File content as of revision 5:f225e0c61cfc:

//特別研究Ⅰで用いたプログラムを改良したもの
//ねじ運動を入力し,0.01秒ごとに1脚について各関節角度を出力する
//brent法の部分は『numerical recipes in c』 参照
#include "mbed.h"
#include <PCA9685.h> 
#include "Eigen/Geometry.h"
#include "Eigen/Dense.h"
#include <math.h>

#define ITMAX 100
#define CGOLD 0.3819660
#define SHIFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);
#define ZEPS 1.0e-10
#define GOLD 1.618034
#define TINY 1.0e-20
#define GLIMIT 100.0
#define SERVOMIN 700       
#define SERVOMAX 2300
#define SERVOGAIN 29.6296300
#define PI 3.14159265358979323846264338327950288

PCA9685 pwm;//クラス宣言
Serial pc2(USBTX,USBRX);
Timer tim;
Timer manage;
int times= 200;//実行回数:実行時間は (sampling)*(times)秒

using namespace Eigen;

//以下変数定義

//brent法に必要な変数
double ax=-0.1*PI/180.0,bx=0.1*PI/180.0,cx=0.0;
double fa,fb,fc;
//サーボの書き込みに必要な変数
double servo0[16]={7700.0, 5850.0, 7050.0, 6850.0, 6000.0, 6300.0, 8400.0, 7200.0, 6700.0, 7000.0, 5650.0, 8400.0, 6000.0, 5100.0, 5600.0, 6570.0};//servoの初期値
int ch[4][4]={{0 ,1 ,2 ,3} ,
              {4 ,5 ,6 ,7} ,
              {8 ,9 ,10,11},
              {12,13,14,15} };
double r=0.0*PI/180;//斜面の傾き[°]
double sampling=0.01;//δtの時間[s]
double L[4] = {65.0,35.0,110.0,38.0};//4本のリンク長 後から足したのでL[3]を理論中のL0に対応させる
double tip[4][3];//足先座標
double con[4][3] = {  {-55.0, 55.0,0.0},
                      { 55.0, 55.0,0.0},
                      { 55.0,-55.0,0.0},
                      {-55.0,-55.0,0.0}};//脚のコーナー座標,zは必ず0
double th_ready[4][4] = { {135 * PI / 180, 30 * PI / 180, -75 * PI / 180, -30 * PI / 180},
                          {45  * PI / 180, 30 * PI / 180, -75 * PI / 180, -30 * PI / 180},
                          {-45  * PI / 180, 30 * PI / 180, -75 * PI / 180, -30 * PI / 180},
                          {-135 * PI / 180, 30 * PI / 180, -75 * PI / 180, -30 * PI / 180} };//初期状態                   
double th0[4][4]= { 0.0,0.0,0.0,0.0, 
                    0.0,0.0, 0.0,0.0, 
                    0.0,0.0, 0.0,0.0, 
                    0.0,0.0, 0.0,0.0 }; //計算用の関節角度
double th[4][4];//サーボに入力する角度                    
double Jacbi[4][3][4];//ヤコビアン 脚数×関節×次元
double a,a0, h,fi;//評価関数内の変数 fi=φ
double X,tan_u, tan_d;//計算用

//ねじ軸
//Lin:方向, L0:原点座標, vin:ねじ時に沿った速度, win:角速度ベクトルの大きさ
double Lin[3], L0[3]={0.0,0.0,0.0}, vin,v[3],wg[3],win,nol;//ねじ軸条件 
double dfdth[4];//評価関数のナブラ


//以下行列定義
MatrixXd Q(3, 3);//Q行列
MatrixXd R(3, 4);//R行列
Vector3d vP[4];//各脚の速度ベクトル


