cob_kinematics: ikfast_ur10.cpp Source File

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00001 #define IKFAST_HAS_LIBRARY
00002 #include "ikfast.h" // found inside share/openrave-X.Y/python/ikfast.h
00003 using namespace ikfast;
00004 
00005 #include <math.h>
00006 #include <stdio.h>
00007 
00008 #define ZERO_THRESH 0.00000001
00009 #define SIGN(x) ( ( (x) > 0 ) - ( (x) < 0 ) )
00010 #define PI M_PI
00011 #define UR10_PARAMS
00012 
00013 #ifdef UR10_PARAMS
00014 #define d1  0.1273
00015 #define a2 -0.612
00016 #define a3 -0.5723
00017 #define d4  0.163941
00018 #define d5  0.1157
00019 #define d6  0.0922
00020 #endif
00021 
00022 namespace ur_kinematics {
00023 
00024   void forward(const double* q, double* T) {
00025     double s1 = sin(*q), c1 = cos(*q); q++;
00026     double q234 = *q, s2 = sin(*q), c2 = cos(*q); q++;
00027     double s3 = sin(*q), c3 = cos(*q); q234 += *q; q++;
00028     q234 += *q; q++;
00029     double s5 = sin(*q), c5 = cos(*q); q++;
00030     double s6 = sin(*q), c6 = cos(*q); 
00031     double s234 = sin(q234), c234 = cos(q234);
00032     *T = ((c1*c234-s1*s234)*s5)/2.0 - c5*s1 + ((c1*c234+s1*s234)*s5)/2.0; T++;
00033     *T = (c6*(s1*s5 + ((c1*c234-s1*s234)*c5)/2.0 + ((c1*c234+s1*s234)*c5)/2.0) - 
00034           (s6*((s1*c234+c1*s234) - (s1*c234-c1*s234)))/2.0); T++;
00035     *T = (-(c6*((s1*c234+c1*s234) - (s1*c234-c1*s234)))/2.0 - 
00036           s6*(s1*s5 + ((c1*c234-s1*s234)*c5)/2.0 + ((c1*c234+s1*s234)*c5)/2.0)); T++;
00037     *T = ((d5*(s1*c234-c1*s234))/2.0 - (d5*(s1*c234+c1*s234))/2.0 - 
00038           d4*s1 + (d6*(c1*c234-s1*s234)*s5)/2.0 + (d6*(c1*c234+s1*s234)*s5)/2.0 - 
00039           a2*c1*c2 - d6*c5*s1 - a3*c1*c2*c3 + a3*c1*s2*s3); T++;
00040     *T = c1*c5 + ((s1*c234+c1*s234)*s5)/2.0 + ((s1*c234-c1*s234)*s5)/2.0; T++;
00041     *T = (c6*(((s1*c234+c1*s234)*c5)/2.0 - c1*s5 + ((s1*c234-c1*s234)*c5)/2.0) + 
00042           s6*((c1*c234-s1*s234)/2.0 - (c1*c234+s1*s234)/2.0)); T++;
00043     *T = (c6*((c1*c234-s1*s234)/2.0 - (c1*c234+s1*s234)/2.0) - 
00044           s6*(((s1*c234+c1*s234)*c5)/2.0 - c1*s5 + ((s1*c234-c1*s234)*c5)/2.0)); T++;
00045     *T = ((d5*(c1*c234-s1*s234))/2.0 - (d5*(c1*c234+s1*s234))/2.0 + d4*c1 + 
00046           (d6*(s1*c234+c1*s234)*s5)/2.0 + (d6*(s1*c234-c1*s234)*s5)/2.0 + d6*c1*c5 - 
00047           a2*c2*s1 - a3*c2*c3*s1 + a3*s1*s2*s3); T++;
00048     *T = ((c234*c5-s234*s5)/2.0 - (c234*c5+s234*s5)/2.0); T++;
00049     *T = ((s234*c6-c234*s6)/2.0 - (s234*c6+c234*s6)/2.0 - s234*c5*c6); T++;
00050     *T = (s234*c5*s6 - (c234*c6+s234*s6)/2.0 - (c234*c6-s234*s6)/2.0); T++;
00051     *T = (d1 + (d6*(c234*c5-s234*s5))/2.0 + a3*(s2*c3+c2*s3) + a2*s2 - 
00052          (d6*(c234*c5+s234*s5))/2.0 - d5*c234); T++;
00053     *T = 0.0; T++; *T = 0.0; T++; *T = 0.0; T++; *T = 1.0;
00054   }
00055 
