File content as of revision 1:a12ef11ea8d6:

#include "mbed.h"
#include "Matrix.h"
#include "MatrixMath.h"

CAN can1(PD_0, PD_1);  // rd, td Transmitter 

//Ticker tick1;
//Ticker tick2;
//Ticker tick3;


const double Mn=9.8; //Nominalni moment
const double mi_x=1.2l; //Koeficijent trenja gume po x osi
const double mi_y=1.2l; //Koeficijent trenja gume po y osi
const double g=9.81;
const double m_sprung=1100; //sprung masa vozila
const double m_unsprung=110; //unsprung masa vozila
const double L=2.64; //Medjuosovinsko rastojanje
const double lf=1.35; //Rastojanje centra mase do prednje osovine
const double lr=L-lf; //Rastojanje centra mase do zadnje osovine
const double Wfl=1.458/2; //Rastojanje levog tocka od centra prednje osovine
const double Wfr=1.458/2; //Rastojanje desnog tocka od centra prednje osovine
const double Wrl=1.455/2; //Rastojanje levog tocka od centra zadnje osovine
const double Wrr=1.455/2; //Rastojanje desnog tocka od centra zadnje osovine
const double h=0.507; //Visina centra mase
const double Ixx=441; //Moment inercije oko x ose
const double Iyy=1748; //Moment inercije oko y ose
const double Izz=1945; //Moment inercije oko z ose
const double Ixy=0;
const double Iyz=0;
const double Ixz=0;
const double It=2; //Moment inercije tocka oko ose rotacije(uracunati i motor i planetarac)
const double rt=0.3; //poluprecnik pneumatika
const double Cv=1.14;  //koeficijent otpora vazduha
const double Ap=1.23;  //ref. ceona povrs
const double fo=0.011; //koef. kotrljanja staticki
const double ro=1.2; //gustina vazduha
const double kp=0.9; //Koeficijent efikasnosti planetarca PROVERITI
const double sw_ratio=12.0; //Prenosni odnos volana
const double N=12.3; //PROVERITI
const double Ts=0.002;


const double m[3]={m_sprung+m_unsprung, m_sprung+m_unsprung, m_sprung};// matrica mase

const double I[3][3]={
                    {Ixx, Ixy, Ixz},
                    {Ixy, Iyy, Iyz},
                    {Ixz, Iyz, Izz}
                    };// tenzor inercije

double I_inv[3][3];// inverzija tenzora inercije

const double Iw[4]={It, It, It, It};//momenti inercije tockova

const double mi[2][4]={
                     {1.2, 1.2, 1.3, 1.3},  // flx frx rlx rrx
                     {1.2, 1.2, 1.3, 1.3}   //fly fry rly rry
                     };//koeficijenti trenja gume po x i y osi za sve tockove

const double in[2][4]={
                     {0.8, 0.8, 0.9, 0.9},
                     {0.8, 0.8, 0.9, 0.9}
                     };// Coefficient of friction with infinite slip [no unit]

const double C[2][4]={
                    {70000, 70000, 100000, 100000},
                    {70000, 70000, 100000, 100000}
                    };//Cornering stiffness [x - N; y - N/rad]
                    
const double r[4]={rt, rt, rt, rt};// Matrica poluprecnika tockova [rfl rfr rrl rrr]

const double cs[4]={26125, 26125, 26125, 26125};//Spring effective stiffness [N/m]

const double ca[2]={12000, 15000};// Antiroll bar stiffnes [N/m]

const double cd[4]={2000, 2000, 2000, 2000};//Damper effective dampening [N*s/m]

const double p_init[3]={0, 0, h};// inital position of CM in global fixed coord sys [m]

const double v_init[3]={0, 0, 0};// inital velocity in body fixed coord sys [m/s]

const double pa_init[3]={0, 0, 0};// Initial roll pitch and yaw [rad]

const double va_init[3]={0, 0, 0};// initial roll pitch and yaw velocities [rad/s]

const double pw_init[3][4]={
                          {lf, lf, -lr, -lr},     //xfl xfr xrl xrr
                          {Wfl, -Wfr, Wrl, -Wrr},  //yfl yfr yrl yrr
                          {h, h, h, h}            //zfl zfr zrl zrr
                          };// initial wheel positions in body fixed coord sys
                          
const double w_init[4]={v_init[0]/rt, v_init[0]/rt, v_init[0]/rt, v_init[0]/rt} ;// Initial wheel angular speed around spin axis [rad/s]

const double mg_unsprung[4]={lr/(lr+lf)*Wfl/(Wfl+Wfr)*m_unsprung*g, lr/(lr+lf)*Wfr/(Wfl+Wfr)*m_unsprung*g, lf/(lr+lf)*Wrl/(Wrl+Wrr)*m_unsprung*g, lf/(lr+lf)*Wrr/(Wrl+Wrr)*m_unsprung*g};//Static weight distribution force [N] [Ffl Ffr Frl Frr]