void QR(int leg);//QR分解用関数,引数は脚番号
void vp(int leg);//引数は脚番号,与条件から各脚先の速度を導出する
void fwd(int leg);//順運動学より脚先の座標を導出する
void Jac(int leg);//指定した脚のヤコビアンを計算
void deff(int leg);//評価関数計算, legは距離と傾きから指定する
void dfd( int leg);//評価関数の勾配をとる
double search(int leg);//最大のthetaを探索するための関数
void solve(double w3,int leg,int det);//theta3の角速度から全関節の関節角度を導き出す
double fe(int leg,double dth3);//brent法に合わせてeを関数化,search文を一部抜粋したもの
double num_nolm(int leg , double dth3);//ノルム最小の解を導く際に使用する関数
double f(int leg,double dth3);//テーラー展開第1項の値を返す, brent法用
void mnbrak(int leg,int discrimination);//brentに必要な極小値の囲い込んだ3点を決定する関数
double brent(int leg,double min,double mid,double max,double tol,int discrimination);//brent法により1次元探索するプログラム 
//discrimination 0:谷側(fe), 1:山側(nolm), 2:谷側(f),3:テスト用の関数(f_test)
double SIGN(double x,double y);//xにyの符号をつけたものを返す
double FMAX(double x,double y);//大きいほうの値が返される
double f_test(double x);//テスト用の関数

//以下サーボ関係
void setup_servo();//サーボセットアップ用関数
void servo_write(int ch,double ang);//angに
void servo_write7(int ch, double ang);
void servo_calib();//全ての角度を0度にする
void servo_ready();//初期状態

int main()
{ 
    double t;
    pc2.baud(921600);
    //setup_servo();
    for(int u=0; u<4; u++)
    {
     for(int i=0; i<4; i++)
     {
        th[u][i]=th_ready[u][i];
        }
    }
    for(int i=0; i<4; i++)
     {
        fwd(i);
        }
    //servo_ready();
    wait(2);
    //while(1);
    /*for(int u=0; u<4; u++)
    {
     for(int i=0; i<4; i++)
     {
        servo_write(ch[u][i],th[u][i]);
        }
        }*/
    //while(1);    
    wait(2);    
    int count = 0;
    //入力したねじ運動を換算する
    Lin[0] = cos(30.0*PI/180); //ねじ軸x
    Lin[1] = sin(30.0*PI/180); //ねじ軸y
    Lin[2] = 0.0;//ねじ軸z
    L0[0] = 0.0;//ねじ軸原点座標
    L0[1] = 0.0;
    L0[2] = 0.0;
    vin = 0.0;
    win = 2.0;
    printf("\r\n\r\n");
    nol = (double)sqrt(Lin[0] * Lin[0] + Lin[1] * Lin[1] + Lin[2] * Lin[2]);
    for (int i = 0; i < 3; i++)
    {
        wg[i] = Lin[i] * win / nol;
        v[i] = Lin[i] * vin / nol;
    }
    //printf("%lf , %lf , %lf",vP[0](0,0), vP[0](1, 0), vP[0](2, 0));

    //times*δtの時間だけサーボを動かす
    tim.start();
    
    manage.start();
    //for (int i = 0; i < times;i++){
    while(tim.read()<=5.0) {   
        int l=2;
        //count = count + 1;
        double dth;
        //for(int l=0;l<4;l++)
        //{
            //////////計算部/////////////////
            t=tim.read();
            fwd(l);
            pc2.printf("%3.3lf %3.4lf %3.4lf %3.4lf\r\n",t,tip[l][0],tip[l][1],tip[l][2]);
            vp(l);
            Jac(l);
            QR(l);
            deff(l);
            dfd(l);
            ax=-0.15*PI/180.0;bx=0.15*PI/180.0;cx=0.0;
            //2:谷,1:山
            mnbrak(l,2);
            dth=brent(l,ax,bx,cx,0.01,2);
            solve(dth, l, 1);
            ////////////////////////////////
            ///*
      //}      
            /*for(int u=0; u<4; u++)
            {
              for(int i=0; i<4; i++)
              { 
               servo_write(ch[u][i],th[u][i]);
               }
             }//*/    
        //t=tim.read();
        //pc2.printf("%2.4lf:( %3.3lf, %3.3lf, %3.3lf, %3.3lf )\n\r",t,th[0][0]*180/PI,  th[1][0]*180/PI , th[2][0]*180/PI , th[3][0]*180/PI );
        //pc2.printf("%2.4lf:( %3.3lf, %3.3lf, %3.3lf, %3.3lf )\n\r",t,th[0][1]*180/PI,  th[1][1]*180/PI , th[2][1]*180/PI , th[3][1]*180/PI );
        //pc2.printf("%2.4lf:( %3.3lf, %3.3lf, %3.3lf, %3.3lf )\n\r",t,th[0][2]*180/PI,  th[1][2]*180/PI , th[2][2]*180/PI , th[3][2]*180/PI );
        //pc2.printf("%2.4lf:( %3.3lf, %3.3lf, %3.3lf, %3.3lf )\n\r",t,th[0][3]*180/PI,  th[1][3]*180/PI , th[2][3]*180/PI , th[3][3]*180/PI );
        //pc2.printf("%2.4lf:x( %3.3lf, %3.3lf, %3.3lf, %3.3lf )y( %3.3lf, %3.3lf, %3.3lf, %3.3lf )z( %3.3lf, %3.3lf, %3.3lf, %3.3lf )\n\r",
        //t,tip[0][0],tip[1][0],tip[2][0],tip[3][0],tip[0][1],tip[1][1],tip[2][1],tip[3][1],tip[0][2],tip[1][2],tip[2][2],,tip[3][2]);
        //pc2.printf("\r\n");
        while(1)
        {
            if(manage.read()>sampling)break;
            }
        manage.reset();    
            
