Competition path design of beacon group

Jane Medium ： This paper presents the route design of the beacon competition of the 17th National College Student smart car competition . Path parameter ： The number of lights on is 18 Lights ; How difficult is the path to locate 5975 ~ 5990; The total number of paths to be selected 6888 strip , This paper gives one of them 50 Of the path .

key word ： The smart car race , Beacon group , route

 

§01 Letter Mark the path

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   stay The 17th National College Student smart car competition In the beacon group competition , It is required to use different routes for each departure . Here is On line track design of the 17th smart car race About beacon group track specifications , On this basis , Design eight beacon competition paths .

▲ chart 1.1 The competition venue of the balanced beacon Group

One 、 Race path design

   The following figure shows the position coordinates of the four beacons in the beacon group and the departure area .

▲ chart 1.1.1 The coordinate position between the beacon in the beacon group and the departure area

1、 Search all possible paths

   Design a reasonable competition path , Follow the following principles ：

• Starting from a given area , To the end of the designated beacon , For example, starting from the departure area , To 4 The light is over ;
• Given the number of lights , such as 12 individual ;
• Remove the light sequence connected closely in the path , such as 1-2, 2-3;

   The following is the departure from the departure area obtained through the program , To 4 The light is over , Lighten up 5 All of the beacon lights 25 Bar light sequence .

[-1, 1, 3, 1, 3, 4]
[-1, 1, 3, 4, 1, 4]
[-1, 1, 3, 4, 2, 4]
[-1, 1, 3, 4, 3, 4]
[-1, 1, 4, 1, 3, 4]
[-1, 1, 4, 3, 1, 4]
[-1, 2, 4, 1, 3, 4]
[-1, 2, 4, 3, 1, 4]
[-1, 3, 1, 3, 1, 4]
[-1, 3, 1, 4, 1, 4]
[-1, 3, 1, 4, 2, 4]
[-1, 3, 1, 4, 3, 4]
[-1, 3, 4, 1, 3, 4]
[-1, 3, 4, 3, 1, 4]
[-1, 4, 1, 3, 1, 4]
[-1, 4, 1, 4, 1, 4]
[-1, 4, 1, 4, 2, 4]
[-1, 4, 1, 4, 3, 4]
[-1, 4, 2, 4, 1, 4]
[-1, 4, 2, 4, 2, 4]
[-1, 4, 2, 4, 3, 4]
[-1, 4, 3, 1, 3, 4]
[-1, 4, 3, 4, 1, 4]
[-1, 4, 3, 4, 2, 4]
[-1, 4, 3, 4, 3, 4]

   As the number of lights increases , The total number of light sequences shows an exponential increasing trend . The following table shows the relationship between lamp sequence length and number .

Number of lights	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Total number of lamp sequences	25	59	121	273	577	1275	2733	5981	12905	28115	60849	132289	286721	622739	1350613	2932109

2、 Measure the difficulty of the path

   In all possible paths , The difficulty of running a car model is mainly determined by two factors ：

• The length of the path （L）： It determines the running time of the car model and the difficulty of beacon positioning ;
• Steering angle of the car model （A）： It affects the turning time of car models and the difficulty of beacon search ;

   Combined with the above factors , The length in the path （ Company ： centimeter ） And angle （ Company degree ） With 4:1 The proportions of are weighted together , That is, the difficulty of the path （H） Expressed as ： $$H=L+0.25A$$

   Below is the 622739 individual 18 Histogram of the difficulty degree of the lamp . You can see that there are a lot of low score paths , There are also some paths that are more difficult 5000 above .

▲ Light up 18 The statistical result of the difficulty score of a lamp

   The following figure shows all the difficulties beyond 5000 Divide the path of histogram statistics . The average score is 5903, The standard deviation is ：231.

▲ The path is more difficult than 5000 Path histogram

   For path difficulty, the score is 5991 The path of points , All in all 105 strip . The first two of these paths are 2 Lights And 4 Lights .

