动态窗口法_version1.3

Posted 2020-11-01 最后的绝地武士

  1 """
  2 version1.3
  3 Mobile robot motion planning sample with Dynamic Window Approach
  4 结合https://blog.csdn.net/heyijia0327/article/details/44983551来看，里面含中文注释
  5 符号参考《煤矿救援机器人地图构建与路径规划研究》矿大硕士论文
  6 """
  7 
  8 import math
  9 import numpy as np
 10 import matplotlib.pyplot as plt
 11 
 12 show_animation = True  # 动画
 13 
 14 
 15 class Config(object):
 16     """
 17     用来仿真的参数，
 18     """
 19 
 20     def __init__(self):
 21         # robot parameter
 22         self.max_speed = 1.4  # [m/s]  # 最大速度
 23         # self.min_speed = -0.5  # [m/s]  # 最小速度，设置为可以倒车
 24         self.min_speed = 0  # [m/s]  # 最小速度，设置为不倒车
 25         self.max_yawrate = 40.0 * math.pi / 180.0  # [rad/s]  # 最大角速度
 26         self.max_accel = 0.2  # [m/ss]  # 最大加速度
 27         self.max_dyawrate = 40.0 * math.pi / 180.0  # [rad/ss]  # 最大角加速度
 28         self.v_reso = 0.01  # [m/s]，速度分辨率
 29         self.yawrate_reso = 0.1 * math.pi / 180.0  # [rad/s]，角速度分辨率
 30         self.dt = 0.1  # [s]  # 采样周期
 31         self.predict_time = 3.0  # [s]  # 向前预估三秒
 32         self.to_goal_cost_gain = 1.0  # 目标代价增益
 33         self.speed_cost_gain = 1.0  # 速度代价增益
 34         self.robot_radius = 1.0  # [m]  # 机器人半径
 35 
 36 
 37 def motion(x, u, dt):
 38     """
 39     :param x: 位置参数，在此叫做位置空间
 40     :param u: 速度和加速度，在此叫做速度空间
 41     :param dt: 采样时间
 42     :return:
 43     """
 44     # 速度更新公式比较简单，在极短时间内，车辆位移也变化较大
 45     # 采用圆弧求解如何？
 46     x[0] += u[0] * math.cos(x[2]) * dt  # x方向位移
 47     x[1] += u[0] * math.sin(x[2]) * dt  # y
 48     x[2] += u[1] * dt  # 航向角
 49     x[3] = u[0]  # 速度v
 50     x[4] = u[1]  # 角速度w
 51     # print(x)
 52 
 53     return x
 54 
 55 
 56 def calc_dynamic_window(x, config):
 57     """
 58     位置空间集合
 59     :param x:当前位置空间,符号参考硕士论文
 60     :param config:
 61     :return:目前是两个速度的交集，还差一个
 62     """
 63 
 64     # 车辆能够达到的最大最小速度
 65     vs = [config.min_speed, config.max_speed,
 66           -config.max_yawrate, config.max_yawrate]
 67 
 68     # 一个采样周期能够变化的最大最小速度
 69     vd = [x[3] - config.max_accel * config.dt,
 70           x[3] + config.max_accel * config.dt,
 71           x[4] - config.max_dyawrate * config.dt,
 72           x[4] + config.max_dyawrate * config.dt]
 73     #  print(Vs, Vd)
 74 
 75     # 求出两个速度集合的交集
 76     vr = [max(vs[0], vd[0]), min(vs[1], vd[1]),
 77           max(vs[2], vd[2]), min(vs[3], vd[3])]
 78 
 79     return vr
 80 
 81 
 82 def calc_trajectory(x_init, v, w, config):
 83     """
 84     预测3秒内的轨迹
 85     :param x_init:位置空间
 86     :param v:速度
 87     :param w:角速度
 88     :param config:
 89     :return: 每一次采样更新的轨迹，位置空间垂直堆叠
 90     """
 91     x = np.array(x_init)
 92     trajectory = np.array(x)
 93     time = 0
 94     while time <= config.predict_time:
 95         x = motion(x, [v, w], config.dt)
 96         trajectory = np.vstack((trajectory, x))  # 垂直堆叠，vertical
 97         time += config.dt
 98 
 99         # print(trajectory)
100     return trajectory
101 
102 
103 def calc_to_goal_cost(trajectory, goal, config):
104     """
105     计算轨迹到目标点的代价
106     :param trajectory:轨迹搜索空间
107     :param goal:
108     :param config:
109     :return: 轨迹到目标点欧式距离
110     """
111     # calc to goal cost. It is 2D norm.