        }
        t=tim.read();
        wait(3);
        servo_ready();
    return 0;               // ソフトの終了 
}

void QR(int leg) {
    double s, t;//要素計算用
    MatrixXd ma(3, 4), ma1(3, 4);
    
    ma << Jacbi[leg][0][0], Jacbi[leg][0][1], Jacbi[leg][0][2], Jacbi[leg][0][3],
        Jacbi[leg][1][0], Jacbi[leg][1][1], Jacbi[leg][1][2], Jacbi[leg][1][3],
        Jacbi[leg][2][0], Jacbi[leg][2][1], Jacbi[leg][2][2], Jacbi[leg][2][3];
    
    //ハウスホルダー変換1回目
    MatrixXd A1(3, 3);
    A1 << 1.0, 0.0, 0.0,
        0.0, 1.0, 0.0,
        0.0, 0.0, 1.0;

    s = (double)sqrt(ma(0, 0) * ma(0, 0) + ma(1, 0) * ma(1, 0) + ma(2, 0) * ma(2, 0));//分母のやつ

    MatrixXd H1(3, 3);//1回目の行列
    MatrixXd X11(3, 1), X12(1, 3);
    Vector3d a11, a12;//a11が変換前,a12が変換後
    a11 << ma(0, 0), ma(1, 0), ma(2, 0);
    a12 << s, 0.0, 0.0;
    X11 = a11 - a12;
    X12 = X11.transpose();
    t = (double)sqrt(X11(0, 0) * X11(0, 0) + X11(1, 0) * X11(1, 0) + X11(2, 0) * X11(2, 0));
    H1 = A1 - 2.0 * (X11 * X12) / (t * t);
    ma1 = H1 * ma;
    //2回目
    MatrixXd H2(3, 3), A2(2, 2), h2(2, 2);
    A2 << 1.0, 0.0,
        0.0, 1.0;
    Vector2d a21, a22;
    MatrixXd X21(2, 1), X22(1, 2);
    a21 << ma1(1, 1), ma1(2, 1);
    s = (double)sqrt(ma1(1, 1) * ma1(1, 1) + ma1(2, 1) * ma1(2, 1));
    a22 << s, 0;
    X21 = a21 - a22;
    X22 = X21.transpose();
    t = (double)sqrt(X21(0, 0) * X21(0, 0) + X21(1, 0) * X21(1, 0));
    h2 = A2 - 2 * (X21 * X22) / (t * t);
    H2 << 1.0, 0.0, 0.0,
        0.0, h2(0, 0), h2(0, 1),
        0.0, h2(1, 0), h2(1, 1);
    R = H2 * ma1;
    MatrixXd H1T(3, 3), H2T(3, 3);
    H1T = H1.transpose();
    H2T = H2.transpose();
    Q = H1T * H2T;    
}

