control part

Astar.py

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+import sys
+import matplotlib.pyplot as plt
+import numpy as np
+import scipy.interpolate
+import math
+import random
+import time
+import heapq  # https://docs.python.org/3/library/heapq.html
+
+
+def load_poses(pose_gt_file) :
+    pose_gt = np.loadtxt(pose_gt_file, delimiter = ",")
+
+    return pose_gt
+
+
+def plot_position(pose_gt):
+    # NED (North, East, Down)
+    x = pose_gt[:, 1]
+    y = pose_gt[:, 2]
+    z = pose_gt[:, 3]
+
+    plt.figure()
+    plt.scatter(y, x, 1, c=-z, linewidth=2)  # Note Z points down
+    plt.axis('equal')
+    plt.title('Ground Truth Position of Nodes in SLAM Graph')
+    plt.xlabel('East (m)')
+    plt.ylabel('North (m)')
+    plt.colorbar()
+
+    plt.show()
+
+    return
+
+
+class PriorityQueue:
+    def __init__(self):
+        self.elements = []
+
+    def empty(self):
+        return len(self.elements) == 0
+
+    def put(self, item, priority):
+        heapq.heappush(self.elements, (priority, item))
+
+    def get(self):
+        return heapq.heappop(self.elements)[1]
+
+
+def find_path(cur_node, parent_idx, start_idx):
+    next_idx = cur_node
+    path = [next_idx]
+
+    while next_idx != start_idx:
+        next_idx = parent_idx[next_idx]
+        path.append(next_idx)
+
+    return path[::-1]
+
+
+def Astar(start_idx, goal_idx, poses, k=20):
+    visit_queue = PriorityQueue()
+    visited_flag, queueed_flag = np.zeros(poses.shape[0]), np.zeros(poses.shape[0])
+    g_score, h_score = np.full(poses.shape[0], np.inf), np.full(poses.shape[0], np.inf)
+    parent_idx = np.zeros(poses.shape[0], dtype='int')
+
+    test_tree = scipy.spatial.KDTree(poses)
+
+    # initialize
+    goal = poses[goal_idx]
+    g_score[start_idx] = 0
+    visit_queue.put(start_idx, np.inf)
+    queueed_flag[start_idx] = 1
+
+    while not visit_queue.empty():
+        cur_node = visit_queue.get()
+        visited_flag[cur_node] = 1
+
+        if cur_node == goal_idx:
+            print('find optimal path from {} to {}'.format(start_idx, goal_idx))
+            break
+
+        # find neighbours
+        neighbors = test_tree.query(poses[cur_node], k=k)
+
+        for nb_cur_dist, nb_idx in zip(neighbors[0][1:], neighbors[1][1:]):
+            if visited_flag[nb_idx] == 1:
+                continue
+
+            temp_dist = g_score[cur_node] + np.linalg.norm(poses[cur_node] - poses[nb_idx])
+            # temp_dist = g_score[cur_node] + nb_cur_dist     ## this not work
+            if g_score[nb_idx] > temp_dist:
+                g_score[nb_idx] = temp_dist
+                parent_idx[nb_idx] = cur_node
+                f_score = g_score[nb_idx] + np.linalg.norm(poses[nb_idx] - goal)
+
+            # put into queen
+            if queueed_flag[nb_idx] == 0:
+                visit_queue.put(nb_idx, f_score)
+                queueed_flag[nb_idx] = 1
+
+    if cur_node != goal_idx:
+        print('find closest path from {} to {}'.format(start_idx, cur_node))
+    return cur_node, parent_idx