112 
113     dx = goal[0] - trajectory[-1, 0]
114     dy = goal[1] - trajectory[-1, 1]
115     goal_dis = math.sqrt(dx ** 2 + dy ** 2)
116     cost = config.to_goal_cost_gain * goal_dis
117 
118     return cost
119 
120 
121 def calc_obstacle_cost(traj, ob, config):
122     """
123     计算预测轨迹和障碍物的最小距离，dist(v,w)
124     :param traj:
125     :param ob:
126     :param config:
127     :return:
128     """
129     # calc obstacle cost inf: collision, 0:free
130 
131     min_r = float("inf")  # 距离初始化为无穷大
132 
133     for ii in range(0, len(traj[:, 1])):
134         for i in range(len(ob[:, 0])):
135             ox = ob[i, 0]
136             oy = ob[i, 1]
137             dx = traj[ii, 0] - ox
138             dy = traj[ii, 1] - oy
139 
140             r = math.sqrt(dx ** 2 + dy ** 2)
141             if r <= config.robot_radius:
142                 return float("Inf")  # collision
143 
144             if min_r >= r:
145                 min_r = r
146 
147     return 1.0 / min_r  # 越小越好
148 
149 
150 def calc_final_input(x, u, vr, config, goal, ob):
151     """
152     计算采样空间的评价函数，选择最合适的那一个作为最终输入
153     :param x:位置空间
154     :param u:速度空间
155     :param vr:速度空间交集
156     :param config:
157     :param goal:目标位置
158     :param ob:障碍物
159     :return:
160     """
161     x_init = x[:]
162     min_cost = 10000.0
163     min_u = u
164 
165     best_trajectory = np.array([x])
166 
167     trajectory_space = np.array([x])  # 记录搜索所有采样的轨迹，用来画图
168 
169     # evaluate all trajectory with sampled input in dynamic window
170     # v,生成一系列速度，w，生成一系列角速度
171     for v in np.arange(vr[0], vr[1], config.v_reso):
172         for w in np.arange(vr[2], vr[3], config.yawrate_reso):
173 
174             trajectory = calc_trajectory(x_init, v, w, config)
175 
176             trajectory_space = np.vstack((trajectory_space, trajectory))
177 
178             # calc cost
179             to_goal_cost = calc_to_goal_cost(trajectory, goal, config)
180             speed_cost = config.speed_cost_gain * (config.max_speed - trajectory[-1, 3])
181             ob_cost = calc_obstacle_cost(trajectory, ob, config)
182             #  print(ob_cost)
183 
184             # 评价函数多种多样，看自己选择
185             # 本文构造的是越小越好
186             final_cost = to_goal_cost + speed_cost + ob_cost
187 
188             # search minimum trajectory
189             if min_cost >= final_cost:
190                 min_cost = final_cost
191                 min_u = [v, w]
192                 best_trajectory = trajectory
193 
194     # print(min_u)
195     #  input()
196 
197     return min_u, best_trajectory, trajectory_space
198 
199 
200 def dwa_control(x, u, config, goal, ob):
201     """
202     调用前面的几个函数，生成最合适的速度空间和轨迹搜索空间
203     :param x:
204     :param u:
205     :param config:
206     :param goal:
207     :param ob:
208     :return:
209     """
210     # Dynamic Window control
211 
212     vr = calc_dynamic_window(x, config)
213 
214     u, trajectory, trajectory_space = calc_final_input(x, u, vr, config, goal, ob)
215 
216     return u, trajectory, trajectory_space
217 
218 
219 def plot_arrow(x, y, yaw, length=0.5, width=0.1):
220     """
221     arrow函数绘制箭头,表示搜索过程中选择的航向角
222     :param x:
223     :param y:
224     :param yaw:航向角
225     :param length:
226     :param width:参数值为浮点数，代表箭头尾部的宽度，默认值为0.001
227     :return:
228     length_includes_head：代表箭头整体长度是否包含箭头头部的长度，默认值为False
229     head_width：代表箭头头部的宽度，默认值为3*width，即尾部宽度的3倍
230     head_length：代表箭头头部的长度度，默认值为1.5*head_width，即头部宽度的1.5倍
231     shape：参数值为‘full‘、‘left‘、‘right‘，表示箭头的形状，默认值为‘full‘
232     overhang：代表箭头头部三角形底边与箭头尾部直接的夹角关系，通过该参数可改变箭头的形状。
233     默认值为0，即头部为三角形，当该值小于0时，头部为菱形，当值大于0时，头部为鱼尾状
234     """
235     plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw),
236               head_length=1.5 * width, head_width=width)
237     plt.plot(x, y)
238 
239 
240 def main():
241     """
242     主函数
243     :return:
244     """
245     # print(__file__ + " start!!")