const double mg_sprung[4]={m_sprung/m_unsprung*mg_unsprung[0], m_sprung/m_unsprung*mg_unsprung[1], m_sprung/m_unsprung*mg_unsprung[2], m_sprung/m_unsprung*mg_unsprung[3]}; //Static weight distribution force on acting on springs [N]

const double h_spring[4]={mg_sprung[0]/cs[0]+h, mg_sprung[1]/cs[1]+h, mg_sprung[2]/cs[2]+h, mg_sprung[3]/cs[3]+h};


double p[3]; //position in global coordinate system
double v[3]; //velocity in CM fixed coordinate system
double pa[3]; //angular position - x and y are in vehicle local and z is in global coordinate system
double va[3]; //angular velocity
double pw[3][4]; //wheel contact patch position in CM fixed coordinate system
double vw[3][4]; //wheel contact patch speed in CM fixed coordinate system
double w[4]; //wheel angular speed
double Fs[4]; //spring force from each wheel
double Fa[4]; //antiroll bar force from each wheel
double Fd[4]; //damper force from each wheel
double Fi[3][4]; //force of each wheel in CM fixed coordinate system

double FL[3];



double d=0;


double T_1=0, T_2=0, T_3=0, T_4=0;
double T_1p=0, T_2p=0, T_3p=0, T_4p=0;

int cnt=0;
volatile bool flag=0;


int brojac=0;
const unsigned int  RX_ID = 0x0184;
CANMessage messageOutVel1;
CANMessage messageOutVel2;
CANMessage messageOutVel3;
CANMessage messageOutVel4;


 
Serial pc(USBTX, USBRX);     
 
void initialize(){
    Matrix I_mat(3,3);
    I_mat<<Ixx<<Ixy<<Ixz
         <<Ixy<<Iyy<<Iyz
         <<Ixz<<Iyz<<Izz;
    
    Matrix I_mat_inv(3,3);
    I_mat_inv=MatrixMath::Inv(I_mat);
    
    I_inv[0][0]=I_mat_inv(1,1);
    I_inv[0][1]=I_mat_inv(1,2);
    I_inv[0][2]=I_mat_inv(1,3);
    
    I_inv[1][0]=I_mat_inv(2,1);
    I_inv[1][1]=I_mat_inv(2,2);
    I_inv[1][2]=I_mat_inv(2,3);
    
    I_inv[2][0]=I_mat_inv(3,1);
    I_inv[2][1]=I_mat_inv(3,2);
    I_inv[2][2]=I_mat_inv(3,3);
    
    p[0]=p_init[0];
    p[1]=p_init[1];
    p[2]=p_init[2];
    
    v[0]=v_init[0];
    v[1]=v_init[1];
    v[2]=v_init[2];
    
    pa[0]=pa_init[0];
    pa[1]=pa_init[1];
    pa[2]=pa_init[2];
    
    va[0]=va_init[0];
    va[1]=va_init[1];
    va[2]=va_init[2];
    
    pw[0][0]=pw_init[0][0];
    pw[0][1]=pw_init[0][1];
    pw[0][2]=pw_init[0][2];
    pw[0][3]=pw_init[0][3];
    
    pw[1][0]=pw_init[1][0];
    pw[1][1]=pw_init[1][1];
    pw[1][2]=pw_init[1][2];
    pw[1][3]=pw_init[1][3];
    
    pw[2][0]=pw_init[2][0];
    pw[2][1]=pw_init[2][1];
    pw[2][2]=pw_init[2][2];
    pw[2][3]=pw_init[2][3];
    
    w[0]=w_init[0];
    w[1]=w_init[1];
    w[2]=w_init[2];
    w[3]=w_init[3];
    
    
}

    
void model(double Tfl, double Tfr, double Trl, double Trr, double Steering_angle){
    double d=Steering_angle/sw_ratio;
    //////////////
    pw[2][0]=-(p[2]+pw[1][0]*sin(pa[0])-pw[0][0]*sin(pa[1]));
    pw[2][1]=-(p[2]+pw[1][1]*sin(pa[0])-pw[0][1]*sin(pa[1]));
    pw[2][2]=-(p[2]+pw[1][2]*sin(pa[0])-pw[0][2]*sin(pa[1]));
    pw[2][3]=-(p[2]+pw[1][3]*sin(pa[0])-pw[0][3]*sin(pa[1]));
    