00056   int inverse(const double* T, double* q_sols, double q6_des) {
00057     int num_sols = 0;
00058     double T02 = -*T; T++; double T00 =  *T; T++; double T01 =  *T; T++; double T03 = -*T; T++; 
00059     double T12 = -*T; T++; double T10 =  *T; T++; double T11 =  *T; T++; double T13 = -*T; T++; 
00060     double T22 =  *T; T++; double T20 = -*T; T++; double T21 = -*T; T++; double T23 =  *T;
00061 
00063     double q1[2];
00064     {
00065       double A = d6*T12 - T13;
00066       double B = d6*T02 - T03;
00067       double R = A*A + B*B;
00068       if(fabs(A) < ZERO_THRESH) {
00069         double div;
00070         if(fabs(fabs(d4) - fabs(B)) < ZERO_THRESH)
00071           div = -SIGN(d4)*SIGN(B);
00072         else
00073           div = -d4/B;
00074         double arcsin = asin(div);
00075         if(fabs(arcsin) < ZERO_THRESH)
00076           arcsin = 0.0;
00077         if(arcsin < 0.0)
00078           q1[0] = arcsin + 2.0*PI;
00079         else
00080           q1[0] = arcsin;
00081         q1[1] = PI - arcsin;
00082       }
00083       else if(fabs(B) < ZERO_THRESH) {
00084         double div;
00085         if(fabs(fabs(d4) - fabs(A)) < ZERO_THRESH)
00086           div = SIGN(d4)*SIGN(A);
00087         else
00088           div = d4/A;
00089         double arccos = acos(div);
00090         q1[0] = arccos;
00091         q1[1] = 2.0*PI - arccos;
00092       }
00093       else if(d4*d4 > R) {
00094         return num_sols;
00095       }
00096       else {
00097         double arccos = acos(d4 / sqrt(R)) ;
00098         double arctan = atan2(-B, A);
00099         double pos = arccos + arctan;
00100         double neg = -arccos + arctan;
00101         if(fabs(pos) < ZERO_THRESH)
00102           pos = 0.0;
00103         if(fabs(neg) < ZERO_THRESH)
00104           neg = 0.0;
00105         if(pos >= 0.0)
00106           q1[0] = pos;
00107         else
00108           q1[0] = 2.0*PI + pos;
00109         if(neg >= 0.0)
00110           q1[1] = neg; 
00111         else
00112           q1[1] = 2.0*PI + neg;
00113       }
00114     }
00116 
00118     double q5[2][2];
00119     {
00120       for(int i=0;i<2;i++) {
00121         double numer = (T03*sin(q1[i]) - T13*cos(q1[i])-d4);
00122         double div;
00123         if(fabs(fabs(numer) - fabs(d6)) < ZERO_THRESH)
00124           div = SIGN(numer) * SIGN(d6);
00125         else
00126           div = numer / d6;
00127         double arccos = acos(div);
00128         q5[i][0] = arccos;
00129         q5[i][1] = 2.0*PI - arccos;
00130       }
00131     }
00133 
00134     {
00135       for(int i=0;i<2;i++) {
00136         for(int j=0;j<2;j++) {
00137           double c1 = cos(q1[i]), s1 = sin(q1[i]);
00138           double c5 = cos(q5[i][j]), s5 = sin(q5[i][j]);
00139           double q6;
00141           if(fabs(s5) < ZERO_THRESH)