246     # 初始化位置空间
247     x = np.array([0.0, 0.0, math.pi / 2.0, 0.2, 0.0])
248 
249     goal = np.array([10, 10])
250 
251     # matrix二维矩阵
252     ob = np.matrix([[-1, -1],
253                     [0, 2],
254                     [4.0, 2.0],
255                     [5.0, 4.0],
256                     [5.0, 5.0],
257                     [5.0, 6.0],
258                     [5.0, 9.0],
259                     [8.0, 9.0],
260                     [7.0, 9.0],
261                     [12.0, 12.0]
262                     ])
263     # ob = np.matrix([[0, 2]])
264     u = np.array([0.2, 0.0])
265     config = Config()
266     trajectory = np.array(x)
267 
268     for i in range(1000):
269 
270         u, best_trajectory, trajectory_space = dwa_control(x, u, config, goal, ob)
271 
272         x = motion(x, u, config.dt)
273         # print(x)
274 
275         trajectory = np.vstack((trajectory, x))  # store state history
276 
277         if show_animation:
278             draw_dynamic_search(best_trajectory, x, goal, ob, trajectory_space)
279 
280         # check goal
281         if math.sqrt((x[0] - goal[0]) ** 2 + (x[1] - goal[1]) ** 2) <= config.robot_radius:
282             print("Goal!!")
283 
284             break
285 
286     print("Done")
287 
288     # draw_path(trajectory, goal, ob, x)
289 
290 
291 def draw_dynamic_search(best_trajectory, x, goal, ob, trajectory_space):
292     """
293     画出动态搜索过程图
294     :return:
295     """
296     plt.cla()  # 清除上次绘制图像
297     plt.plot(best_trajectory[:, 0], best_trajectory[:, 1], "-g")
298 
299     plt.plot(trajectory_space[:, 0], trajectory_space[:, 1], ‘-g‘)
300 
301     plt.plot(x[0], x[1], "xr")
302     plt.plot(0, 0, "og")
303     plt.plot(goal[0], goal[1], "ro")
304     plt.plot(ob[:, 0], ob[:, 1], "bs")
305     plot_arrow(x[0], x[1], x[2])
306     plt.axis("equal")
307     plt.grid(True)
308     plt.pause(0.0001)
309 
310 
311 def draw_path(trajectory, goal, ob, x):
312     """
313     画图函数
314     :return:
315     """
316     plt.cla()  # 清除上次绘制图像
317 
318     plt.plot(x[0], x[1], "xr")
319     plt.plot(0, 0, "og")
320     plt.plot(goal[0], goal[1], "ro")
321     plt.plot(ob[:, 0], ob[:, 1], "bs")
322     plot_arrow(x[0], x[1], x[2])
323     plt.axis("equal")
324     plt.grid(True)
325     plt.plot(trajectory[:, 0], trajectory[:, 1], ‘r‘)
326     plt.show()
327 
328 
329 if __name__ == ‘__main__‘:
330     main()