    //pc.printf("pw \n");
    //pc.printf("%f  %f  %f %f\n",pw[0][0],pw[0][1],pw[0][2],pw[0][3]);
    //pc.printf("%f  %f  %f %f\n",pw[1][0],pw[1][1],pw[1][2],pw[1][3]);
    //pc.printf("%f  %f  %f %f\n",pw[2][0],pw[2][1],pw[2][2],pw[2][3]);
    //pc.printf("aaaaaaaa \n");
    /////////////
    vw[0][0]=v[0]-va[2]*pw[1][0];
    vw[0][1]=v[0]-va[2]*pw[1][1];
    vw[0][2]=v[0]-va[2]*pw[1][2];
    vw[0][3]=v[0]-va[2]*pw[1][3];
    
    vw[1][0]=v[1]+va[2]*pw[0][0];
    vw[1][1]=v[1]+va[2]*pw[0][1];
    vw[1][2]=v[1]+va[2]*pw[0][2];
    vw[1][3]=v[1]+va[2]*pw[0][3];
    
    vw[2][0]=v[2]+va[0]*pw[1][0]-va[1]*pw[0][0];
    vw[2][1]=v[2]+va[0]*pw[1][1]-va[1]*pw[0][1];
    vw[2][2]=v[2]+va[0]*pw[1][2]-va[1]*pw[0][2];
    vw[2][3]=v[2]+va[0]*pw[1][3]-va[1]*pw[0][3];

    //pc.printf("vw \n");
    //pc.printf("%f  %f  %f %f\n",vw[0][0],vw[0][1],vw[0][2],vw[0][3]);
    //pc.printf("%f  %f  %f %f\n",vw[1][0],vw[1][1],vw[1][2],vw[1][3]);
    //pc.printf("%f  %f  %f %f\n",vw[2][0],vw[2][1],vw[2][2],vw[2][3]);

    ////////////
    double cosin=cos(d);
    double sinus=sin(d);
    double p1 = cosin*vw[0][0]+sinus*vw[1][0];
    double p2 = cosin*vw[0][1]+sinus*vw[1][1];
    double p3 = -sinus*vw[0][0]+cosin*vw[1][0];
    double p4 = -sinus*vw[0][1]+cosin*vw[1][1];
    
    vw[0][0]=p1;
    vw[0][1]=p2;
    vw[1][0]=p3;
    vw[1][1]=p4;
    //pc.printf("vw 2 put \n");
    //pc.printf("%f  %f  %f %f\n",vw[0][0],vw[0][1],vw[0][2],vw[0][3]);
    //pc.printf("%f  %f  %f %f\n",vw[1][0],vw[1][1],vw[1][2],vw[1][3]);
    //pc.printf("%f  %f  %f %f\n",vw[2][0],vw[2][1],vw[2][2],vw[2][3]);

    ////////////
    double pw_dif[2]={0.5*(pw[2][0]-pw[2][1]),0.5*(pw[2][2]-pw[2][3])};
    
    //pc.printf("pw_dif \n");
    //pc.printf("%f   %f\n",pw_dif[0],pw_dif[1]);
    ///////////
    Fs[0]=cs[0]*(h_spring[0]+pw[2][0]);
    Fs[1]=cs[1]*(h_spring[1]+pw[2][1]);
    Fs[2]=cs[2]*(h_spring[2]+pw[2][2]);
    Fs[3]=cs[3]*(h_spring[3]+pw[2][3]);
    //pc.printf("Fs \n");
    //pc.printf("%.20f  %.20f  %.20f %.20f\n",Fs[0],Fs[1],Fs[2],Fs[3]);
    ///////////
    Fa[0]=ca[0]*pw_dif[0]*1+ca[1]*pw_dif[1]*0;
    Fa[1]=ca[0]*pw_dif[0]*(-1)+ca[1]*pw_dif[1]*0;
    Fa[2]=ca[0]*pw_dif[0]*0+ca[1]*pw_dif[1]*1;
    Fa[3]=ca[0]*pw_dif[0]*0+ca[1]*pw_dif[1]*(-1);
    //pc.printf("Fa \n");
    //pc.printf("%.20f  %.20f  %.20f %.20f\n",Fa[0],Fa[1],Fa[2],Fa[3]);
    //////////
    Fd[0]=-cd[0]*vw[2][0];
    Fd[1]=-cd[1]*vw[2][1];
    Fd[2]=-cd[2]*vw[2][2];
    Fd[3]=-cd[3]*vw[2][3];
    
