00001 #include <ur_kinematics/ur_kin.h>
00002
00003 namespace ur_kinematics {
00004
00005 void forward(const double* q, double* T) {
00006 double s1 = sin(*q), c1 = cos(*q); q++;
00007 double q234 = *q, s2 = sin(*q), c2 = cos(*q); q++;
00008 double s3 = sin(*q), c3 = cos(*q); q234 += *q; q++;
00009 q234 += *q; q++;
00010 double s5 = sin(*q), c5 = cos(*q); q++;
00011 double s6 = sin(*q), c6 = cos(*q);
00012 double s234 = sin(q234), c234 = cos(q234);
00013 *T = ((c1*c234-s1*s234)*s5)/2.0 - c5*s1 + ((c1*c234+s1*s234)*s5)/2.0; T++;
00014 *T = (c6*(s1*s5 + ((c1*c234-s1*s234)*c5)/2.0 + ((c1*c234+s1*s234)*c5)/2.0) -
00015 (s6*((s1*c234+c1*s234) - (s1*c234-c1*s234)))/2.0); T++;
00016 *T = (-(c6*((s1*c234+c1*s234) - (s1*c234-c1*s234)))/2.0 -
00017 s6*(s1*s5 + ((c1*c234-s1*s234)*c5)/2.0 + ((c1*c234+s1*s234)*c5)/2.0)); T++;
00018 *T = ((d5*(s1*c234-c1*s234))/2.0 - (d5*(s1*c234+c1*s234))/2.0 -
00019 d4*s1 + (d6*(c1*c234-s1*s234)*s5)/2.0 + (d6*(c1*c234+s1*s234)*s5)/2.0 -
00020 a2*c1*c2 - d6*c5*s1 - a3*c1*c2*c3 + a3*c1*s2*s3); T++;
00021 *T = c1*c5 + ((s1*c234+c1*s234)*s5)/2.0 + ((s1*c234-c1*s234)*s5)/2.0; T++;
00022 *T = (c6*(((s1*c234+c1*s234)*c5)/2.0 - c1*s5 + ((s1*c234-c1*s234)*c5)/2.0) +
00023 s6*((c1*c234-s1*s234)/2.0 - (c1*c234+s1*s234)/2.0)); T++;
00024 *T = (c6*((c1*c234-s1*s234)/2.0 - (c1*c234+s1*s234)/2.0) -
00025 s6*(((s1*c234+c1*s234)*c5)/2.0 - c1*s5 + ((s1*c234-c1*s234)*c5)/2.0)); T++;
00026 *T = ((d5*(c1*c234-s1*s234))/2.0 - (d5*(c1*c234+s1*s234))/2.0 + d4*c1 +
00027 (d6*(s1*c234+c1*s234)*s5)/2.0 + (d6*(s1*c234-c1*s234)*s5)/2.0 + d6*c1*c5 -
00028 a2*c2*s1 - a3*c2*c3*s1 + a3*s1*s2*s3); T++;
00029 *T = ((c234*c5-s234*s5)/2.0 - (c234*c5+s234*s5)/2.0); T++;
00030 *T = ((s234*c6-c234*s6)/2.0 - (s234*c6+c234*s6)/2.0 - s234*c5*c6); T++;
00031 *T = (s234*c5*s6 - (c234*c6+s234*s6)/2.0 - (c234*c6-s234*s6)/2.0); T++;
00032 *T = (d1 + (d6*(c234*c5-s234*s5))/2.0 + a3*(s2*c3+c2*s3) + a2*s2 -
00033 (d6*(c234*c5+s234*s5))/2.0 - d5*c234); T++;
00034 *T = 0.0; T++; *T = 0.0; T++; *T = 0.0; T++; *T = 1.0;
00035 }
00036
00037 void forward_all(const double* q, double* T1, double* T2, double* T3,
00038 double* T4, double* T5, double* T6) {
00039 double s1 = sin(*q), c1 = cos(*q); q++;
00040 double q23 = *q, q234 = *q, s2 = sin(*q), c2 = cos(*q); q++;
00041 double s3 = sin(*q), c3 = cos(*q); q23 += *q; q234 += *q; q++;
00042 q234 += *q; q++;
00043 double s5 = sin(*q), c5 = cos(*q); q++;
00044 double s6 = sin(*q), c6 = cos(*q);
00045 double s23 = sin(q23), c23 = cos(q23);
00046 double s234 = sin(q234), c234 = cos(q234);
00047
