//正解
void forward(const double* q, double* T) {
double s1 = sin(*q), c1 = cos(*q); q++;
double q234 = *q, s2 = sin(*q), c2 = cos(*q); q++;
double s3 = sin(*q), c3 = cos(*q); q234 += *q; q++;
q234 += *q; q++;
double s5 = sin(*q), c5 = cos(*q); q++;
double s6 = sin(*q), c6 = cos(*q);
double s234 = sin(q234), c234 = cos(q234);
*T = ((c1*c234-s1*s234)*s5)/2.0 - c5*s1 + ((c1*c234+s1*s234)*s5)/2.0; T++;
*T = (c6*(s1*s5 + ((c1*c234-s1*s234)*c5)/2.0 + ((c1*c234+s1*s234)*c5)/2.0) -
(s6*((s1*c234+c1*s234) - (s1*c234-c1*s234)))/2.0); T++;
*T = (-(c6*((s1*c234+c1*s234) - (s1*c234-c1*s234)))/2.0 -
s6*(s1*s5 + ((c1*c234-s1*s234)*c5)/2.0 + ((c1*c234+s1*s234)*c5)/2.0)); T++;
*T = ((d5*(s1*c234-c1*s234))/2.0 - (d5*(s1*c234+c1*s234))/2.0 -
d4*s1 + (d6*(c1*c234-s1*s234)*s5)/2.0 + (d6*(c1*c234+s1*s234)*s5)/2.0 -
a2*c1*c2 - d6*c5*s1 - a3*c1*c2*c3 + a3*c1*s2*s3); T++;
*T = c1*c5 + ((s1*c234+c1*s234)*s5)/2.0 + ((s1*c234-c1*s234)*s5)/2.0; T++;
*T = (c6*(((s1*c234+c1*s234)*c5)/2.0 - c1*s5 + ((s1*c234-c1*s234)*c5)/2.0) +
s6*((c1*c234-s1*s234)/2.0 - (c1*c234+s1*s234)/2.0)); T++;
*T = (c6*((c1*c234-s1*s234)/2.0 - (c1*c234+s1*s234)/2.0) -
s6*(((s1*c234+c1*s234)*c5)/2.0 - c1*s5 + ((s1*c234-c1*s234)*c5)/2.0)); T++;
*T = ((d5*(c1*c234-s1*s234))/2.0 - (d5*(c1*c234+s1*s234))/2.0 + d4*c1 +
(d6*(s1*c234+c1*s234)*s5)/2.0 + (d6*(s1*c234-c1*s234)*s5)/2.0 + d6*c1*c5 -
a2*c2*s1 - a3*c2*c3*s1 + a3*s1*s2*s3); T++;
*T = ((c234*c5-s234*s5)/2.0 - (c234*c5+s234*s5)/2.0); T++;
*T = ((s234*c6-c234*s6)/2.0 - (s234*c6+c234*s6)/2.0 - s234*c5*c6); T++;
*T = (s234*c5*s6 - (c234*c6+s234*s6)/2.0 - (c234*c6-s234*s6)/2.0); T++;
*T = (d1 + (d6*(c234*c5-s234*s5))/2.0 + a3*(s2*c3+c2*s3) + a2*s2 -
(d6*(c234*c5+s234*s5))/2.0 - d5*c234); T++;
*T = 0.0; T++; *T = 0.0; T++; *T = 0.0; T++; *T = 1.0;
}
//逆解
int inverse(const double* T, double* q_sols, double q6_des) {
int num_sols = 0;
double T02 = -*T; T++; double T00 = *T; T++; double T01 = *T; T++; double T03 = -*T; T++;
double T12 = -*T; T++; double T10 = *T; T++; double T11 = *T; T++; double T13 = -*T; T++;
double T22 = *T; T++; double T20 = -*T; T++; double T21 = -*T; T++; double T23 = *T;
// shoulder rotate joint (q1) //
double q1[2];
{
double A = d6*T12 - T13;
double B = d6*T02 - T03;
double R = A*A + B*B;
if(fabs(A) < ZERO_THRESH) {
double div;
if(fabs(fabs(d4) - fabs(B)) < ZERO_THRESH)
div = -SIGN(d4)*SIGN(B);
else
div = -d4/B;
double arcsin = asin(div);
if(fabs(arcsin) < ZERO_THRESH)
arcsin = 0.0;
if(arcsin < 0.0)
q1[0] = arcsin + 2.0*PI;
else
q1[0] = arcsin;
q1[1] = PI - arcsin;
}
else if(fabs(B) < ZERO_THRESH) {
double div;
if(fabs(fabs(d4) - fabs(A)) < ZERO_THRESH)
div = SIGN(d4)*SIGN(A);
else