    //pc.printf("Fd \n");
    //pc.printf("%.20f  %.20f  %.20f %.20f\n",Fd[0],Fd[1],Fd[2],Fd[3]);
    //////////
    Fi[2][0]=Fs[0]+Fd[0]+Fa[0]-mg_sprung[0];
    Fi[2][1]=Fs[1]+Fd[1]+Fa[1]-mg_sprung[1];
    Fi[2][2]=Fs[2]+Fd[2]+Fa[2]-mg_sprung[2];
    Fi[2][3]=Fs[3]+Fd[3]+Fa[3]-mg_sprung[3];
    //pc.printf("mg_sprung \n");
    //pc.printf("%.20f  %.20f  %.20f %.20f\n",mg_sprung[0],mg_sprung[1],mg_sprung[2],mg_sprung[3]);
    //pc.printf("Fi \n");
    //pc.printf("%f  %f  %f %f\n",Fi[0][0],Fi[0][1],Fi[0][2],Fi[0][3]);
    //pc.printf("%f  %f  %f %f\n",Fi[1][0],Fi[1][1],Fi[1][2],Fi[1][3]);
     //pc.printf("%.20f  %.20f  %.20f %.20f\n",Fi[2][0],Fi[2][1],Fi[2][2],Fi[2][3]);
    //////////
    // if dealing with vx = 0, vy = 0 state, use these two lines
    double sx[4];
    sx[0]=(w[0]*r[0]-vw[0][0])/(abs(vw[0][0])+0.5);
    sx[1]=(w[1]*r[1]-vw[0][1])/(abs(vw[0][1])+0.5);
    sx[2]=(w[2]*r[2]-vw[0][2])/(abs(vw[0][2])+0.5);
    sx[3]=(w[3]*r[3]-vw[0][3])/(abs(vw[0][3])+0.5);
    //pc.printf("sx \n");
    //pc.printf("%f  %f  %f %f\n",sx[0],sx[1],sx[2],sx[3]);
    //////////
    double sy[4];
    sy[0]=atan2(vw[1][0],(abs(vw[0][0])+0.5));
    sy[1]=atan2(vw[1][1],(abs(vw[0][1])+0.5));
    sy[2]=atan2(vw[1][2],(abs(vw[0][2])+0.5));
    sy[3]=atan2(vw[1][3],(abs(vw[0][3])+0.5));
    //pc.printf("sy \n");
    //pc.printf("%f  %f  %f %f\n",sy[0],sy[1],sy[2],sy[3]);
    //////////
    // if vx > e and e is larger than 0 use these
    // sx = w.*r./vw(1, :) - 1;
    // sy = atan2(vw(2, :), abs(vw(1, :)));
    //////////
    double tempF[2][4];
    tempF[0][0]=Fs[0]+Fd[0]+Fa[0]+mg_unsprung[0];
    tempF[0][1]=Fs[1]+Fd[1]+Fa[1]+mg_unsprung[1];
    tempF[0][2]=Fs[2]+Fd[2]+Fa[2]+mg_unsprung[2];
    tempF[0][3]=Fs[3]+Fd[3]+Fa[3]+mg_unsprung[3];
    
    tempF[1][0]=tempF[0][0];
    tempF[1][1]=tempF[0][1];
    tempF[1][2]=tempF[0][2];
    tempF[1][3]=tempF[0][3];
    
    for (int i = 0; i < 2; i++){
        for (int j = 0; j < 4; j++){
            if(tempF[i][j]<1){
                tempF[i][j]=1;
                }
            }
        }

    //pc.printf("tempF \n");
    //pc.printf("%f  %f  %f %f\n",tempF[0][0],tempF[0][1],tempF[0][2],tempF[0][3]);
    //pc.printf("%f  %f  %f %f\n",tempF[1][0],tempF[1][1],tempF[1][2],tempF[1][3]);
    //pc.printf("%f  %f  %f %f\n",tempF[2][0],tempF[2][1],tempF[2][2],tempF[2][3]);

    ////////// TM_easy_combined
    double sy_pom[4];
    sy_pom[0]=sy[0];
    sy_pom[1]=-sy[1];
    sy_pom[2]=sy[2];
    sy_pom[3]=-sy[3];
    
    double K[2][4];  //Isto sto i F_max
    K[0][0]=mi[0][0]*tempF[0][0];
    K[0][1]=mi[0][1]*tempF[0][1];
    K[0][2]=mi[0][2]*tempF[0][2];
    K[0][3]=mi[0][3]*tempF[0][3];
    
    K[1][0]=mi[1][0]*tempF[1][0];
    K[1][1]=mi[1][1]*tempF[1][1];
    K[1][2]=mi[1][2]*tempF[1][2];
    K[1][3]=mi[1][3]*tempF[1][3];
    
    //pc.printf("K \n");
    //pc.printf("%f  %f  %f %f\n",K[0][0],K[0][1],K[0][2],K[0][3]);
    //pc.printf("%f  %f  %f %f\n",K[1][0],K[1][1],K[1][2],K[1][3]);
    //pc.printf("%f  %f  %f %f\n",K[2][0],K[2][1],K[2][2],K[2][3]);

    double F_inf[2][4];
    F_inf[0][0]=in[0][0]*tempF[0][0];
    F_inf[0][1]=in[0][1]*tempF[0][1];
    F_inf[0][2]=in[0][2]*tempF[0][2];
    F_inf[0][3]=in[0][3]*tempF[0][3];
    
