cx) - 1):
+    for i in range(len(cyaw) - 1):
         dyaw = abs(cyaw[i + 1] - cyaw[i])
         switch = math.pi / 4.0 <= dyaw < math.pi / 2.0
 
@@ -256,9 +276,9 @@ def main():
         ax, ay, ds=0.1)
     target_speed = 10.0 / 3.6  # simulation parameter km/h -> m/s
 
-    sp = calc_speed_profile(cx, cy, cyaw, target_speed)
+    sp = calc_speed_profile(cyaw, target_speed)
 
-    t, x, y, yaw, v = closed_loop_prediction(cx, cy, cyaw, ck, sp, goal)
+    t, x, y, yaw, v = do_simulation(cx, cy, cyaw, ck, sp, goal)
 
     if show_animation:  # pragma: no cover
         plt.close()