智能小车的速度控制算法采用模糊控制。
比赛中的控制算法大多采用PID控制算法，PID可以对速度迅速响应，但拥有相应迅速对小车 速度的控制是不够的，还需要根据赛道实际情况设置不同的车速，以达到最快通过不同路况，以下采用模糊推理实现对小车的速度控制。
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1.变量模糊化
在模糊控制中，输入输出变量大小用语言形式进行描述。常选用的7个语言值为{负大，负中，负小，零，正小，正中，正大}，即{NB，NM，NS，O，PS，PM，PB}。
对小车当前行驶方向和赛道方向形成的偏差e及其变化率ec作为模糊控制器的输入，小车的目标车速为模糊控制器的输出。设偏差值的模糊量为E，偏差变化率模糊量为EC，U为目标车速。为了让速度切换更加细腻流畅，设置偏差e、偏差变化ec和控制量u的基本论域为[-6,6]，并划分为13个等级，即{-6，-5，-4，-3，-2，-1，0，1，2，3，4，5，6}。
E、EC和U均使用三角形隶属函数进行模糊化
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/**
* 列坐标：NB,NM,NS,O,PS,PM,PB
* 横坐标：-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6
* @param 建立输入、输出隶属度函数,进行微调调整模糊量的范围
*//***************************************误差隶属度函数***************************************/float Input1_Terms_Membership[7][13] ={ 1,0.15,0,0,0,0,0,0,0,0,0,0,0,0,0.2,1,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0.2,1,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0.1,1,0.1,0,0,0,0,0,0,0,0,0,0,0,0,0.1,1,0.1,0,0,0,0,0,0,0,0,0,0,0,0,0.2,1,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0.2,1};/***************************************误差变化率隶属度函数***************************************/float Input2_Terms_Membership[7][13] ={ 1,0.15,0,0,0,0,0,0,0,0,0,0,0,0,0.2,1,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0.2,1,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0.1,1,0.1,0,0,0,0,0,0,0,0,0,0,0,0,0.1,1,0.1,0,0,0,0,0,0,0,0,0,0,0,0,0.2,1,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0.2,1};/***************************************输出（速度）***************************************/float Output_Terms_Membership[7][13] ={ 1,0.15,0,0,0,0,0,0,0,0,0,0,0,0,0.2,1,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0.2,1,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0.1,1,0.1,0,0,0,0,0,0,0,0,0,0,0,0,0.1,1,0.1,0,0,0,0,0,0,0,0,0,0,0,0,0.2,1,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0.2,1};123456789101112131415161718192021222324252627282930313233343536
2.模糊查询表的计算
对模糊量EC、E和U设置相关的模糊控制规则表
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/**
* 纵轴为E(error)，横轴为EC(error_delta)，值为速度七档NB(0),NM(1),NS(2),Z(3),PS(4),PM(5),PB(6)速度由小变大再变小
* 列坐标：E（NB,NM,NS,O,PS,PM,PB）
* 横坐标：EC（NB,NM,NS,O,PS,PM,PB）
* 值：U（1：NB:2,NM,3:NS,4:O,5:PS,6:PM,7:PB）
* @param 模糊控制规则表，调整速度变化趋势
*/int Rule[7][7] ={ 1,1,2,2,6,7,7,
1,1,2,2,6,6,6,
1,2,3,4,5,6,6,
1,3,4,4,4,5,7,
2,2,3,4,5,6,7,
2,2,2,2,6,7,7,
1,1,2,2,6,7,7};//调试参数12345678910111213141516
规则库蕴含的模糊关系：
其中，模糊运算×表示“取小”。
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计算出模糊规则蕴含的模糊关系R后，通过遍历E和EC所有的论域对模糊值进行选取并计算模糊输出值：
其中，o表示模糊矩阵的合成，类似于普通矩阵的乘积运算，将乘积运算换成“取小”，将加法运算换成“取大”。
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在遍历过程中，对E和EC所有论域对应的模糊输出值一一采取加权平均法去模糊化，得到最终的模糊控制器查询表。
float R[169][13] = { 0 };float R1[13][13] = { 0 };float AdBd1[13][13] = { 0 };float R2[169] = { 0 };float AdBd2[169] = { 0 };float R3[169][13] = { 0 };float Cd[13] = { 0 };float Fuzzy_Table[13][13] = { 0 };float SPEED[13] = { 200,220,230,240,250,270,300,270,250,240,230,220,200 };//调试参数int Max_Input1_value = 0, Max_Input2_value = 0;/**
* @param 模糊化过程实现论域内不同值对应隶属度最大的语言值
*/int E_MAX(int e){
int i = 0, max = 0;
for (i = 0; i < 7; i++)
if (Input1_Terms_Membership[i][e] > Input1_Terms_Membership[max][e])
max = i;
return max;}int EC_MAX(int ex){
int i = 0, max = 0;
for (i = 0; i < 7; i++)
if (Input2_Terms_Membership[i][ex] > Input1_Terms_Membership[max][ex])
max = i;
return max;}void calculate(){
/***************************************计算所有规则模糊关系的并集Rule***************************************/
int i = 0, j = 0, k = 0;
int Input1_value_index = 0, Input2_value_index = 0;
//计算Rule(初始化），计算Rij，并对所有的R取并集，R=(EXEC)XU
for (Input1_Terms_Index = 0; Input1_Terms_Index < 7; Input1_Terms_Index++)