    F_inf[1][0]=in[1][0]*tempF[1][0];
    F_inf[1][1]=in[1][1]*tempF[1][1];
    F_inf[1][2]=in[1][2]*tempF[1][2];
    F_inf[1][3]=in[1][3]*tempF[1][3];
    
    //pc.printf("F_inf \n");
    //pc.printf("%f  %f  %f %f\n",F_inf[0][0],F_inf[0][1],F_inf[0][2],F_inf[0][3]);
    //pc.printf("%f  %f  %f %f\n",F_inf[1][0],F_inf[1][1],F_inf[1][2],F_inf[1][3]);
    //pc.printf("%f  %f  %f %f\n",F_inf[2][0],F_inf[2][1],F_inf[2][2],F_inf[2][3]);

    double B[2][4];
    B[0][0]=3.14159265359-asin(F_inf[0][0]/K[0][0]);
    B[0][1]=3.14159265359-asin(F_inf[0][1]/K[0][1]);
    B[0][2]=3.14159265359-asin(F_inf[0][2]/K[0][2]);
    B[0][3]=3.14159265359-asin(F_inf[0][3]/K[0][3]);
    
    B[1][0]=3.14159265359-asin(F_inf[1][0]/K[1][0]);
    B[1][1]=3.14159265359-asin(F_inf[1][1]/K[1][1]);
    B[1][2]=3.14159265359-asin(F_inf[1][2]/K[1][2]);
    B[1][3]=3.14159265359-asin(F_inf[1][3]/K[1][3]);
    
    
    //pc.printf("B \n");
    //pc.printf("%f  %f  %f %f\n",B[0][0],B[0][1],B[0][2],B[0][3]);
    //pc.printf("%f  %f  %f %f\n",B[1][0],B[1][1],B[1][2],B[1][3]);
    //pc.printf("%f  %f  %f %f\n",B[2][0],B[2][1],B[2][2],B[2][3]);

    double A[2][4];
    A[0][0]=K[0][0]*B[0][0]/C[0][0];
    A[0][1]=K[0][1]*B[0][1]/C[0][1];
    A[0][2]=K[0][2]*B[0][2]/C[0][2];
    A[0][3]=K[0][3]*B[0][3]/C[0][3];
    
    A[1][0]=K[1][0]*B[1][0]/C[1][0];
    A[1][1]=K[1][1]*B[1][1]/C[1][1];
    A[1][2]=K[1][2]*B[1][2]/C[1][2];
    A[1][3]=K[1][3]*B[1][3]/C[1][3];
    
    
    //pc.printf("A \n");
    //pc.printf("%f  %f  %f %f\n",A[0][0],A[0][1],A[0][2],A[0][3]);
    //pc.printf("%f  %f  %f %f\n",A[1][0],A[1][1],A[1][2],A[1][3]);
    //pc.printf("%f  %f  %f %f\n",A[2][0],A[2][1],A[2][2],A[2][3]);

    double G[4];
    G[0]=(A[1][0]*K[0][0]*B[0][0])/(A[0][0]*K[1][0]*B[1][0]);
    G[1]=(A[1][1]*K[0][1]*B[0][1])/(A[0][1]*K[1][1]*B[1][1]);
    G[2]=(A[1][2]*K[0][2]*B[0][2])/(A[0][2]*K[1][2]*B[1][2]);
    G[3]=(A[1][3]*K[0][3]*B[0][3])/(A[0][3]*K[1][3]*B[1][3]);
    
    //p.printf("G \n");
    //pc.printf("%f  %f  %f %f\n",G[0],G[1],G[2],G[3]);
    double s[2][4];
    s[0][0]=sx[0];
    s[0][1]=sx[1];
    s[0][2]=sx[2];
    s[0][3]=sx[3];
    
    s[1][0]=-sy_pom[0]/G[0];
    s[1][1]=-sy_pom[1]/G[1];
    s[1][2]=-sy_pom[2]/G[2];
    s[1][3]=-sy_pom[3]/G[3];
    