void vp(int leg) {//5年生の時に作成したもの
    double crosx, crosy, crosz;
    double wA[3] = { (double)(wg[0] * PI / 180.0),(double)(wg[1] * PI / 180.0),(double)(wg[2] * PI / 180.0) };
    double vA[3] = { (-v[0]),(-v[1]) ,(-v[2]) };
    double AP[3] = { (tip[leg][0] - L0[0]),(tip[leg][1] - L0[1]),tip[leg][2] - L0[2] };
    if (Lin[2] != 0.0)
    {
        double LP[3] = { -(Lin[0] / nol) / (Lin[2] / nol) * tip[leg][2],-(Lin[1] / nol) / (Lin[2] / nol) * tip[leg][2],0.0 };
        for (int i = 0; i < 3; i++) { AP[i] = AP[i] - LP[i]; }
        AP[2] = 0.0;
    }
    crosx = AP[1] * wA[2] + (-AP[2]) * wA[1];
    crosy = AP[2] * wA[0] + (-AP[0]) * wA[2];
    crosz = AP[0] * wA[1] + (-AP[1]) * wA[0];
    vP[leg] << crosx + vA[0], crosy + vA[1], crosz + vA[2];
    //printf(" %lf,%lf,%lf\n", -v[0], -v[1], -v[2]);
    //pc2.printf("input motion %d %lf,%lf,%lf\n\r", leg, vP[leg](0, 0), vP[leg](1, 0), vP[leg](2, 0));
    //printf("vp finish\n");
}
void fwd(int leg) {
    //printf("fwd start\n");
    double c0 = (double)cos(th[leg][0]), s0 = (double)sin(th[leg][0]), c1 = (double)cos(th[leg][1]), s1 = (double)sin(th[leg][1]),
        c12 = (double)cos(th[leg][1] + th[leg][2]), s12 = (double)sin(th[leg][1] + th[leg][2]), c123 = (double)cos(th[leg][1] + th[leg][2] + th[leg][3]),
        s123 = (double)sin(th[leg][1] + th[leg][2] + th[leg][3]);
    tip[leg][0] = (L[3]+L[0] * c1 + L[1] * c12 + L[2]*c123) * c0 + con[leg][0];  //x
    tip[leg][1] = (L[3]+L[0] * c1 + L[1] * c12 + L[2] * c123) * s0 + con[leg][1];  //y
    tip[leg][2] = L[0] * s1 + L[1] * s12+L[2]*s123; //z
    //pc2.printf("leg=%d,(  %3.3lf,  %3.3lf,  %3.3lf))  ",leg,tip[leg][0],tip[leg][1],tip[leg][2]);
}
void Jac(int leg) {
    //printf("Jac start\n");
    double c0 = (double)cos(th[leg][0]), s0 = (double)sin(th[leg][0]), c1 = (double)cos(th[leg][1]), s1 = (double)sin(th[leg][1]),
        c12 = (double)cos(th[leg][1] + th[leg][2]), s12 = (double)sin(th[leg][1] + th[leg][2]), c123 = (double)cos(th[leg][1] + th[leg][2] + th[leg][3]),
        s123 = (double)sin(th[leg][1] + th[leg][2] + th[leg][3]);
    Jacbi[leg][0][0] = -s0 * (L[3]+L[0] * c1 + L[1] * c12 + L[2] * c123);
    Jacbi[leg][0][1] = (-L[0] * s1 - L[1] * s12 - L[2] * s123) * c0;
    Jacbi[leg][0][2] = (-L[1] * s12 - L[2] * s123) * c0;
    Jacbi[leg][0][3] = (-L[2] * s123) * c0;

    Jacbi[leg][1][0] = c0 * (L[3]+L[0] * c1 + L[1] * c12 + L[2] * c123);
    Jacbi[leg][1][1] = (-L[0] * s1 - L[1] * s12 - L[2] * s123) * s0;
    Jacbi[leg][1][2] = (-L[1] * s12 - L[2] * s123) * s0;
    Jacbi[leg][1][3] = (-L[2] * s123) * s0;

    Jacbi[leg][2][0] = 0.0;
    Jacbi[leg][2][1] = L[0] * c1 + L[1] * c12 + L[2] * c123;
    Jacbi[leg][2][2] = L[1] * c12 + L[2] * c123;
    Jacbi[leg][2][3] = L[2] * c123;


