计算机器人自由度的公式,六自由度机器人Jacobian(雅克比)矩阵计算类！
作者：想飞的猪
说明：MLGetIdentityMat为获得单位矩阵函数
MLMatMulti为矩阵相乘函数
和OpenCV求逆矩阵函数cvInvert没有给出请大家自己写一下！很简单的！
typedef struct
RobotJacobian6
{
//变量!
//各关节传递矩阵!
union
{
struct
{
double
AMat[6][4][4];
}; double A0to1[4][4];
double A1to2[4][4];
double A2to3[4][4];
double A3to4[4][4];
double A4to5[4][4];
double A5to6[4][4];
};
union
{
struct
{
double
TMat[6][4][4];
};
struct {
double
T0to6[4][4];
double
T1to6[4][4];
double
T2to6[4][4];
double
T3to6[4][4];
double
T4to6[4][4];
double
T5to6[4][4];
};
};
//末端位姿!
double EndPose[4][4];
//D-H参数表!
double DHParam[6][4];//顺序为：Angle d_L a_L
a_A!
//雅克比矩阵!
double EndJacobian[6][6];
//逆雅克比矩阵!
double EndInvJacobian[6][6];
//基坐标的笛卡尔微分运动到末端坐标的传递矩阵!
double JBasetoEnd[6][6];
double
T_1to6[4][4];//该矩阵的姿态与基坐标一致，位置与末端坐标一致!
//以便可以按照基坐标进行平动和绕基坐标轴方向转动!
double mInput[6]; //输入!
double mOutput[6];//输出!
int mMode;
void GetAMat()
{
for (int
i=0;i<6;i++)
{
MLGetDHTransMat(AMat[i],DHParam[i][0],DHParam[i][1],DHParam[i][2],DHParam[i][3]);
}
}
void
GetTMat()
{
MLGetIdentityMat(T5to6);
MLMatMulti(AMat[5],T5to6);
MLMatMulti(AMat[4],T5to6,T4to6);MLMatMulti(AMat[3],T4to6,T3to6);
MLMatMulti(AMat[2],T3to6,T2to6);
MLMatMulti(AMat[1],T2to6,T1to6);
MLMatMulti(AMat[0],T1to6,T0to6);
}
void
UpdateAngle(double
Angles[6])//Angles为弧度!
{for (int
i=0;i<6;i++)
{
DHParam[i][0]=Angles[i];
}
GetAMat();
GetEndPose();
GetTMat(); GetEndJacobian();
GetEndInvJacobian();
GetJBasetoEnd();
}
void Inti(double DHparameter[6][4])
{
for (int
i=0;i<6;i++)
{
for (int
j=0;j<4;j++)
{
DHParam[i][j]=DHparameter[i][j];
}
}
GetAMat();
GetEndPose();
GetTMat();
GetEndJacobian();
GetEndInvJacobian();
GetJBasetoEnd();
for
(i=0;i<6;i++)
{
mInput[i]=0;
mOutput[i]=0;
}
mMode=BASE;
}
void
GetEndPose()
{
MLGetIdentityMat(EndPose);
for (int
i=0;i<6;i++)
{
MLMatMulti(AMat[5-i],EndPose);
}
}
void
GetEndJacobian()
{
for (int
i=0;i<6;i++)
{
EndJacobian[0][i]=-1*TMat[i][Xx][Nn]*TMat[i][Yy][Pp]+TMat[i][Yy][Nn]*TMat[i][Xx][Pp];
EndJacobian[1][i]=-1*TMat[i][Xx][Oo]*TMat[i][Yy][Pp]+TMat[i][Yy][Oo]*TMat[i][Xx][Pp];
EndJacobian[2][i]=-1*TMat[i][Xx][Aa]*TMat[i][Yy][Pp]+TMat[i][Yy][Aa]*TMat[i][Xx][Pp];
EndJacobian[3][i]=TMat[i][Zz][Nn];
EndJacobian[4][i]=TMat[i][Zz][Oo];
EndJacobian[5][i]=TMat[i][Zz][Aa];
}
}
void
GetEndInvJacobian()
{
double Data1[36];
CvMat Mat1 = cvMat(
6,6,CV_64FC1,Data1);
double
Data2[36];
CvMat Mat2 = cvMat(
6,6,CV_64FC1,Data2);
for (int
i=0;i<6;i++)
{
for (int
j=0;j<6;j++)
{
cvmSet(&Mat1,i,j,EndJacobian[i][j]);
}
}
cvInvert(&Mat1,&Mat2,CV_SVD);
for
(i=0;i<6;i++)
{
for (int
j=0;j<6;j++)
{
EndInvJacobian[i][j]=cvmGet(&Mat2,i,j);
}
}
}
void
EndOutput(double Input[6], double Output[6])//Output为角速度!