    //%s_norm = sqrt(s(1, :).^2 + s(2, :).^2);
    
    double angle[4];
    angle[0]=atan2(s[1][0],s[0][0]);
    angle[1]=atan2(s[1][1],s[0][1]);
    angle[2]=atan2(s[1][2],s[0][2]);
    angle[3]=atan2(s[1][3],s[0][3]);
    
    double f[2][4];
    f[0][0]=K[0][0]*sin(B[0][0]*(1-exp(-abs(s[0][0])/A[0][0])));
    f[0][1]=K[0][1]*sin(B[0][1]*(1-exp(-abs(s[0][1])/A[0][1])));
    f[0][2]=K[0][2]*sin(B[0][2]*(1-exp(-abs(s[0][2])/A[0][2])));
    f[0][3]=K[0][3]*sin(B[0][3]*(1-exp(-abs(s[0][3])/A[0][3])));
    
    f[1][0]=K[1][0]*sin(B[1][0]*(1-exp(-abs(s[1][0])/A[1][0])));
    f[1][1]=K[1][1]*sin(B[1][1]*(1-exp(-abs(s[1][1])/A[1][1])));
    f[1][2]=K[1][2]*sin(B[1][2]*(1-exp(-abs(s[1][2])/A[1][2])));
    f[1][3]=K[1][3]*sin(B[1][3]*(1-exp(-abs(s[1][3])/A[1][3])));
    
    double f_norm[4];
    f_norm[0]=0.5*(f[0][0]+f[1][0]+(f[0][0]-f[1][0])*cos(2*angle[0]));
    f_norm[1]=0.5*(f[0][1]+f[1][1]+(f[0][1]-f[1][1])*cos(2*angle[1]));
    f_norm[2]=0.5*(f[0][2]+f[1][2]+(f[0][2]-f[1][2])*cos(2*angle[2]));
    f_norm[3]=0.5*(f[0][3]+f[1][3]+(f[0][3]-f[1][3])*cos(2*angle[3]));
    
    
    Fi[0][0]=f_norm[0]*cos(angle[0]);
    Fi[0][1]=f_norm[1]*cos(angle[1]);
    Fi[0][2]=f_norm[2]*cos(angle[2]);
    Fi[0][3]=f_norm[3]*cos(angle[3]);
    
    Fi[1][0]=f_norm[0]*sin(angle[0]);
    Fi[1][1]=f_norm[1]*sin(angle[1]);
    Fi[1][2]=f_norm[2]*sin(angle[2]);
    Fi[1][3]=f_norm[3]*sin(angle[3]);
    ////////////
    Fi[1][1]=-Fi[1][1];
    Fi[1][3]=-Fi[1][3];
    
    //pc.printf("Fi \n");
    //pc.printf("%f  %f  %f %f\n",Fi[0][0],Fi[0][1],Fi[0][2],Fi[0][3]);
    //pc.printf("%f  %f  %f %f\n",Fi[1][0],Fi[1][1],Fi[1][2],Fi[1][3]);
    //pc.printf("%.20f  %.20f  %.20f %.20f\n",Fi[2][0],Fi[2][1],Fi[2][2],Fi[2][3]);

    // right wheel should have antisymmetric 
    // characteristic compared to left -> right(x) = -left(-x) because generally
    // left and right wheels of same axle have same characteristic but
    // antisymmetric (implementation can be further optimized by calculating
    // only front and rear frictions and than just distributing those)\
    
    double aw[4];
    aw[0]=(Tfl-Fi[0][0]*r[0])/Iw[0];
    aw[1]=(Tfr-Fi[0][1]*r[1])/Iw[1];
    aw[2]=(Trl-Fi[0][2]*r[2])/Iw[2];
    aw[3]=(Trr-Fi[0][3]*r[3])/Iw[3];
    //pc.printf("aw \n");
    //pc.printf("%f  %f  %f %f\n",aw[0],aw[1],aw[2],aw[3]);
    ////////////
    double  FL[4];
    FL[0]=Fi[0][0];
    FL[1]=Fi[1][0];
    FL[2]=tempF[0][0];
    
    double FR[3];
    FR[0]=Fi[0][1];
    FR[1]=Fi[1][1];
    FR[2]=tempF[0][1];
    
    double RL[3];
    RL[0]=Fi[0][2];
    RL[1]=Fi[1][2];
    RL[2]=tempF[0][2];

    double RR[3];
    RR[0]=Fi[0][3];
    RR[1]=Fi[1][3];
    RR[2]=tempF[0][3];
    ////////////
    
    cosin=cos(-d);
    sinus=sin(-d);
    p1 = cosin*Fi[0][0]+sinus*Fi[1][0];
    p2 = cosin*Fi[0][1]+sinus*Fi[1][1];
    p3 = -sinus*Fi[0][0]+cosin*Fi[1][0];
    p4 = -sinus*Fi[0][1]+cosin*Fi[1][1];
    
    Fi[0][0]=p1;
    Fi[0][1]=p2;
    Fi[1][0]=p3;
    Fi[1][1]=p4;
    
