2021深圳杯A题思路 火星探测器着陆控制方案
A题 火星探测器着陆控制方案
本题聚焦于探测器从火星同步轨道出发到探测器在火星地表上方悬停的过程（以下简称着陆过程），要求参赛队收集有关天问一号探测器的音像和文字等公开资料，建立数学模型，研究如下问题：
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确定探测器着陆过程时间最短的操控方案（包括环绕器与着陆巡视器分离、阻尼伞打开、发动机系统点火等时间，以及发动机系统运行方案）；
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对给定的着陆过程时间，确定消耗能量最少的操控方案；
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如果希望探测器着陆过程与公开的音像和文字资料尽量一致，如何设计操控方案。
天问一号数据
思路
从 探测器飞离地球到达目标火星 4个阶段入手
即：
-
停泊分离段
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过渡轨道段
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动力下降段
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最终着陆段
建立相应数学模型，并分析
这题第二问需要用到蚁群优化，这里给个简单的蚁群demo
from mpl_toolkits.mplot3d import proj3d
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
height3d = np.array([[2000,1400,800,650,500,750,1000,950,900,800,700,900,1100,1050,1000,1150,1300,1250,1200,1350,1500], [1100,900,700,625,550,825,1100,1150,1200,925,650,750,850,950,1050,1175,1300,1350,1400,1425,1450], [200,400,600,600,600,900,1200,1350,1500,1050,600,600,600,850,1100,1200,1300,1450,1600,1500,1400], [450,500,550,575,600,725,850,875,900,750,600,600,600,725,850,900,950,1150,1350,1400,1450], [700,600,500,550,600,550,500,400,300,450,600,600,600,600,600,600,600,850,1100,1300,1500], [500,525,550,575,600,575,550,450,350,475,600,650,700,650,600,600,600,725,850,1150,1450], [300,450,600,600,600,600,600,500,400,500,600,700,800,700,600,600,600,600,600,1000,1400], [550,525,500,550,600,875,1150,900,650,725,800,700,600,875,1150,1175,1200,975,750,875,1000], [800,600,400,500,600,1150,1700,1300,900,950,1000,700,400,1050,1700,1750,1800,1350,900,750,600], [650,600,550,625,700,1175,1650,1275,900,1100,1300,1275,1250,1475,1700,1525,1350,1200,1050,950,850], [500,600,700,750,800,1200,1600,1250,900,1250,1600,1850,2100,1900,1700,1300,900,1050,1200,1150,1100], [400,375,350,600,850,1200,1550,1250,950,1225,1500,1750,2000,1950,1900,1475,1050,975,900,1175,1450], [300,150,0,450,900,1200,1500,1250,1000,1200,1400,1650,1900,2000,2100,1650,1200,900,600,1200,1800], [600,575,550,750,950,1275,1600,1450,1300,1300,1300,1525,1750,1625,1500,1450,1400,1125,850,1200,1550], [900,1000,1100,1050,1000,1350,1700,1650,1600,1400,1200,1400,1600,1250,900,1250,1600,1350,1100,1200,1300], [750,850,950,900,850,1000,1150,1175,1200,1300,1400,1325,1250,1125,1000,1150,1300,1075,850,975,1100], [600,700,800,750,700,650,600,700,800,1200,1600,1250,900,1000,1100,1050,1000,800,600,750,900], [750,775,800,725,650,700,750,775,800,1000,1200,1025,850,975,1100,950,800,900,1000,1050,1100], [900,850,800,700,600,750,900,850,800,800,800,800,800,950,1100,850,600,1000,1400,1350,1300], [750,800,850,850,850,850,850,825,800,750,700,775,850,1000,1150,875,600,925,1250,1100,950], [600,750,900,1000,1100,950,800,800,800,700,600,750,900,1050,1200,900,600,850,1100,850,600]])
fig = figure()
ax = Axes3D(fig)
X = np.arange(21)
Y = np.arange(21)
X, Y = np.meshgrid(X, Y)
Z = -20*np.exp(-0.2*np.sqrt(np.sqrt(((X-10)**2+(Y-10)**2)/2)))+20+np.e-np.exp((np.cos(2*np.pi*X)+np.sin(2*np.pi*Y))/2)
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap='cool')
ax.set_xlabel('X axis')
ax.set_ylabel('Y axis')
ax.set_zlabel('Z')
ax.set_title('3D map')
point0 = [0,9,Z[0][9]]
point1 = [20,7,Z[20][7]]
ax.plot([point0[0]],[point0[1]],[point0[2]],'r',marker = u'o',markersize = 15)
ax.plot([point1[0]],[point1[1]],[point1[2]],'r',marker = u'o',markersize = 15)
x0,y0,_ = proj3d.proj_transform(point0[0],point0[1],point0[2], ax.get_proj())
x1,y1,_ = proj3d.proj_transform(point1[0],point1[1],point1[2], ax.get_proj())
label = pylab.annotate(
"start",
xy = (x0, y0), xytext = (-20, 20),
textcoords = 'offset points', ha = 'right', va = 'bottom',
bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 1),
arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0'),fontsize=15)
label2 = pylab.annotate(
"end",
xy = (x1, y1), xytext = (-20, 20),
textcoords = 'offset points', ha = 'right', va = 'bottom',
bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 1),
arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0'),fontsize=15)
def update_position(e):
x2, y2, _ = proj3d.proj_transform(point0[0],point0[1],point0[2],ax.get_proj())