{
MLMatMulti_3(EndInvJacobian,Input,Output);
}
void
GetJBasetoEnd()
{
double TransMat[4][4];
MLGetIdentityMat(TransMat);
TransMat[0][3]=-1*EndPose[0][3];
TransMat[1][3]=-1*EndPose[1][3];
TransMat[2][3]=-1*EndPose[2][3];
MLMatMulti(TransMat,EndPose,T_1to6);
JBasetoEnd[0][0]=T_1to6[Xx][Nn];
JBasetoEnd[0][1]=T_1to6[Yy][Nn];
JBasetoEnd[0][2]=T_1to6[Zz][Nn];
JBasetoEnd[1][0]=T_1to6[Xx][Oo];
JBasetoEnd[1][1]=T_1to6[Yy][Oo];
JBasetoEnd[1][2]=T_1to6[Zz][Oo];
JBasetoEnd[2][0]=T_1to6[Xx][Aa];
JBasetoEnd[2][1]=T_1to6[Yy][Aa];
JBasetoEnd[2][2]=T_1to6[Zz][Aa];
for (int
i=3;i<6;i++)
{
for (int
j=0;j<3;j++)
{
JBasetoEnd[i][j]=0;
}
}
JBasetoEnd[3][3]=T_1to6[Xx][Nn];
JBasetoEnd[3][4]=T_1to6[Yy][Nn];
JBasetoEnd[3][5]=T_1to6[Zz][Nn];
JBasetoEnd[4][3]=T_1to6[Xx][Oo];
JBasetoEnd[4][4]=T_1to6[Yy][Oo];
JBasetoEnd[4][5]=T_1to6[Zz][Oo];
JBasetoEnd[5][3]=T_1to6[Xx][Aa];
JBasetoEnd[5][4]=T_1to6[Yy][Aa];
JBasetoEnd[5][5]=T_1to6[Zz][Aa];
JBasetoEnd[0][3]=T_1to6[Yy][Pp]*T_1to6[Zz][Nn]-T_1to6[Zz][Pp]*T_1to6[Yy][Nn];//(P×N)x
JBasetoEnd[0][4]=T_1to6[Zz][Pp]*T_1to6[Xx][Nn]-T_1to6[Xx][Pp]*T_1to6[Zz][Nn];//(P×N)y
JBasetoEnd[0][5]=T_1to6[Xx][Pp]*T_1to6[Yy][Nn]-T_1to6[Yy][Pp]*T_1to6[Xx][Nn];//(P×N)z
JBasetoEnd[1][3]=T_1to6[Yy][Pp]*T_1to6[Zz][Oo]-T_1to6[Zz][Pp]*T_1to6[Yy][Oo];//(P×O)x
JBasetoEnd[1][4]=T_1to6[Zz][Pp]*T_1to6[Xx][Oo]-T_1to6[Xx][Pp]*T_1to6[Zz][Oo];//(P×O)y
JBasetoEnd[1][5]=T_1to6[Xx][Pp]*T_1to6[Yy][Oo]-T_1to6[Yy][Pp]*T_1to6[Xx][Oo];//(P×O)z
JBasetoEnd[2][3]=T_1to6[Yy][Pp]*T_1to6[Zz][Aa]-T_1to6[Zz][Pp]*T_1to6[Yy][Aa];//(P×A)x
JBasetoEnd[2][4]=T_1to6[Zz][Pp]*T_1to6[Xx][Aa]-T_1to6[Xx][Pp]*T_1to6[Zz][Aa];//(P×A)y
JBasetoEnd[2][5]=T_1to6[Xx][Pp]*T_1to6[Yy][Aa]-T_1to6[Yy][Pp]*T_1to6[Xx][Aa];//(P×A)z
}
void
BaseOutput(double BaseInput[6], double
Output[6])//Output为角速度!
{
double EndInput[6];
MLMatMulti_3(JBasetoEnd,BaseInput,EndInput);
EndOutput(EndInput,Output);
}
void
SetInput(double Input[6])
{
for (int
i=0;i<6;i++)
{
mInput[i]=Input[i];
}
}
void SetMode(int
mode)
{
mMode=mode;
}
void
GetOutput(int mode=BASE)
{
int i=0;
int j=0;
switch(mode)
{
case eND:
EndOutput(mInput,mOutput);
break;
case BASE:
BaseOutput(mInput,mOutput);
break;
}
}
RobotJacobian6()
{
}
RobotJacobian6(double
DHparameter[6][4])
{
Inti(DHparameter);
}
}MLJacobian;