00048 if(T1 != NULL) {
00049 *T1 = c1; T1++;
00050 *T1 = 0; T1++;
00051 *T1 = s1; T1++;
00052 *T1 = 0; T1++;
00053 *T1 = s1; T1++;
00054 *T1 = 0; T1++;
00055 *T1 = -c1; T1++;
00056 *T1 = 0; T1++;
00057 *T1 = 0; T1++;
00058 *T1 = 1; T1++;
00059 *T1 = 0; T1++;
00060 *T1 =d1; T1++;
00061 *T1 = 0; T1++;
00062 *T1 = 0; T1++;
00063 *T1 = 0; T1++;
00064 *T1 = 1; T1++;
00065 }
00066
00067 if(T2 != NULL) {
00068 *T2 = c1*c2; T2++;
00069 *T2 = -c1*s2; T2++;
00070 *T2 = s1; T2++;
00071 *T2 =a2*c1*c2; T2++;
00072 *T2 = c2*s1; T2++;
00073 *T2 = -s1*s2; T2++;
00074 *T2 = -c1; T2++;
00075 *T2 =a2*c2*s1; T2++;
00076 *T2 = s2; T2++;
00077 *T2 = c2; T2++;
00078 *T2 = 0; T2++;
00079 *T2 = d1 + a2*s2; T2++;
00080 *T2 = 0; T2++;
00081 *T2 = 0; T2++;
00082 *T2 = 0; T2++;
00083 *T2 = 1; T2++;
00084 }
00085
00086 if(T3 != NULL) {
00087 *T3 = c23*c1; T3++;
00088 *T3 = -s23*c1; T3++;
00089 *T3 = s1; T3++;
00090 *T3 =c1*(a3*c23 + a2*c2); T3++;
00091 *T3 = c23*s1; T3++;
00092 *T3 = -s23*s1; T3++;
00093 *T3 = -c1; T3++;
00094 *T3 =s1*(a3*c23 + a2*c2); T3++;
00095 *T3 = s23; T3++;
00096 *T3 = c23; T3++;
00097 *T3 = 0; T3++;
00098 *T3 = d1 + a3*s23 + a2*s2; T3++;
00099 *T3 = 0; T3++;
00100 *T3 = 0; T3++;
00101 *T3 = 0; T3++;
00102 *T3 = 1; T3++;
00103 }
00104
00105 if(T4 != NULL) {
00106 *T4 = c234*c1; T4++;
00107 *T4 = s1; T4++;
00108 *T4 = s234*c1; T4++;
00109 *T4 =c1*(a3*c23 + a2*c2) + d4*s1; T4++;
00110 *T4 = c234*s1; T4++;
00111 *T4 = -c1; T4++;
00112 *T4 = s234*s1; T4++;
00113 *T4 =s1*(a3*c23 + a2*c2) - d4*c1; T4++;
00114 *T4 = s234; T4++;
00115 *T4 = 0; T4++;
00116 *T4 = -c234; T4++;
00117 *T4 = d1 + a3*s23 + a2*s2; T4++;
00118 *T4 = 0; T4++;
00119 *T4 = 0; T4++;
00120 *T4 = 0; T4++;
00121 *T4 = 1; T4++;
00122 }
00123
00124 if(T5 != NULL) {
00125 *T5 = s1*s5 + c234*c1*c5; T5++;
00126 *T5 = -s234*c1; T5++;
00127 *T5 = c5*s1 - c234*c1*s5; T5++;
00128 *T5 =c1*(a3*c23 + a2*c2) + d4*s1 + d5*s234*c1; T5++;
00129 *T5 = c234*c5*s1 - c1*s5; T5++;
00130 *T5 = -s234*s1; T5++;
00131 *T5 = - c1*c5 - c234*s1*s5; T5++;
00132 *T5 =s1*(a3*c23 + a2*c2) - d4*c1 + d5*s234*s1; T5++;
00133 *T5 = s234*c5; T5++;
00134 *T5 = c234; T5++;
00135 *T5 = -s234*s5; T5++;
00136 *T5 = d1 + a3*s23 + a2*s2 - d5*c234; T5++;
00137 *T5 = 0; T5++;
00138 *T5 = 0; T5++;
00139 *T5 = 0; T5++;
00140 *T5 = 1; T5++;
00141 }
00142
00143 if(T6 != NULL) {
00144 *T6 = c6*(s1*s5 + c234*c1*c5) - s234*c1*s6; T6++;
00145 *T6 = - s6*(s1*s5 + c234*c1*c5) - s234*c1*c6; T6++;
00146 *T6 = c5*s1 - c234*c1*s5; T6++;
00147 *T6 =d6*(c5*s1 - c234*c1*s5) + c1*(a3*c23 + a2*c2) + d4*s1 + d5*s234*c1; T6++;