[2 4 1 3 1 4 1 4 1 4 2 4 2 4 2 4 2 4]
[2 4 1 3 1 4 1 4 2 4 1 4 2 4 2 4 2 4]
[2 4 1 3 1 4 1 4 2 4 2 4 1 4 2 4 2 4]
[2 4 1 3 1 4 1 4 2 4 2 4 2 4 1 4 2 4]
[2 4 1 3 1 4 1 4 2 4 2 4 2 4 2 4 1 4]
[2 4 1 3 1 4 2 4 1 4 1 4 2 4 2 4 2 4]
[2 4 1 3 1 4 2 4 1 4 2 4 1 4 2 4 2 4]
[2 4 1 3 1 4 2 4 2 4 2 4 1 4 2 4 1 4]
[2 4 1 3 1 4 2 4 2 4 2 4 2 4 1 4 1 4]
[2 4 1 4 1 3 1 4 1 4 2 4 2 4 2 4 2 4]
[2 4 1 4 1 3 1 4 2 4 1 4 2 4 2 4 2 4]

.....................
.....................

[2 4 2 4 2 4 1 4 2 4 1 3 1 4 1 4 2 4]
[2 4 2 4 2 4 1 4 2 4 1 3 1 4 2 4 1 4]
[2 4 2 4 2 4 1 4 2 4 1 4 1 3 1 4 2 4]
[2 4 2 4 2 4 1 4 2 4 1 4 2 4 1 3 1 4]
[2 4 2 4 2 4 1 4 2 4 2 4 1 3 1 4 1 4]
[2 4 2 4 2 4 1 4 2 4 2 4 1 4 1 3 1 4]
[2 4 2 4 2 4 2 4 1 3 1 4 1 4 1 4 2 4]

[2 4 2 4 2 4 2 4 1 4 2 4 1 4 1 3 1 4]
[2 4 2 4 2 4 2 4 2 4 1 3 1 4 1 4 1 4]
[2 4 2 4 2 4 2 4 2 4 1 4 1 3 1 4 1 4]
[2 4 2 4 2 4 2 4 2 4 1 4 1 4 1 3 1 4]

   To increase the randomness of the path , Score the path at 5975 to 5990 Between 6888 Four routes were selected as candidates for the competition route . The first of these paths 50 The two paths are shown in the figure below ：

