2012年高教杯数学建模竞赛的机器人避障问题在OA段最短距离lingo代码
时间: 2023-05-29 11:01:50 浏览: 125
该问题中,我们需要求出机器人避开障碍物的最短路径。可以通过Lingo软件来进行建模和求解问题。
首先,我们需要定义一些参数和变量:
Parameters:
n: the number of obstacles
Obs_i_x, Obs_i_y: the coordinates of obstacle i (i = 1,...,n)
start_x, start_y: the starting position of the robot
goal_x, goal_y: the goal position of the robot
Variables:
x_i, y_i: the coordinates of the point i on the path (i = 0,...,m)
d: the total distance of the path
where m is the total number of points on the path, which will be determined later.
Next, we need to set up the objective function and constraints:
Minimize d
Subject to:
x_0 = start_x
y_0 = start_y
x_m = goal_x
y_m = goal_y
for i = 1,...,m-1:
(x_i - Obs_j_x)^2 + (y_i - Obs_j_y)^2 >= d_min^2, j = 1,...,n
(x_i - x_i+1)^2 + (y_i - y_i+1)^2 = delta^2
where d_min is the minimum distance to each obstacle, delta is the distance between each pair of adjacent points on the path.
Finally, we can write the Lingo code:
Minimize:
d
Subject to:
x_0 = start_x
y_0 = start_y
x_m = goal_x
y_m = goal_y
for(i, 1, m-1):
sum(j, ((x(i) - Obs(j)_x)^2 + (y(i) - Obs(j)_y)^2) - d_min^2) >= 0
for(i, 1, m-1):
(x(i) - x(i+1))^2 + (y(i) - y(i+1))^2 = delta^2
where Obs(j)_x and Obs(j)_y represent the coordinates of the j-th obstacle.
After running the Lingo code, the optimal path can be obtained by extracting the values of x_i and y_i.