00148 *T6 = - c6*(c1*s5 - c234*c5*s1) - s234*s1*s6; T6++;
00149 *T6 = s6*(c1*s5 - c234*c5*s1) - s234*c6*s1; T6++;
00150 *T6 = - c1*c5 - c234*s1*s5; T6++;
00151 *T6 =s1*(a3*c23 + a2*c2) - d4*c1 - d6*(c1*c5 + c234*s1*s5) + d5*s234*s1; T6++;
00152 *T6 = c234*s6 + s234*c5*c6; T6++;
00153 *T6 = c234*c6 - s234*c5*s6; T6++;
00154 *T6 = -s234*s5; T6++;
00155 *T6 = d1 + a3*s23 + a2*s2 - d5*c234 - d6*s234*s5; T6++;
00156 *T6 = 0; T6++;
00157 *T6 = 0; T6++;
00158 *T6 = 0; T6++;
00159 *T6 = 1; T6++;
00160 }
00161 }
00162
00163 int inverse(const double* T, double* q_sols, double q6_des) {
00164 int num_sols = 0;
00165 double T02 = -*T; T++; double T00 = *T; T++; double T01 = *T; T++; double T03 = -*T; T++;
00166 double T12 = -*T; T++; double T10 = *T; T++; double T11 = *T; T++; double T13 = -*T; T++;
00167 double T22 = *T; T++; double T20 = -*T; T++; double T21 = -*T; T++; double T23 = *T;
00168
00170 double q1[2];
00171 {
00172 double A = d6*T12 - T13;
00173 double B = d6*T02 - T03;
00174 double R = A*A + B*B;
00175 if(fabs(A) < ZERO_THRESH) {
00176 double div;
00177 if(fabs(fabs(d4) - fabs(B)) < ZERO_THRESH)
00178 div = -SIGN(d4)*SIGN(B);
00179 else
00180 div = -d4/B;
00181 double arcsin = asin(div);
00182 if(fabs(arcsin) < ZERO_THRESH)
00183 arcsin = 0.0;
00184 if(arcsin < 0.0)
00185 q1[0] = arcsin + 2.0*PI;
00186 else
00187 q1[0] = arcsin;
00188 q1[1] = PI - arcsin;
00189 }
00190 else if(fabs(B) < ZERO_THRESH) {
00191 double div;
00192 if(fabs(fabs(d4) - fabs(A)) < ZERO_THRESH)
00193 div = SIGN(d4)*SIGN(A);
00194 else
00195 div = d4/A;
00196 double arccos = acos(div);
00197 q1[0] = arccos;
00198 q1[1] = 2.0*PI - arccos;
00199 }
00200 else if(d4*d4 > R) {
00201 return num_sols;
00202 }
00203 else {
00204 double arccos = acos(d4 / sqrt(R)) ;
00205 double arctan = atan2(-B, A);
00206 double pos = arccos + arctan;
00207 double neg = -arccos + arctan;
00208 if(fabs(pos) < ZERO_THRESH)
00209 pos = 0.0;
00210 if(fabs(neg) < ZERO_THRESH)
00211 neg = 0.0;
00212 if(pos >= 0.0)
00213 q1[0] = pos;
00214 else
00215 q1[0] = 2.0*PI + pos;
00216 if(neg >= 0.0)
00217 q1[1] = neg;
00218 else
00219 q1[1] = 2.0*PI + neg;
00220 }
00221 }
00223
00225 double q5[2][2];
00226 {
00227 for(int i=0;i<2;i++) {
00228 double numer = (T03*sin(q1[i]) - T13*cos(q1[i])-d4);
00229 double div;
00230 if(fabs(fabs(numer) - fabs(d6)) < ZERO_THRESH)
00231 div = SIGN(numer) * SIGN(d6);
00232 else
00233 div = numer / d6;
00234 double arccos = acos(div);
00235 q5[i][0] = arccos;
00236 q5[i][1] = 2.0*PI - arccos;
00237 }
00238 }
00240
00241 {
00242 for(int i=0;i<2;i++) {