label.xy = x2,y2
label.update_positions(fig.canvas.renderer)
x1,y1,_ = proj3d.proj_transform(point1[0],point1[1],point1[2],ax.get_proj())
label2.xy = x1,y1
label2.update_positions(fig.canvas.renderer)
fig.canvas.draw()
fig.canvas.mpl_connect('button_release_event', update_position)
from mpl_toolkits.mplot3d import proj3d
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
height3d = np.array([[2000,1400,800,650,500,750,1000,950,900,800,700,900,1100,1050,1000,1150,1300,1250,1200,1350,1500], [1100,900,700,625,550,825,1100,1150,1200,925,650,750,850,950,1050,1175,1300,1350,1400,1425,1450], [200,400,600,600,600,900,1200,1350,1500,1050,600,600,600,850,1100,1200,1300,1450,1600,1500,1400], [450,500,550,575,600,725,850,875,900,750,600,600,600,725,850,900,950,1150,1350,1400,1450], [700,600,500,550,600,550,500,400,300,450,600,600,600,600,600,600,600,850,1100,1300,1500], [500,525,550,575,600,575,550,450,350,475,600,650,700,650,600,600,600,725,850,1150,1450], [300,450,600,600,600,600,600,500,400,500,600,700,800,700,600,600,600,600,600,1000,1400], [550,525,500,550,600,875,1150,900,650,725,800,700,600,875,1150,1175,1200,975,750,875,1000], [800,600,400,500,600,1150,1700,1300,900,950,1000,700,400,1050,1700,1750,1800,1350,900,750,600], [650,600,550,625,700,1175,1650,1275,900,1100,1300,1275,1250,1475,1700,1525,1350,1200,1050,950,850], [500,600,700,750,800,1200,1600,1250,900,1250,1600,1850,2100,1900,1700,1300,900,1050,1200,1150,1100], [400,375,350,600,850,1200,1550,1250,950,1225,1500,1750,2000,1950,1900,1475,1050,975,900,1175,1450], [300,150,0,450,900,1200,1500,1250,1000,1200,1400,1650,1900,2000,2100,1650,1200,900,600,1200,1800], [600,575,550,750,950,1275,1600,1450,1300,1300,1300,1525,1750,1625,1500,1450,1400,1125,850,1200,1550], [900,1000,1100,1050,1000,1350,1700,1650,1600,1400,1200,1400,1600,1250,900,1250,1600,1350,1100,1200,1300], [750,850,950,900,850,1000,1150,1175,1200,1300,1400,1325,1250,1125,1000,1150,1300,1075,850,975,1100], [600,700,800,750,700,650,600,700,800,1200,1600,1250,900,1000,1100,1050,1000,800,600,750,900], [750,775,800,725,650,700,750,775,800,1000,1200,1025,850,975,1100,950,800,900,1000,1050,1100], [900,850,800,700,600,750,900,850,800,800,800,800,800,950,1100,850,600,1000,1400,1350,1300], [750,800,850,850,850,850,850,825,800,750,700,775,850,1000,1150,875,600,925,1250,1100,950], [600,750,900,1000,1100,950,800,800,800,700,600,750,900,1050,1200,900,600,850,1100,850,600]])
fig = figure()
ax = Axes3D(fig)
X = np.arange(21)
Y = np.arange(21)
X, Y = np.meshgrid(X, Y)
Z = -20*np.exp(-0.2*np.sqrt(np.sqrt(((X-10)**2+(Y-10)**2)/2)))+20+np.e-np.exp((np.cos(2*np.pi*X)+np.sin(2*np.pi*Y))/2)
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap='cool')
ax.set_xlabel('X axis')
ax.set_ylabel('Y axis')
ax.set_zlabel('Z')
ax.set_title('3D map')
point0 = [0,9,Z[0][9]]
point1 = [20,7,Z[20][7]]
ax.plot([point0[0]],[point0[1]],[point0[2]],'r',marker = u'o',markersize = 15)
ax.plot([point1[0]],[point1[1]],[point1[2]],'r',marker = u'o',markersize = 15)
x0,y0,_ = proj3d.proj_transform(point0[0],point0[1],point0[2], ax.get_proj())
x1,y1,_ = proj3d.proj_transform(point1[0],point1[1],point1[2], ax.get_proj())
label = pylab.annotate(
"start",
xy = (x0, y0), xytext = (-20, 20),
textcoords = 'offset points', ha = 'right', va = 'bottom',
bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 1),
arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0'),fontsize=15)
label2 = pylab.annotate(
"end",
xy = (x1, y1), xytext = (-20, 20),
textcoords = 'offset points', ha = 'right', va = 'bottom',
bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 1),
arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0'),fontsize=15)
def update_position(e):
x2, y2, _ = proj3d.proj_transform(point0[0],point0[1],point0[2],ax.get_proj())
label.xy = x2,y2
label.update_positions(fig.canvas.renderer)
x1,y1,_ = proj3d.proj_transform(point1[0],point1[1],point1[2],ax.get_proj())
label2.xy = x1,y1
label2.update_positions(fig.canvas.renderer)
fig.canvas.draw()
fig.canvas.mpl_connect('button_release_event', update_position)
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