[1 3 1 3 1 4 2 4 2 4 2 4 2 4 3 4 3 4]
[1 3 1 3 4 2 4 3 1 4 2 4 3 4 2 4 2 4]
[1 3 1 4 3 4 2 4 2 4 2 4 2 4 3 1 3 4]
[1 3 4 2 4 2 4 2 4 3 4 2 4 1 3 1 3 4]
[1 3 4 3 1 3 4 1 3 4 2 4 2 4 2 4 2 4]
[1 4 2 4 3 1 3 4 3 1 3 4 2 4 2 4 2 4]
[2 4 1 3 1 4 2 4 1 4 1 4 2 4 1 4 1 4]
[2 4 1 4 1 4 1 3 1 4 2 4 2 4 1 4 1 4]
[2 4 1 4 1 4 2 4 1 4 2 4 1 3 1 4 1 4]
[2 4 1 4 2 4 1 4 2 4 2 4 1 3 1 4 1 4]
[2 4 2 4 1 4 1 4 1 3 1 4 2 4 1 4 2 4]
[2 4 2 4 2 4 1 4 1 4 1 3 1 4 2 4 1 4]
[2 4 2 4 3 4 3 1 3 4 2 4 3 4 3 1 3 4]
[2 4 3 1 3 4 3 4 3 1 3 4 3 4 2 4 2 4]
[2 4 3 4 3 4 2 4 3 1 3 1 3 4 3 4 2 4]
[3 1 3 4 1 4 1 4 1 4 3 4 2 4 2 4 1 4]
[3 1 3 4 1 4 2 4 1 4 1 4 2 4 2 4 3 4]
[3 1 3 4 1 4 3 4 1 4 1 4 1 4 1 4 1 4]
[3 1 3 4 2 4 1 4 1 4 3 4 1 4 2 4 2 4]
[3 1 3 4 2 4 2 4 2 4 3 4 1 4 1 4 1 4]
[3 1 3 4 3 4 1 4 2 4 1 4 1 4 2 4 2 4]
[3 1 4 1 3 4 1 4 1 4 1 4 2 4 3 4 1 4]
[3 1 4 1 3 4 1 4 2 4 3 4 1 4 2 4 2 4]
[3 1 4 1 3 4 2 4 2 4 1 4 1 4 3 4 2 4]
[3 1 4 1 4 1 3 4 1 4 1 4 1 4 1 4 3 4]
[3 1 4 1 4 1 3 4 2 4 2 4 3 4 1 4 1 4]
[3 1 4 1 4 1 4 1 3 4 3 4 1 4 1 4 2 4]
[3 1 4 1 4 1 4 1 4 2 4 1 4 3 4 3 1 4]
[3 1 4 1 4 1 4 1 4 3 4 3 1 4 1 4 2 4]
[3 1 4 1 4 1 4 2 4 2 4 2 4 3 4 3 1 4]
[3 1 4 1 4 1 4 3 1 4 1 4 1 4 2 4 3 4]
[3 1 4 1 4 1 4 3 4 1 4 1 4 3 1 4 2 4]
[3 1 4 1 4 2 4 1 3 4 1 4 2 4 2 4 3 4]
[3 1 4 1 4 2 4 1 4 1 4 3 1 4 3 4 2 4]
[3 1 4 1 4 2 4 1 4 3 4 1 4 1 3 4 2 4]
[3 1 4 1 4 2 4 2 4 1 4 3 4 3 1 4 1 4]
[3 1 4 1 4 2 4 3 1 4 1 4 3 4 1 4 2 4]
[3 1 4 1 4 2 4 3 4 2 4 1 3 4 1 4 1 4]
[3 1 4 1 4 3 1 4 1 4 3 4 1 4 1 4 2 4]
[3 1 4 1 4 3 4 1 3 4 1 4 1 4 1 4 1 4]
[3 1 4 1 4 3 4 1 4 2 4 1 3 4 2 4 2 4]
[3 1 4 1 4 3 4 2 4 1 4 2 4 1 4 1 3 4]
[3 1 4 2 4 1 3 4 1 4 1 4 1 4 1 4 3 4]
[3 1 4 2 4 1 3 4 3 4 1 4 2 4 2 4 1 4]
[3 1 4 2 4 1 4 1 4 1 4 1 4 3 1 4 3 4]
[3 1 4 2 4 1 4 1 4 3 1 4 2 4 3 4 2 4]
[3 1 4 2 4 1 4 2 4 1 4 3 1 4 1 4 3 4]
[3 1 4 2 4 1 4 2 4 3 4 3 1 4 2 4 1 4]
[3 1 4 2 4 1 4 3 4 1 4 2 4 1 4 1 3 4]
[3 1 4 2 4 2 4 1 3 4 3 4 2 4 1 4 1 4]

▲ The path is difficult and easy to score 5975 to 5990 Distribution of scores

 

※ total    junction ※

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   Ben This paper gives the route design of the beacon competition of the 17th National College Students' smart car competition . Path parameter ：

• The number of lights on is 18 Lights ;
• How difficult is the path to locate 5975 ~ 5990;

   The total number of paths to be selected 6888 strip , This paper gives one of them 50 Of the path .