00243 for(int j=0;j<2;j++) {
00244 double c1 = cos(q1[i]), s1 = sin(q1[i]);
00245 double c5 = cos(q5[i][j]), s5 = sin(q5[i][j]);
00246 double q6;
00248 if(fabs(s5) < ZERO_THRESH)
00249 q6 = q6_des;
00250 else {
00251 q6 = atan2(SIGN(s5)*-(T01*s1 - T11*c1),
00252 SIGN(s5)*(T00*s1 - T10*c1));
00253 if(fabs(q6) < ZERO_THRESH)
00254 q6 = 0.0;
00255 if(q6 < 0.0)
00256 q6 += 2.0*PI;
00257 }
00259
00260 double q2[2], q3[2], q4[2];
00262 double c6 = cos(q6), s6 = sin(q6);
00263 double x04x = -s5*(T02*c1 + T12*s1) - c5*(s6*(T01*c1 + T11*s1) - c6*(T00*c1 + T10*s1));
00264 double x04y = c5*(T20*c6 - T21*s6) - T22*s5;
00265 double p13x = d5*(s6*(T00*c1 + T10*s1) + c6*(T01*c1 + T11*s1)) - d6*(T02*c1 + T12*s1) +
00266 T03*c1 + T13*s1;
00267 double p13y = T23 - d1 - d6*T22 + d5*(T21*c6 + T20*s6);
00268
00269 double c3 = (p13x*p13x + p13y*p13y - a2*a2 - a3*a3) / (2.0*a2*a3);
00270 if(fabs(fabs(c3) - 1.0) < ZERO_THRESH)
00271 c3 = SIGN(c3);
00272 else if(fabs(c3) > 1.0) {
00273
00274 continue;
00275 }
00276 double arccos = acos(c3);
00277 q3[0] = arccos;
00278 q3[1] = 2.0*PI - arccos;
00279 double denom = a2*a2 + a3*a3 + 2*a2*a3*c3;
00280 double s3 = sin(arccos);
00281 double A = (a2 + a3*c3), B = a3*s3;
00282 q2[0] = atan2((A*p13y - B*p13x) / denom, (A*p13x + B*p13y) / denom);
00283 q2[1] = atan2((A*p13y + B*p13x) / denom, (A*p13x - B*p13y) / denom);
00284 double c23_0 = cos(q2[0]+q3[0]);
00285 double s23_0 = sin(q2[0]+q3[0]);
00286 double c23_1 = cos(q2[1]+q3[1]);
00287 double s23_1 = sin(q2[1]+q3[1]);
00288 q4[0] = atan2(c23_0*x04y - s23_0*x04x, x04x*c23_0 + x04y*s23_0);
00289 q4[1] = atan2(c23_1*x04y - s23_1*x04x, x04x*c23_1 + x04y*s23_1);
00291 for(int k=0;k<2;k++) {
00292 if(fabs(q2[k]) < ZERO_THRESH)
00293 q2[k] = 0.0;
00294 else if(q2[k] < 0.0) q2[k] += 2.0*PI;
00295 if(fabs(q4[k]) < ZERO_THRESH)
00296 q4[k] = 0.0;
00297 else if(q4[k] < 0.0) q4[k] += 2.0*PI;
00298 q_sols[num_sols*6+0] = q1[i]; q_sols[num_sols*6+1] = q2[k];
00299 q_sols[num_sols*6+2] = q3[k]; q_sols[num_sols*6+3] = q4[k];
00300 q_sols[num_sols*6+4] = q5[i][j]; q_sols[num_sols*6+5] = q6;
00301 num_sols++;
00302 }
00303
00304 }
00305 }
00306 }
00307 return num_sols;
00308 }
00309 };
00310
00311
00312 #define IKFAST_HAS_LIBRARY
00313 #include <ur_kinematics/ikfast.h>
00314 using namespace ikfast;
00315
00316
00317 #define IKFAST_COMPILE_ASSERT(x) extern int __dummy[(int)x]
00318 IKFAST_COMPILE_ASSERT(IKFAST_VERSION==61);
00319
00320 #ifdef IKFAST_NAMESPACE
00321 namespace IKFAST_NAMESPACE {
00322 #endif
00323
00324 void to_mat44(double * mat4_4, const IkReal* eetrans, const IkReal* eerot)