    //printf("Jac finish\n");
}//ok
void deff(int leg) {
    //printf(" 評価関数定義\n");
    fi = r  + atan2(-tip[leg][2], (double)sqrt((tip[leg][0]) * (tip[leg][0]) + (tip[leg][1]) * (tip[leg][1])));//y,xの順
    a0 = (double)sqrt((tip[leg][0]) * (tip[leg][0]) + (tip[leg][1]) * (tip[leg][1]) + (tip[leg][2]) * (tip[leg][2]));
    a = a0 * (double)cos(fi);
    h = a * (1 / (double)cos(fi) - tan(fi));
    X = tip[leg][2]*(double)sqrt((tip[leg][0]* (tip[leg][0])) + (tip[leg][1]) * (tip[leg][1]));//tan-1の中身
    //tan-1の分母分子
    tan_u = tip[leg][2];
    tan_d = (double)sqrt((tip[leg][0]) * (tip[leg][0]) + (tip[leg][1]) * (tip[leg][1]));
    //printf("評価関数計算完了\n");
}
void dfd(int leg) {
    //printf("評価関数微分\n");
    double c0 = (double)cos(th[leg][0]), s0 = (double)sin(th[leg][0]), c1 = (double)cos(th[leg][1]), s1 = (double)sin(th[leg][1]), s2 = (double)sin(th[leg][2]), s3 = (double)sin(th[leg][2]);
    double c12 = (double)cos(th[leg][1] + th[leg][2]), s12 = (double)sin(th[leg][1] + th[leg][2]), s23 = (double)sin(th[leg][2] + th[leg][3]), c23 = (double)cos(th[leg][2] + th[leg][3]);
    double c123 = (double)cos(th[leg][1] + th[leg][2] + th[leg][3]), s123 = (double)sin(th[leg][1] + th[leg][2] + th[leg][3]);
    double cfi=cos(fi),sfi=sin(fi);
    double x=tip[leg][0],y=tip[leg][1],z=tip[leg][2];
    
    double df_da=1/cfi-tan(fi);
    double df_dfi=a*(-sfi-1)/(cfi*cfi);
    double da_dx=x*cfi/sqrt(x*x+y*y);
    double da_dy=y*cfi/sqrt(x*x+y*y);
    double da_dfi=-sqrt(x*x+y*y)*sfi;
    double dfi_dx=-x*z/((x*x+y*y+z*z)*sqrt(x*x+y*y));
    double dfi_dy=-y*z/((x*x+y*y+z*z)*sqrt(x*x+y*y));
    double dfi_dz=sqrt(x*x+y*y)*z/(x*x+y*y+z*z);
   
    dfdth[0]=df_da*(da_dx*Jacbi[leg][0][0]+da_dy*Jacbi[leg][1][0]+da_dfi*(dfi_dx*Jacbi[leg][0][0]+dfi_dy*Jacbi[leg][1][0]+dfi_dz*Jacbi[leg][2][0]))
             +df_dfi*(dfi_dx*Jacbi[leg][0][0]+dfi_dy*Jacbi[leg][1][0]+dfi_dz*Jacbi[leg][2][0]); 
             
    dfdth[1]=df_da*(da_dx*Jacbi[leg][0][1]+da_dy*Jacbi[leg][1][1]+da_dfi*(dfi_dx*Jacbi[leg][0][1]+dfi_dy*Jacbi[leg][1][1]+dfi_dz*Jacbi[leg][2][1]))
             +df_dfi*(dfi_dx*Jacbi[leg][0][1]+dfi_dy*Jacbi[leg][1][1]+dfi_dz*Jacbi[leg][2][1]);
              
    dfdth[2]=df_da*(da_dx*Jacbi[leg][0][2]+da_dy*Jacbi[leg][1][2]+da_dfi*(dfi_dx*Jacbi[leg][0][2]+dfi_dy*Jacbi[leg][1][2]+dfi_dz*Jacbi[leg][2][2]))
             +df_dfi*(dfi_dx*Jacbi[leg][0][2]+dfi_dy*Jacbi[leg][1][2]+dfi_dz*Jacbi[leg][2][2]); 
    
    dfdth[3]=df_da*(da_dx*Jacbi[leg][0][3]+da_dy*Jacbi[leg][1][3]+da_dfi*(dfi_dx*Jacbi[leg][0][3]+dfi_dy*Jacbi[leg][1][3]+dfi_dz*Jacbi[leg][2][3]))
             +df_dfi*(dfi_dx*Jacbi[leg][0][3]+dfi_dy*Jacbi[leg][1][3]+dfi_dz*Jacbi[leg][2][3]);                              
   