    //pc.printf("Fi 2 put \n");
    //pc.printf("%f  %f  %f %f\n",Fi[0][0],Fi[0][1],Fi[0][2],Fi[0][3]);
    //pc.printf("%f  %f  %f %f\n",Fi[1][0],Fi[1][1],Fi[1][2],Fi[1][3]);
     //pc.printf("%.20f  %.20f  %.20f %.20f\n",Fi[2][0],Fi[2][1],Fi[2][2],Fi[2][3]);
    ///////////
    double Mi[3][4];
    Mi[0][0]=pw[1][0]*Fi[2][0]-pw[2][0]*Fi[1][0];
    Mi[1][0]=pw[0][0]*Fi[2][0]-pw[2][0]*Fi[0][0];
    Mi[2][0]=pw[0][0]*Fi[1][0]-pw[1][0]*Fi[0][0];
    
    Mi[0][1]=pw[1][1]*Fi[2][1]-pw[2][1]*Fi[1][1];
    Mi[1][1]=pw[0][1]*Fi[2][1]-pw[2][1]*Fi[0][1];
    Mi[2][1]=pw[0][1]*Fi[1][1]-pw[1][1]*Fi[0][1];
    
    Mi[0][2]=pw[1][2]*Fi[2][2]-pw[2][2]*Fi[1][2];
    Mi[1][2]=pw[0][2]*Fi[2][2]-pw[2][2]*Fi[0][2];
    Mi[2][2]=pw[0][2]*Fi[1][2]-pw[1][2]*Fi[0][2];
    
    Mi[0][3]=pw[1][3]*Fi[2][3]-pw[2][3]*Fi[1][3];
    Mi[1][3]=pw[0][3]*Fi[2][3]-pw[2][3]*Fi[0][3];
    Mi[2][3]=pw[0][3]*Fi[1][3]-pw[1][3]*Fi[0][3];
    
    //pc.printf("Mi \n");
    //pc.printf("%f  %f  %f %f\n",Mi[0][0],Mi[0][1],Mi[0][2],Mi[0][3]);
    //pc.printf("%f  %f  %f %f\n",Mi[1][0],Mi[1][1],Mi[1][2],Mi[1][3]);
    //pc.printf("%f  %f  %f %f\n",Mi[2][0],Mi[2][1],Mi[2][2],Mi[2][3]);

    
    ///////////
    double F[3];
    F[0]=Fi[0][0]+Fi[0][1]+Fi[0][2]+Fi[0][3];
    F[1]=Fi[1][0]+Fi[1][1]+Fi[1][2]+Fi[1][3];
    F[2]=Fi[2][0]+Fi[2][1]+Fi[2][2]+Fi[2][3];
    //pc.printf("F \n");
    //pc.printf("%f  %f  %f\n",F[0],F[1],F[2]);
    ///////////
    double M[3];
    M[0]=Mi[0][0]+Mi[0][1]+Mi[0][2]+Mi[0][3];
    M[1]=Mi[1][0]+Mi[1][1]+Mi[1][2]+Mi[1][3];
    M[2]=Mi[2][0]+Mi[2][1]+Mi[2][2]+Mi[2][3];
    //pc.printf("M \n");
    //pc.printf("%f  %f  %f\n",M[0],M[1],M[2]);
    ///////////
    double acp[3];
    acp[0]=va[1]*v[2]-va[2]*v[1];
    acp[1]=va[0]*v[2]-va[2]*v[0];
    acp[2]=va[0]*v[1]-va[1]*v[0];
    //pc.printf("acp \n");
    //pc.printf("%f  %f  %f\n",acp[0],acp[1],acp[2]);
    ///////////
    double a[3];
    a[0]=F[0]/m[0]-acp[0];
    a[1]=F[1]/m[1]-acp[1];
    a[2]=F[2]/m[2]-acp[2];
    //pc.printf("a \n");
    //pc.printf("%f  %f  %f\n",a[0],a[1],a[2]);
    ///////////
    /////////// aa = I_inv * (M - cross(va, I*va)); % Euler's equation
    double pom1[3];
    pom1[0]=I[0][0]*va[0]+I[0][1]*va[1]+I[0][2]*va[2];
    pom1[1]=I[1][0]*va[0]+I[1][1]*va[1]+I[1][2]*va[2];
    pom1[2]=I[2][0]*va[0]+I[2][1]*va[1]+I[2][2]*va[2];
    double pom2[3];
    pom2[0]=va[1]*pom1[2]-va[2]*pom1[1];
    pom2[1]=va[0]*pom1[2]-va[2]*pom1[0];
    pom2[2]=va[0]*pom1[1]-va[1]*pom1[0];
    double pom3[3];
    pom3[0]=M[0]-pom2[0];
    pom3[1]=M[1]-pom2[1];
    pom3[2]=M[2]-pom2[2];
    double aa[3];
    aa[0]=I_inv[0][0]*pom3[0]+I_inv[0][1]*pom3[1]+I_inv[0][2]*pom3[2];
    aa[1]=I_inv[1][0]*pom3[0]+I_inv[1][1]*pom3[1]+I_inv[1][2]*pom3[2];
    aa[2]=I_inv[2][0]*pom3[0]+I_inv[2][1]*pom3[1]+I_inv[2][2]*pom3[2];
    //pc.printf("aa \n");
    //pc.printf("%f  %f  %f\n",aa[0],aa[1],aa[2]);
    ////////////
    v[0]=v[0]+a[0]*Ts;
    v[1]=v[1]+a[1]*Ts;
    v[2]=v[2]+a[2]*Ts;
    //pc.printf("v \n");
    //pc.printf("%f  %f  %f\n",v[0],v[1],v[2]);
    ////////////
    va[0]=va[0]+aa[0]*Ts;
    va[1]=va[1]+aa[1]*Ts;
    va[2]=va[2]+aa[2]*Ts;
    //pc.printf("va \n");
    //pc.printf("%f  %f  %f\n",va[0],va[1],va[2]);
    ////////////
    w[0]=w[0]+aw[0]*Ts;
    w[1]=w[1]+aw[1]*Ts;
    w[2]=w[2]+aw[2]*Ts;
    w[3]=w[3]+aw[3]*Ts;
    //pc.printf("w \n");
    //pc.printf("%f  %f  %f  %f\n",w[0],w[1],w[2],w[3]);
    //////////// R3D_xyz (Rx=I, Ry=I)
    double Rz[3][3]={
                    {cos(pa[2]), -sin(pa[2]), 0},
                    {sin(pa[2]),  cos(pa[2]), 0},
                    {0,       0,              1}
                    };
   p[0]=p[0]+(Rz[0][0]*v[0]+Rz[0][1]*v[1]+Rz[0][2]*v[2])*Ts;
   p[1]=p[1]+(Rz[1][0]*v[0]+Rz[1][1]*v[1]+Rz[1][2]*v[2])*Ts;
   p[2]=p[2]+(Rz[2][0]*v[0]+Rz[2][1]*v[1]+Rz[2][2]*v[2])*Ts;
   //pc.printf("p \n");
   pc.printf("%f  %f  %f\n",p[0],p[1],p[2]);
   /////////////
   pa[0]=pa[0]+va[0]*Ts;
   pa[1]=pa[1]+va[1]*Ts;
   pa[2]=pa[2]+va[2]*Ts;
   //pc.printf("pa \n");
   //pc.printf("%f  %f  %f\n",pa[0],pa[1],pa[2]); 
    