mpc_along_trajectory.py

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+from mpc_func import *
+from Astar import *
+
+poses = load_poses('pose_gt.csv')
+sparseness = 100
+print(poses.shape[0]/sparseness)
+# plot_position(poses[1::sparseness])
+sparse_poses = poses[1::sparseness, 1:3]
+
+start_idx = np.random.randint(sparse_poses.shape[0])
+goal_idx = np.random.randint(sparse_poses.shape[0])
+
+# start_idx = 148
+# goal_idx = 6976
+# start_time = time.time()
+cur_node, parent_idx = Astar(start_idx, goal_idx, sparse_poses, k=20)
+path = find_path(cur_node, parent_idx, start_idx)
+# print(time.time() - start_time)
+print(start_idx, goal_idx)
+print(path)
+# print(len(path))
+# print(total_dist(path))
+
+plt.figure(figsize=(10,10))
+plt.scatter(sparse_poses[:,0], sparse_poses[:,1], s=8)
+plt.scatter(sparse_poses[path,0], sparse_poses[path,1], c='y', s=80)
+plt.scatter(sparse_poses[start_idx,0], sparse_poses[start_idx,1], marker='o', c='g', s=200, label='start')
+plt.scatter(sparse_poses[goal_idx,0], sparse_poses[goal_idx,1], marker='*', c='r', s=200, label='goal')
+plt.legend()
+plt.show()
+
+
+# along trajectory
+path_poses = sparse_poses[path, :]
+
+dt = 1  # [s] discrete time
+lr = 1.0  # [m]
+T = 6  # number of horizon
+max_speed = 5
+min_speed = -5
+
+speed_now = 1
+theta = -1.5
+
+for interval in range(len(path)//T):
+  short_path_poses = path_poses[interval*T:(interval+1)*T,:]
+  u, next_x, xstar, ustar = path_poses_to_input(path_poses, speed_now, theta,
+                                                dt, lr, T, max_speed, min_speed)
+  speed_now = xstar.value[2,-1]
+  theta = xstar.value[3,-1]
+  print(ustar.value)

mpc_func.py

@@ -0,0 +1,126 @@
+import cvxpy
+import numpy as np
+from cvxpy import *
+import matplotlib.pyplot as plt
+from math import *
+import time
+
+
+def LinearizeCarModel(xb, u, dt, lr):
+    x = xb[0]
+    y = xb[1]
+    v = xb[2]
+    theta = xb[3]
+
+    a = u[0]
+    beta = u[1]
+
+    t1 = -dt * v * sin(theta + beta)
+    t2 = dt * v * cos(theta + beta)
+
+    A = np.eye(xb.shape[0])
+    A[0, 2] = dt * cos(theta + beta)
+    A[1, 2] = dt * sin(theta + beta)
+    A[3, 2] = dt * sin(beta) / lr
+    #A[0, 3] = t1
+    #A[1, 3] = t2
+
+    B = np.zeros((xb.shape[0], u.shape[0]))
+    B[2, 0] = dt
+    B[0, 1] = t1
+    B[1, 1] = t2
+    B[3, 1] = dt * v * cos(beta) / lr
+
+    tm = np.zeros((4, 1))
+    tm[0, 0] = v * cos(theta + beta) * dt
+    tm[1, 0] = v * sin(theta + beta) * dt
+    tm[2, 0] = a * dt
+    tm[3, 0] = v / lr * sin(beta) * dt
+    C = xb + tm
+    C = C - A @ xb - B @ u
+
+    # print(A, B, C)
+
+    return A, B, C
+
+
+def NonlinearModel(x, u, dt, lr):
+    print(x.value)
+    x[0] = x[0] + x[2] * cos(x[3] + u[1]) * dt
+    x[1] = x[1] + x[2] * sin(x[3] + u[1]) * dt
+    x[2] = x[2] + u[0] * dt
+    x[3] = x[3] + x[2] / lr * sin(u[1]) * dt
+
+    return x
+
+
+def CalcInput(A, B, C, x, u, T, max_speed, min_speed, path_poses):
+
+    x_0 = x[:]
+    x = Variable((x.shape[0], T + 1))
+    u = Variable((u.shape[0], T))
+
+    # MPC controller
+    states = []
+    constr = [x[:, 0] == (x_0.T)[0]]#, x[2, T] == 0.0]
+    for t in range(1,T):
+        #pdb.set_trace()
+        
+        constr += [x[:, t + 1] == A * x[:, t] + B * u[:, t] +(C.T)[0]]
+        constr += [abs(u[:, t]) <= 5]
+        constr += [x[2, t + 1] <= max_speed]
+        constr += [x[2, t + 1] >= min_speed]
+        #  cost = sum_squares(u[:,t])
+        cost = sum_squares(abs(x[0, t] - path_poses[t][0])) * 1 * (10-2*t)
+        cost += sum_squares(abs(x[1, t] - path_poses[t][1])) * 1 * (10-2*t)
+        cost += sum_squares(abs(u[1, t])) * 10 * (t+1)
+        if t == T - 1:
+            cost += (x[0, t + 1] - path_poses[t][0]) ** 2 * 100.0
+            cost += (x[1, t + 1] - path_poses[t][1]) ** 2 * 100.0
+
+        states.append(Problem(Minimize(cost), constr))
+
+    prob = sum(states)
+    #pdb.set_trace()
+    #prob.constraints += [x[:, 0] == (x_0.T)[0]]#, x[2, T] == 0.0]
+
+    start = time.time()
+    #  result=prob.solve(verbose=True)
+    result = prob.solve()
+    elapsed_time = time.time() - start
+    # print("calc time:{0}".format(elapsed_time) + "[sec]")
+    # print(prob.value)
+
+    if prob.status != OPTIMAL:
+        print("Cannot calc opt")
+
+    #  print(prob.status)
+    return u, x, prob.value
+
+
+def GetListFromMatrix(x):
+    return np.array(x).flatten().tolist()
+
+
+def path_poses_to_input(path_poses, speed_now, theta, dt, lr, T, max_speed, min_speed):
+    x0 = np.array([[path_poses[0][0], path_poses[0][1], speed_now, theta]]).T  # [x,y,v theta]
+    u = np.array([[0.0, 0.0]]).T  # [a,beta]
+
+    x = x0
+
+    A, B, C = LinearizeCarModel(x, u, dt, lr)
+    ustar, xstar, cost = CalcInput(A, B, C, x, u, T, max_speed, min_speed, path_poses)
+
+    u[0, 0] = GetListFromMatrix(ustar.value[0, :])[0]
+    u[1, 0] = float(ustar[1, 0].value)
+
+    x = A @ x + B @ u
+
+    return u, x, xstar, ustar
+
+
+def load_poses(pose_gt_file) :
+    pose_gt = np.loadtxt(pose_gt_file, delimiter = ",")
+
+    return pose_gt
+