   //pc2.printf("df_da=%lf  df_dfi=%lf  da_dx=%lf  da_dy=%lf  da_dfi=%lf  dfi_dx=%lf  dfi_dy=%lf  dfi_dz=%lf\r\n",df_da,df_dfi,da_dx,da_dy,da_dfi,dfi_dx,dfi_dy,dfi_dz);  
}
//使わない
double fe(int leg,double dth3) {
    //brent法のための関数, 事前にdfdを実行してから使う
    double dfd_nolm,th0_nolm,e=0.0;
    //∇hを正規化する
    dfd(leg);
    dfd_nolm = sqrt(dfdth[0]* dfdth[0]+ dfdth[1]* dfdth[1]+ dfdth[2]* dfdth[2]+ dfdth[3]* dfdth[3]);
    for (int i = 0; i < 4; i++) {
        dfdth[i]=dfdth[i]/dfd_nolm;
    }
    
    solve(dth3, leg, 2);//後退代入でほかの3つのパラメータを導出
    
    //dthベクトルを正規化
    th0_nolm = sqrt(th0[leg][0] * th0[leg][0]+ th0[leg][1]* th0[leg][1]+ th0[leg][2]* th0[leg][2]+ th0[leg][3]*th0[leg][3]);
    for (int i = 0; i < 4; i++) {
        th0[leg][i] = th0[leg][i] / th0_nolm;
    }
    for (int i = 0; i < 4; i++) {
         e += (th0[leg][i] - dfdth[i]) * (th0[leg][i] - dfdth[i]);
    }    
    return e;//eベクトルのノルムの2乗を返す

    }
double f(int leg,double dth3) {
    double f_return=0.0;
    solve(dth3, leg, 2);//後退代入でほかの3つのパラメータを導出
    f_return=dfdth[0]*th0[leg][0]+dfdth[1]*th0[leg][1]+dfdth[2]*th0[leg][2]+dfdth[3]*th0[leg][3];   
    
    return -f_return;//テイラー展開第二項を返すがbrent法は極小値を求めるため、符号を反転させる

    } 
void mnbrak(int leg,int discrimination)
{
    double ulim,u,r,q,fu,fu_2,dum,fa,fb,fc;
    //fa=f(ax);
    //fb=f(bx);
    if(discrimination==0){fa=fe(leg,ax);fb=fe(leg,bx);}
    if(discrimination==1){fa=num_nolm(leg,ax);fb=num_nolm(leg,bx);}
    if(discrimination==2){fa=f(leg,ax);fb=f(leg,bx);}
    if(discrimination==3){fa=f_test(ax);fb=f_test(bx);}
    
    if(fb>fa)
    {
        SHIFT(dum,ax,bx,dum);
        SHIFT(dum,fb,fa,dum);
        }
    cx=bx+GOLD*(bx-ax);
    //fc=f(cx);
    if(discrimination==0){fc=fe(leg,cx);}
    if(discrimination==1){fc=num_nolm(leg,cx);}
    if(discrimination==2){fc=f(leg,cx);}
    if(discrimination==3){fc=f_test(cx);}
    while (fb>fc)
    {
        r=(bx-ax)*(fb-fc);
        q=(bx-cx)*(fb-fa);
        u=bx-((bx-cx)*q-(bx-cx)*r)/
        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));
        ulim=bx+GLIMIT*(cx-bx);
        