00142             q6 = q6_des;
00143           else {
00144             q6 = atan2(SIGN(s5)*-(T01*s1 - T11*c1), 
00145                        SIGN(s5)*(T00*s1 - T10*c1));
00146             if(fabs(q6) < ZERO_THRESH)
00147               q6 = 0.0;
00148             if(q6 < 0.0)
00149               q6 += 2.0*PI;
00150           }
00152 
00153           double q2[2], q3[2], q4[2];
00155           double c6 = cos(q6), s6 = sin(q6);
00156           double x04x = -s5*(T02*c1 + T12*s1) - c5*(s6*(T01*c1 + T11*s1) - c6*(T00*c1 + T10*s1));
00157           double x04y = c5*(T20*c6 - T21*s6) - T22*s5;
00158           double p13x = d5*(s6*(T00*c1 + T10*s1) + c6*(T01*c1 + T11*s1)) - d6*(T02*c1 + T12*s1) + 
00159                         T03*c1 + T13*s1;
00160           double p13y = T23 - d1 - d6*T22 + d5*(T21*c6 + T20*s6);
00161 
00162           double c3 = (p13x*p13x + p13y*p13y - a2*a2 - a3*a3) / (2.0*a2*a3);
00163           if(fabs(fabs(c3) - 1.0) < ZERO_THRESH)
00164             c3 = SIGN(c3);
00165           else if(fabs(c3) > 1.0) {
00166             // TODO NO SOLUTION
00167             continue;
00168           }
00169           double arccos = acos(c3);
00170           q3[0] = arccos;
00171           q3[1] = 2.0*PI - arccos;
00172           double denom = a2*a2 + a3*a3 + 2*a2*a3*c3;
00173           double s3 = sin(arccos);
00174           double A = (a2 + a3*c3), B = a3*s3;
00175           q2[0] = atan2((A*p13y - B*p13x) / denom, (A*p13x + B*p13y) / denom);
00176           q2[1] = atan2((A*p13y + B*p13x) / denom, (A*p13x - B*p13y) / denom);
00177           double c23_0 = cos(q2[0]+q3[0]);
00178           double s23_0 = sin(q2[0]+q3[0]);
00179           double c23_1 = cos(q2[1]+q3[1]);
00180           double s23_1 = sin(q2[1]+q3[1]);
00181           q4[0] = atan2(c23_0*x04y - s23_0*x04x, x04x*c23_0 + x04y*s23_0);
00182           q4[1] = atan2(c23_1*x04y - s23_1*x04x, x04x*c23_1 + x04y*s23_1);
00184           for(int k=0;k<2;k++) {
00185             if(fabs(q2[k]) < ZERO_THRESH)
00186               q2[k] = 0.0;
00187             else if(q2[k] < 0.0) q2[k] += 2.0*PI;
00188             if(fabs(q4[k]) < ZERO_THRESH)
00189               q4[k] = 0.0;
00190             else if(q4[k] < 0.0) q4[k] += 2.0*PI;
00191             q_sols[num_sols*6+0] = q1[i];    q_sols[num_sols*6+1] = q2[k]; 
00192             q_sols[num_sols*6+2] = q3[k];    q_sols[num_sols*6+3] = q4[k]; 
00193             q_sols[num_sols*6+4] = q5[i][j]; q_sols[num_sols*6+5] = q6; 
00194             num_sols++;
00195           }
00196 
00197         }
00198       }
00199     }
00200     return num_sols;
00201   }
00202 };
00203 
00204 using namespace std;
00205 using namespace ur_kinematics;
00206 
00207 #ifdef IKFAST_NAMESPACE
00208 namespace IKFAST_NAMESPACE {
00209 #endif
00210 