One 、 The handler

1、 Path generation and score calculation

#!/usr/local/bin/python
# -*- coding: gbk -*-
#============================================================
# TEST1.PY -- by Dr. ZhuoQing 2022-07-19
#
# Note:
#============================================================

from headm import *
import math

#------------------------------------------------------------
posdim = [(100,325), (75, 200), (75,75), (425,200)]
start1 = (250, 22.5)

def routearg(r, s):
    global posdim
    lenall = 0
    angleall = 0

    lastangle = 0
    lastr = s
    for id,rr in enumerate(r):
        rrr = posdim[rr-1]
        deltax = rrr[0] - lastr[0]
        deltay = rrr[1] - lastr[1]
        lenall += sqrt(deltax**2 + deltay**2)

        angle = math.atan2(deltay, deltax)

        lastr = rrr

        if id > 0:
            deltaangle = angle - lastangle

            while deltaangle < -pi:
                deltaangle += pi
            while deltaangle > pi:
                deltaangle -= pi

            angleall += abs(deltaangle)

        lastangle = angle
    return lenall, angleall

#------------------------------------------------------------
''' r = tspload('route18', 'r') rscore = [] for id,rr in enumerate(r): rscore.append(routearg(rr[1:], start1)) if id % 10000 == 0: printf(id) tspsave('score', rscore=rscore) '''
#------------------------------------------------------------
rscore = tspload('score', 'rscore')

plt.hist(rscore, 50)
plt.xlabel(" The path is difficult ")
plt.ylabel(" Frequency of occurrence ")
plt.grid(True)
plt.tight_layout()
plt.show()

exit()



#------------------------------------------------------------
def routerandall(r, endp, num):
    global routeall

# printff(r, endp, num)
    if len(r) >= num - 1:
        rc = r.copy()
        rc.append(endp)
        routeall.append(rc)
        return


    rr = list(range(1,5))

    if r[-1] in rr:
        rr.remove(r[-1])

    if r[-1] == 1:
        if 2 in rr: rr.remove(2)

    if r[-1] == 2:
        if 1 in rr: rr.remove(1)
        if 3 in rr: rr.remove(3)

    if r[-1] == 3:
        if 2 in rr: rr.remove(2)

    if len(r) >= num - 2:
        if endp in rr:
            rr.remove(endp)

    for rrr in rr:
        rc = r.copy()
        rc.append(rrr)
        routerandall(rc, endp, num)


#------------------------------------------------------------
routeall = []
r = [-1]
routerandall(r, 4, 19)
tspsave('route18', r = routeall)

#------------------------------------------------------------
printf(len(routeall))
#for r in routeall:
# printf(r)

#------------------------------------------------------------
# END OF FILE : TEST1.PY
#============================================================

2、 Path Statistics

#!/usr/local/bin/python
# -*- coding: gbk -*-
#============================================================
# TEST2.PY -- by Dr. ZhuoQing 2022-07-19
#
# Note:
#============================================================

from headm import *

r = tspload('route18', 'r')
rscore = tspload('score', 'rscore')

printf(shape(r))

c = where((rscore >= 5975) & (rscore < 5990))
rhigh = rscore[c]
route = r[c[0],1:]

printf(len(route), len(route))
printf(shape(route))

rsel = route[::50][:50]

for rr in rsel:
    printf(rr)




#------------------------------------------------------------
#for r in route:
# printf(r)

#------------------------------------------------------------
printf(mean(rhigh), std(rhigh))

plt.hist(rhigh, 500)

plt.xlabel(" The path is difficult ")
plt.ylabel(" Frequency of occurrence ")
plt.grid(True)
plt.tight_layout()
plt.show()




#------------------------------------------------------------
# END OF FILE : TEST2.PY
#============================================================

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■ Links to related literature :

• The 17th National College Student smart car competition
• Track design of the 17th National College Student intelligent car competition online race

● Related chart Links :

• chart 1.1 The competition venue of the balanced beacon Group
• chart 1.1.1 The coordinate position between the beacon in the beacon group and the departure area
• Light up 18 The statistical result of the difficulty score of a lamp
• The path is more difficult than 5000 Path histogram
• The path is difficult and easy to score 5975 to 5990 Distribution of scores