one_round_demo.py

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+from mpc_func import *
+
+poses = load_poses('pose_gt.csv')
+sparseness = 100
+sparse_poses = poses[1::sparseness, 1:3]
+
+path = [148, 150, 151, 153, 154, 156, 158, 160, 162, 163]
+
+
+dt = 1  # [s] discrete time
+lr = 1.0  # [m]
+T = 6  # number of horizon
+max_speed = 5
+min_speed = -5
+
+speed_now = 1
+theta = -1.5
+
+path_poses = sparse_poses[path[:T+1], :]
+u, next_x, xstar, ustar = path_poses_to_input(path_poses, speed_now, theta,
+                                              dt, lr, T, max_speed, min_speed)
+
+
+# plot the result
+plt.figure(figsize=(10,10))
+plt.subplot(3, 1, 1)
+plt.plot(path_poses[0][0], path_poses[0][1], 'xb', label='current pose')
+plt.plot(next_x[0], next_x[1], 'xr', label='next pose given current control output')
+plt.plot(GetListFromMatrix(xstar.value[0, :]), GetListFromMatrix(
+    xstar.value[1, :]), '-.', label='estimated trajectory given control outputs')
+plt.plot(path_poses[:T,0], path_poses[:T,1], label='reference trajectory')
+plt.axis("equal")
+plt.xlabel("x[m]")
+plt.ylabel("y[m]")
+plt.legend()
+plt.grid(True)
+
+plt.subplot(3, 1, 2)
+plt.cla()
+plt.plot(GetListFromMatrix(xstar.value[2, :]), '-b',label='linear velocity')
+plt.plot(GetListFromMatrix(xstar.value[3, :]), '-r',label='pose angle')
+#plt.ylim([-1.0, 1.0])
+plt.ylabel("velocity[m/s]")
+plt.xlabel("horizon")
+plt.legend()
+plt.grid(True)
+
+plt.subplot(3, 1, 3)
+plt.cla()
+plt.plot(GetListFromMatrix(ustar.value[0, :]), '-r', label="acceleration")
+plt.plot(GetListFromMatrix(ustar.value[1, :]), '-b', label="beta")
+#plt.ylim([-0.5, 0.5])
+plt.legend()
+plt.grid(True)
+plt.show()

requirement.txt

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+sys
+matplotlib
+numpy
+scipy
+math
+random
+time
+cvxpy
+heapq