00211 void to_mat44(double * mat4_4, const IkReal* eetrans, const IkReal* eerot)
00212 {
00213     for(int i=0; i< 3;++i){
00214         mat4_4[i*4+0] = eerot[i*3+0];
00215         mat4_4[i*4+1] = eerot[i*3+1];
00216         mat4_4[i*4+2] = eerot[i*3+2];
00217         mat4_4[i*4+3] = eetrans[i];
00218     }
00219     mat4_4[3*4+0] = 0;
00220     mat4_4[3*4+1] = 0;
00221     mat4_4[3*4+2] = 0;
00222     mat4_4[3*4+3] = 1;
00223     
00224 }
00225 
00226 void from_mat44(const double * mat4_4, IkReal* eetrans, IkReal* eerot)
00227 {
00228     for(int i=0; i< 3;++i){
00229         eerot[i*3+0] = mat4_4[i*4+0];
00230         eerot[i*3+1] = mat4_4[i*4+1];
00231         eerot[i*3+2] = mat4_4[i*4+2];
00232         eetrans[i] = mat4_4[i*4+3];
00233     }
00234 }
00235 
00236 
00237 IKFAST_API bool ComputeIk(const IkReal* eetrans, const IkReal* eerot, const IkReal* pfree, IkSolutionListBase<IkReal>& solutions) {
00238   if(!pfree) return false;
00239   
00240   int n = GetNumJoints();
00241   double q_sols[8*6];
00242   double T[16];
00243   to_mat44(T, eetrans, eerot);
00244   int num_sols = 0;
00245   num_sols = inverse(T, q_sols,pfree[0]);
00246   for (int i=0; i < num_sols; ++i){
00247     std::vector<IkSingleDOFSolutionBase<IkReal> > vinfos(n);
00248     for (int j=0; j < n; ++j) vinfos[j].foffset = q_sols[i*n+j];
00249     std::vector<int> vfree(0);
00250     solutions.AddSolution(vinfos,vfree);
00251   }
00252   //printf("WAAAAAAAAAAAAAAAAAAAAAAAAAAAAH  %d\n", num_sols);
00253   return num_sols > 0;
00254 }
00255 
00256 IKFAST_API void ComputeFk(const IkReal* j, IkReal* eetrans, IkReal* eerot)
00257 {
00258     double T[16];
00259     forward(j,T);
00260     from_mat44(T,eetrans,eerot);
00261 }
00262 
00263 IKFAST_API int GetNumFreeParameters() { return 1; }
00264 IKFAST_API int* GetFreeParameters() { static int freeparams[] = {5}; return freeparams; }
00265 IKFAST_API int GetNumJoints() { return 6; }
00266 
00267 IKFAST_API int GetIkRealSize() { return sizeof(IkReal); }
00268 
00269 #ifdef IKFAST_NAMESPACE
00270 } // end namespace
00271 #endif
00272 
00273 #ifndef IKFAST_NO_MAIN
00274 /*
00275 int main(int argc, char* argv[])
00276 {
00277   double q[6] = {0.0, 0.0, 1.0, 0.0, 1.0, 0.0};
00278   double* T = new double[16];
00279   forward(q, T);
00280   for(int i=0;i<4;i++) {
00281     for(int j=i*4;j<(i+1)*4;j++)
00282       printf("%1.3f ", T[j]);
00283     printf("\n");
00284   }
00285   double q_sols[8*6];
00286   int num_sols;
00287   num_sols = inverse(T, q_sols);
00288   for(int i=0;i<num_sols;i++) 
00289     printf("%1.6f %1.6f %1.6f %1.6f %1.6f %1.6f\n", 
00290        q_sols[i*6+0], q_sols[i*6+1], q_sols[i*6+2], q_sols[i*6+3], q_sols[i*6+4], q_sols[i*6+5]);
00291   for(int i=0;i<=4;i++)
00292     printf("%f ", PI/2.0*i);
00293   printf("\n");
00294   return 0;
00295 }
00296 */
00297 #endif