        if((bx-u)*(u-cx)>0.0)
        {
            //fu=f(u);
            if(discrimination==0){fu=fe(leg,u);}
            if(discrimination==1){fu=num_nolm(leg,u);}
            if(discrimination==2){fu=f(leg,u);}
            if(discrimination==3){fu=f_test(u);}
            if(fu<fc)
            {
                ax=bx;
                bx=u;
                fa=fb;
                fb=fu;
                return;
                }
            else if(fu>fb)
            {
                cx=u;
                fc=fu;
                return;
                }
             u=cx*+GOLD*(cx-bx);
             //fu=f(u);
             if(discrimination==0){fu=fe(leg,u);}
             if(discrimination==1){fu=num_nolm(leg,u);}
             if(discrimination==2){fu=f(leg,u);}
             if(discrimination==3){fu=f_test(u);}       
            }
        else if((cx-u)*(u-ulim)>0.0)
        {
            //fu=f(u);
            if(discrimination==0){fu=fe(leg,u);}
            if(discrimination==1){fu=num_nolm(leg,u);}
            if(discrimination==2){fu=f(leg,u);}
            if(discrimination==3){fu=f_test(u);}
            if(fu<fc)
            {
                SHIFT(bx,cx,u,cx+GOLD*(cx-bx));
                if(discrimination==0){fu_2=fe(leg,u);}
                if(discrimination==1){fu_2=num_nolm(leg,u);}
                if(discrimination==2){fu_2=f(leg,u);}
                if(discrimination==3){fu_2=f_test(u);}
                //SHIFT(fb,fc,fu,f(u));
                SHIFT(fb,fc,fu,fu_2);
                }
            
            }
        else if((u-ulim)*(ulim-cx)>=0.0)
        {
            u=ulim;
            //fu=f(u);
            if(discrimination==0){fu=fe(leg,u);}
            if(discrimination==1){fu=num_nolm(leg,u);}
            if(discrimination==2){fu=f(leg,u);}
            if(discrimination==3){fu=f_test(u);}
            }
        else
        {
            u=cx+GOLD*(cx-bx);
            //fu=f(u);
            if(discrimination==0){fu=fe(leg,u);}
            if(discrimination==1){fu=num_nolm(leg,u);}
            if(discrimination==2){fu=f(leg,u);}
            if(discrimination==3){fu=f_test(u);}
            }
        SHIFT(ax,bx,cx,u);
        SHIFT(fa,fb,fc,fu);
        }
    }
double brent(int leg,double min,double mid,double max,double tol,int discrimination)//成功したやつ
{

    int iter;
    double a,b,d,etemp,fu,fv,fw,fx,p,q,r,tol1,tol2,u,v,w,x,xm,xmin;
    double e=0.0;
    a=(ax <cx ? ax : cx);
    b=(ax >cx ? ax : cx);
    x=w=v=bx;
    if(discrimination==0){fw=fv=fx=fe(leg,x);}
    if(discrimination==1){fw=fv=fx=num_nolm(leg,x);}
    if(discrimination==2){fw=fv=fx=f(leg,x);}
    if(discrimination==3){fw=fv=fx=f_test(x);}
    //fw=fv=fx=f(x);//関数部分
    for(iter=1;iter<=ITMAX;iter++)
    {
        xm=0.5*(a+b);
        tol2=2.0*(tol1=tol*fabs(x)+ZEPS);
        //pc2.printf("x =%lf,w = %lf,u = %lf\n\r",x,w,u);
        if(fabs(x-xm)<=(tol2-0.5*(b-a)))
        {
            //pc.printf("bernt out");
            xmin=x;
             //pc2.printf("xmin=%lf\r\n",x);
             //pc2.printf("fx=%lf\r\n",fx);
            return xmin;
        }
        if(fabs(e)>tol1)
        {
            r=(x-w)*(fx-fv);
            q=(x-v)*(fx-fw);
            p=(x-v)*q-(x-w)*r;
            q=2.0*(q-r);
            if(q>0.0)p=-p;
            q=fabs(q);
            etemp=e;
            e=d;
            if(fabs(p)>=fabs(0.5*q*etemp)||p<=q*(a-x)||p>=q*(b-x))
            {  d=CGOLD*(e= (x>=xm ? a-x : b-x));}
            else
            {
               d=p/q;
               u=x+d;
               if(u-a < tol2 || b-u < tol2)
               {d=SIGN(tol1,xm-x);}
            }
        }
        else
        {
            d=CGOLD*(e= (x>=xm ? a-x : b-x));
            }    
        u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));
        if(discrimination==0){fu=fe(leg,u);}
        if(discrimination==1){fu=num_nolm(leg,u);}
        if(discrimination==2){fu=f(leg,u);}
        if(discrimination==3){fu=f_test(u);}
        //fu=f(u);//関数部分
         if(fu <= fx)
         {
            if(u >= x)a=x; else b=x;
            SHIFT(v,w,x,u);
            SHIFT(fv,fw,fx,fu);
          }
         else{
          if(u < x){a=u;} 
          else {b=u;}
          if(fu <= fw || w==x)
          {
              v=w;
              w=u;
              fv=fw;
              fw=fu;
              }    
          else if (fu <= fv || v==x || v==w)
          {
            v=u;
            fv=fu;
          }
        }
        