    }
    
    
    
 

CANMessage msg;

void callbackCAN(){
    flag=1;
    can1.read(msg);
    if(msg.id==0x0184){
        T_1=(double)((int16_t)((msg.data[4]<<8)+msg.data[5]))*Mn/1000;

        }
    else if(msg.id==0x0185){
        T_2=(double)((int16_t)((msg.data[4]<<8)+msg.data[5]))*Mn/1000;
        }
    else if(msg.id==0x0188){
        T_3=(double)((int16_t)((msg.data[4]<<8)+msg.data[5]))*Mn/1000;
        }
    else if(msg.id==0x0189){
        T_4=(double)((int16_t)((msg.data[4]<<8)+msg.data[5]))*Mn/1000;
        }
        

    cnt++;

 }
 
Timer t;
 
int main() {
    initialize();
    //can1.filter(RX_ID, 0x03F0,CANStandard, 0);
    
    //messageOutVel1.id = 0x282;
    //messageOutVel2.id = 0x283;
    //messageOutVel3.id = 0x287;
    //messageOutVel4.id = 0x288;

   
    
    //messageOut2.format = CANStandard;// or  CANExtended;  // standard or extended ID (can be skipped for standard)
   // messageOut2.len = 1;//length in bytes (1 to 8);
    //messageOut1.format = CANStandard;// or  CANExtended;  // standard or extended ID (can be skipped for standard)
    //messageOut1.len = 1;//length in bytes (1 to 8);
    
    //can1.frequency(500000);
   
   // tick1.attach(&send, 0.0005);
    
    //can1.attach(callbackCAN);
    
    
    
    //while(1){
    //    while(!flag);
    //    pc.printf("V: %f",v*3.6);
    //    pc.printf("  T1: %f",T_1);
    //    pc.printf("  T2: %f",T_2);
    //    pc.printf("  T3: %f",T_3);
    //    pc.printf("  T4: %f",T_4);
    //    pc.printf("  Cnt: %d",cnt);
    //    pc.printf("\n");
    //        
    //        flag=0;
    //}
    
    //t.start();
    while(1){
        model(450,450,450,450,0);
        wait(0.01);
       }  
  
 
    
}