div = d4/A;
double arccos = acos(div);
q1[0] = arccos;
q1[1] = 2.0*PI - arccos;
}
else if(d4*d4 > R) {
return num_sols;
}
else {
double arccos = acos(d4 / sqrt(R)) ;
double arctan = atan2(-B, A);
double pos = arccos + arctan;
double neg = -arccos + arctan;
if(fabs(pos) < ZERO_THRESH)
pos = 0.0;
if(fabs(neg) < ZERO_THRESH)
neg = 0.0;
if(pos >= 0.0)
q1[0] = pos;
else
q1[0] = 2.0*PI + pos;
if(neg >= 0.0)
q1[1] = neg;
else
q1[1] = 2.0*PI + neg;
}
}
// wrist 2 joint (q5) //
double q5[2][2];
{
for(int i=0;i<2;i++) {
double numer = (T03*sin(q1[i]) - T13*cos(q1[i])-d4);
double div;
if(fabs(fabs(numer) - fabs(d6)) < ZERO_THRESH)
div = SIGN(numer) * SIGN(d6);
else
div = numer / d6;
double arccos = acos(div);
q5[i][0] = arccos;
q5[i][1] = 2.0*PI - arccos;
}
}
{
for(int i=0;i<2;i++) {
for(int j=0;j<2;j++) {
double c1 = cos(q1[i]), s1 = sin(q1[i]);
double c5 = cos(q5[i][j]), s5 = sin(q5[i][j]);
double q6;
// wrist 3 joint (q6) //
if(fabs(s5) < ZERO_THRESH)
q6 = q6_des;
else {
q6 = atan2(SIGN(s5)*-(T01*s1 - T11*c1),
SIGN(s5)*(T00*s1 - T10*c1));
if(fabs(q6) < ZERO_THRESH)
q6 = 0.0;
if(q6 < 0.0)
q6 += 2.0*PI;
}
double q2[2], q3[2], q4[2];
/ RRR joints (q2,q3,q4)
double c6 = cos(q6), s6 = sin(q6);
double x04x = -s5*(T02*c1 + T12*s1) - c5*(s6*(T01*c1 + T11*s1) - c6*(T00*c1 + T10*s1));
double x04y = c5*(T20*c6 - T21*s6) - T22*s5;
double p13x = d5*(s6*(T00*c1 + T10*s1) + c6*(T01*c1 + T11*s1)) - d6*(T02*c1 + T12*s1) +
T03*c1 + T13*s1;
double p13y = T23 - d1 - d6*T22 + d5*(T21*c6 + T20*s6);
double c3 = (p13x*p13x + p13y*p13y - a2*a2 - a3*a3) / (2.0*a2*a3);
if(fabs(fabs(c3) - 1.0) < ZERO_THRESH)
c3 = SIGN(c3);
else if(fabs(c3) > 1.0) {
// TODO NO SOLUTION
continue;
}
double arccos = acos(c3);
q3[0] = arccos;
q3[1] = 2.0*PI - arccos;
double denom = a2*a2 + a3*a3 + 2*a2*a3*c3;
double s3 = sin(arccos);
double A = (a2 + a3*c3), B = a3*s3;
q2[0] = atan2((A*p13y - B*p13x) / denom, (A*p13x + B*p13y) / denom);
q2[1] = atan2((A*p13y + B*p13x) / denom, (A*p13x - B*p13y) / denom);
double c23_0 = cos(q2[0]+q3[0]);
double s23_0 = sin(q2[0]+q3[0]);
double c23_1 = cos(q2[1]+q3[1]);
double s23_1 = sin(q2[1]+q3[1]);
q4[0] = atan2(c23_0*x04y - s23_0*x04x, x04x*c23_0 + x04y*s23_0);
q4[1] = atan2(c23_1*x04y - s23_1*x04x, x04x*c23_1 + x04y*s23_1);
for(int k=0;k<2;k++) {
if(fabs(q2[k]) < ZERO_THRESH)
q2[k] = 0.0;
else if(q2[k] < 0.0) q2[k] += 2.0*PI;
if(fabs(q4[k]) < ZERO_THRESH)
q4[k] = 0.0;
else if(q4[k] < 0.0) q4[k] += 2.0*PI;
q_sols[num_sols*6+0] = q1[i]; q_sols[num_sols*6+1] = q2[k];
q_sols[num_sols*6+2] = q3[k]; q_sols[num_sols*6+3] = q4[k];
q_sols[num_sols*6+4] = q5[i][j]; q_sols[num_sols*6+5] = q6;
num_sols++;
}
}
}
}
return num_sols;
}
};