for (Input2_Terms_Index = 0; Input2_Terms_Index < 7; Input2_Terms_Index++)
{
// E和EC的语言值两两组合及其输出计算Rule
Output_Terms_Index = Rule[Input1_Terms_Index][Input2_Terms_Index] - 1;
k = 0;
for (i = 0; i < 13; i++)
for (j = 0; j < 13; j++)
{
// E和EC进行取小运算
if (Input1_Terms_Membership[Input1_Terms_Index][i] < Input2_Terms_Membership[Input2_Terms_Index][j])
R1[i][j] = Input1_Terms_Membership[Input1_Terms_Index][i];
else
R1[i][j] = Input2_Terms_Membership[Input2_Terms_Index][j];
// 转换R1矩阵为R2一维向量
R2[k] = R1[i][j];
k++;
}
///<A=Input1_Terms_Membership[Input1_Terms_Index],B=Input2_Terms_Membership[Input2_Terms_Index]
///<R1=AXB建立13x13的矩阵,R2=R1'把矩阵转成169x1的列向量
for (i = 0; i < 169; i++)
for (j = 0; j < 13; j++)
{
// R1(E, EC)与U进行取小运算
if (R2[i] < Output_Terms_Membership[Output_Terms_Index][j])
R3[i][j] = R2[i];
else
R3[i][j] = Output_Terms_Membership[Output_Terms_Index][j];
// R进行取大运算，为所有规则模糊关系的并集
if (R3[i][j] > R[i][j])
R[i][j] = R3[i][j];
}
}
/*************************对于每种可能的E、EC的精确取值模糊化后进行推理得到模糊输出Cd，Cd=(AdxBd)oR*************************/
for (Input1_value_index = 0; Input1_value_index < 13; Input1_value_index++) {
for (Input2_value_index = 0; Input2_value_index < 13; Input2_value_index++)
{
for (j = 0; j < 13; j++)
Cd[j] = 0;
int kd = 0;
float temp = 0;
Max_Input1_value = E_MAX(Input1_value_index); ///<找出误差隶属度最大的语言值
Max_Input2_value = EC_MAX(Input2_value_index); ///<找出误差变化率隶属度最大的语言值
for (i = 0; i < 13; i++)
for (j = 0; j < 13; j++)
{
// E(Ad)和EC(Bd)进行取小运算
if (Input1_Terms_Membership[Max_Input1_value][i] < Input2_Terms_Membership[Max_Input2_value][j])
AdBd1[i][j] = Input1_Terms_Membership[Max_Input1_value][i];
else
AdBd1[i][j] = Input2_Terms_Membership[Max_Input2_value][j];
AdBd2[kd] = AdBd1[i][j];
kd++;
}
for (i = 0; i < 169; i++)
for (j = 0; j < 13; j++)
{
// 模糊矩阵的合成，将乘积运算换成“取小”，将加法运算换成“取大”
if (AdBd2[i] < R[i][j])
temp = AdBd2[i];
else
temp = R[i][j];
if (temp > Cd[j])
Cd[j] = temp;
}
/*************************去模糊化（加权平均法），计算实际输出*************************/
float sum1 = 0, sum2 = 0;
float OUT;
for (i = 0; i < 13; i++)
{
sum1 = sum1 + Cd[i];
sum2 = sum2 + Cd[i] * SPEED[i];
}
OUT = (int)(sum2 / sum1 + 0.5);///<四舍五入
Fuzzy_Table[Input1_value_index][Input2_value_index] = OUT;
cout << OUT << ",";
}
cout << endl;
}}123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124
3.模糊查询表设置车速
将模糊查询表复制进入代码程序，将实际的e和ec映射到论域中后，在模糊查询表中查询结果并设置目标车速。
int_16 Fuzzy_Table[13][13]= { 203,211,211,211,226,226,230,230,228,210,210,210,210,209,221,221,221,238,238,241,241,237,231,231,231,227,209,221,221,221,238,238,241,241,237,231,231,231,227,209,221,221,221,238,238,241,241,237,231,231,231,227,215,238,238,238,245,245,266,266,246,237,237,237,232,215,238,238,238,245,245,266,266,246,237,237,237,232,218,250,250,250,276,276,283,283,280,245,245,245,216,218,250,250,250,276,276,283,283,280,245,245,245,216,232,240,240,240,250,250,271,271,246,236,236,236,217,226,230,230,230,236,236,239,239,236,214,214,214,208,226,230,230,230,236,236,239,239,236,214,214,214,208,226,230,230,230,236,236,239,239,236,214,214,214,208,211,211,211,211,226,226,230,230,228,208,208,208,203} ;int_16 get_speed_set(void) {
int_16 E = 0, EC = 0;
int_16 speed_target;
static int_16 re_pos = 0, ek = 0, eck = 0;
float ke = 400, kec = 10;
ek = 2500 - row;
eck = 2500 - row - re_pos;
re_pos = ek;
if (ek > 0) {
E = (int_32)(ek / ke + 0.5);
}
else {
E = (int_32)(ek / ke - 0.5);
}
//将E的论域转换到模糊控制器的论域
if (E > 6)
E = 6;
else if (E < -6)
E = -6;
if (eck > 0) {
EC = (int_16)(eck / kec + 0.5);
}
else {
EC = (int_16)(eck / kec - 0.5);
}//将EC的论域转换到模糊控制器的论域
if (EC > 6)
EC = 6;
else if (EC < -6)
EC = -6;
speed_target = (int_16)(Fuzzy_Table[E + 6][EC + 6]);
return speed_target ;}12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455
调好参数，完胜PID
大功告成~