        }
        //pc2.printf("xmin=%lf\r\n",x);
        //pc2.printf("fx=%lf\r\n",fx);
    return xmin;
    }           

double SIGN(double x,double y)
{
    double x_return;
    x_return=abs(x);
    if(y<0.0)x_return=-x_return;
    
    return x_return; 
    }
double FMAX(double x, double y)
{
    if(x>y){return x;}
    if(y>x){return y;}
    return 0;
    }      
double num_nolm(int leg,double dth3)
{
    
    double nolm_return=0.0;
    solve(dth3,leg,2);
    nolm_return=th0[leg][0]*th0[leg][0]+th0[leg][1]*th0[leg][1]+th0[leg][2]*th0[leg][2]+th0[leg][3]*th0[leg][3];
    
    return nolm_return;    
    }
//brent法のテスト用の関数    
//極小値を求めたい関数を定義    
double f_test(double x){
    double x_return;
    x_return=x*x-2*x+1;
    return x_return;
    }              
void solve(double w3, int leg,int det) {
   
    double dth[4];
    MatrixXd v_Q(3,1),QT(3,3);

    QT = Q.transpose();
    v_Q = QT * vP[leg]*sampling;
   
    dth[3] = w3 ;
    dth[2] = (double)((v_Q(2, 0) - R(2, 3) * dth[3]) / R(2, 2));
    dth[1] = (double)((v_Q(1, 0) - R(1, 2) * dth[2] - R(1, 3) * dth[3]) / R(1, 1));
    dth[0] = (double)((v_Q(0, 0) - R(0, 1) * dth[1] - R(0, 2)*dth[2] - R(0, 3) * dth[3])/R(0,0));
    if (det == 1) {
        for (int i=0; i < 4; i++) {
            th[leg][i] = th[leg][i] + dth[i];
        }
    }
    else if (det == 2) {
        for (int u=0; u < 4; u++) {
            th0[leg][u] = dth[u];
        }
    }
            
}

//サーボ関係
void setup_servo() { 
 pwm.begin();               
 pwm.setPWMFreq(200);                
}
void servo_write(int ch,double ang)//引数は[°]
{
    if(ch==0)  ang=ang-135*PI/180;
    if(ch==4)  ang=ang-45*PI/180;
    if(ch==8)  ang=ang+45*PI/180;
    if(ch==12) ang=ang+135*PI/180;
    if( (ch!=2) && (ch!=5)&&(ch!=7) && (ch!=10) && (ch!=13)&&(ch!=15) )ang=-ang;
    ang=servo0[ch]+ang*8000/270*180/PI;
    servo_write7(ch,ang);
    }

void servo_write7(int ch, double ang){ 
  ang = ((ang-3500)/8000)*1600+700;//サーボモータ内部エンコーダは8000段階
  //pc2.printf("%d ang=%5.0lf \r\n ",ch,ang) ;                                               //初期状態を設定するときこの値を参考に設定したためそのまま利用　　 
  pwm.setPWM(ch, 0, ang);
}
void servo_calib()
{
    for(int u=0; u<4; u++)
    {
     for(int i=0; i<4; i++)
     {
        servo_write7(ch[u][i],servo0[ch[u][i]]);
        }
     }
}
void servo_ready()
{
    for(int u=0; u<4; u++)
            {
              for(int i=0; i<4; i++)
              { 
               servo_write(ch[u][i],th_ready[u][i]);
               }
             }
    }