00325 {
00326 for(int i=0; i< 3;++i){
00327 mat4_4[i*4+0] = eerot[i*3+0];
00328 mat4_4[i*4+1] = eerot[i*3+1];
00329 mat4_4[i*4+2] = eerot[i*3+2];
00330 mat4_4[i*4+3] = eetrans[i];
00331 }
00332 mat4_4[3*4+0] = 0;
00333 mat4_4[3*4+1] = 0;
00334 mat4_4[3*4+2] = 0;
00335 mat4_4[3*4+3] = 1;
00336 }
00337
00338 void from_mat44(const double * mat4_4, IkReal* eetrans, IkReal* eerot)
00339 {
00340 for(int i=0; i< 3;++i){
00341 eerot[i*3+0] = mat4_4[i*4+0];
00342 eerot[i*3+1] = mat4_4[i*4+1];
00343 eerot[i*3+2] = mat4_4[i*4+2];
00344 eetrans[i] = mat4_4[i*4+3];
00345 }
00346 }
00347
00348
00349 IKFAST_API bool ComputeIk(const IkReal* eetrans, const IkReal* eerot, const IkReal* pfree, IkSolutionListBase<IkReal>& solutions) {
00350 if(!pfree) return false;
00351
00352 int n = GetNumJoints();
00353 double q_sols[8*6];
00354 double T[16];
00355
00356 to_mat44(T, eetrans, eerot);
00357
00358 int num_sols = ur_kinematics::inverse(T, q_sols,pfree[0]);
00359
00360 std::vector<int> vfree(0);
00361
00362 for (int i=0; i < num_sols; ++i){
00363 std::vector<IkSingleDOFSolutionBase<IkReal> > vinfos(n);
00364 for (int j=0; j < n; ++j) vinfos[j].foffset = q_sols[i*n+j];
00365 solutions.AddSolution(vinfos,vfree);
00366 }
00367 return num_sols > 0;
00368 }
00369
00370 IKFAST_API void ComputeFk(const IkReal* j, IkReal* eetrans, IkReal* eerot)
00371 {
00372 double T[16];
00373 ur_kinematics::forward(j,T);
00374 from_mat44(T,eetrans,eerot);
00375 }
00376
00377 IKFAST_API int GetNumFreeParameters() { return 1; }
00378 IKFAST_API int* GetFreeParameters() { static int freeparams[] = {5}; return freeparams; }
00379 IKFAST_API int GetNumJoints() { return 6; }
00380
00381 IKFAST_API int GetIkRealSize() { return sizeof(IkReal); }
00382
00383 #ifdef IKFAST_NAMESPACE
00384 }
00385 #endif
00386
00387 #ifndef IKFAST_NO_MAIN
00388
00389 using namespace std;
00390 using namespace ur_kinematics;
00391
00392 int main(int argc, char* argv[])
00393 {
00394 double q[6] = {0.0, 0.0, 1.0, 0.0, 1.0, 0.0};
00395 double* T = new double[16];
00396 forward(q, T);
00397 for(int i=0;i<4;i++) {
00398 for(int j=i*4;j<(i+1)*4;j++)
00399 printf("%1.3f ", T[j]);
00400 printf("\n");
00401 }
00402 double q_sols[8*6];
00403 int num_sols;
00404 num_sols = inverse(T, q_sols);
00405 for(int i=0;i<num_sols;i++)
00406 printf("%1.6f %1.6f %1.6f %1.6f %1.6f %1.6f\n",
00407 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]);
00408 for(int i=0;i<=4;i++)
00409 printf("%f ", PI/2.0*i);
00410 printf("\n");
00411 return 0;
00412 }
00413 #endif