Newer
Older
#include <ur_kinematics/ur_kin.h>
namespace ur_kinematics {
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;
}
void forward_all(const double* q, double* T1, double* T2, double* T3,
double* T4, double* T5, double* T6) {
double s1 = sin(*q), c1 = cos(*q); q++; // q1
double q23 = *q, q234 = *q, s2 = sin(*q), c2 = cos(*q); q++; // q2
double s3 = sin(*q), c3 = cos(*q); q23 += *q; q234 += *q; q++; // q3
q234 += *q; q++; // q4
double s5 = sin(*q), c5 = cos(*q); q++; // q5
double s6 = sin(*q), c6 = cos(*q); // q6
double s23 = sin(q23), c23 = cos(q23);
double s234 = sin(q234), c234 = cos(q234);
if(T1 != NULL) {
*T1 = c1; T1++;
*T1 = 0; T1++;
*T1 = s1; T1++;
*T1 = 0; T1++;
*T1 = s1; T1++;
*T1 = 0; T1++;
*T1 = -c1; T1++;
*T1 = 0; T1++;
*T1 = 0; T1++;
*T1 = 1; T1++;
*T1 = 0; T1++;
*T1 =d1; T1++;
*T1 = 0; T1++;
*T1 = 0; T1++;
*T1 = 0; T1++;
*T1 = 1; T1++;
}
if(T2 != NULL) {
*T2 = c1*c2; T2++;
*T2 = -c1*s2; T2++;
*T2 = s1; T2++;
*T2 =a2*c1*c2; T2++;
*T2 = c2*s1; T2++;
*T2 = -s1*s2; T2++;
*T2 = -c1; T2++;
*T2 =a2*c2*s1; T2++;
*T2 = s2; T2++;
*T2 = c2; T2++;
*T2 = 0; T2++;
*T2 = d1 + a2*s2; T2++;
*T2 = 0; T2++;
*T2 = 0; T2++;
*T2 = 0; T2++;
*T2 = 1; T2++;
}
if(T3 != NULL) {
*T3 = c23*c1; T3++;
*T3 = -s23*c1; T3++;
*T3 = s1; T3++;
*T3 =c1*(a3*c23 + a2*c2); T3++;
*T3 = c23*s1; T3++;
*T3 = -s23*s1; T3++;
*T3 = -c1; T3++;
*T3 =s1*(a3*c23 + a2*c2); T3++;
*T3 = s23; T3++;
*T3 = c23; T3++;
*T3 = 0; T3++;
*T3 = d1 + a3*s23 + a2*s2; T3++;
*T3 = 0; T3++;
*T3 = 0; T3++;
*T3 = 0; T3++;
*T3 = 1; T3++;
}
if(T4 != NULL) {
*T4 = c234*c1; T4++;
*T4 = s1; T4++;
*T4 = s234*c1; T4++;
*T4 =c1*(a3*c23 + a2*c2) + d4*s1; T4++;
*T4 = c234*s1; T4++;
*T4 = -c1; T4++;
*T4 = s234*s1; T4++;
*T4 =s1*(a3*c23 + a2*c2) - d4*c1; T4++;
*T4 = s234; T4++;
*T4 = 0; T4++;
*T4 = -c234; T4++;
*T4 = d1 + a3*s23 + a2*s2; T4++;
*T4 = 0; T4++;
*T4 = 0; T4++;
*T4 = 0; T4++;
*T4 = 1; T4++;
}
if(T5 != NULL) {
*T5 = s1*s5 + c234*c1*c5; T5++;
*T5 = -s234*c1; T5++;
*T5 = c5*s1 - c234*c1*s5; T5++;
*T5 =c1*(a3*c23 + a2*c2) + d4*s1 + d5*s234*c1; T5++;
*T5 = c234*c5*s1 - c1*s5; T5++;
*T5 = -s234*s1; T5++;
*T5 = - c1*c5 - c234*s1*s5; T5++;
*T5 =s1*(a3*c23 + a2*c2) - d4*c1 + d5*s234*s1; T5++;
*T5 = s234*c5; T5++;
*T5 = c234; T5++;
*T5 = -s234*s5; T5++;
*T5 = d1 + a3*s23 + a2*s2 - d5*c234; T5++;
*T5 = 0; T5++;
*T5 = 0; T5++;
*T5 = 0; T5++;
*T5 = 1; T5++;
}
if(T6 != NULL) {
*T6 = c6*(s1*s5 + c234*c1*c5) - s234*c1*s6; T6++;
*T6 = - s6*(s1*s5 + c234*c1*c5) - s234*c1*c6; T6++;
*T6 = c5*s1 - c234*c1*s5; T6++;
*T6 =d6*(c5*s1 - c234*c1*s5) + c1*(a3*c23 + a2*c2) + d4*s1 + d5*s234*c1; T6++;
*T6 = - c6*(c1*s5 - c234*c5*s1) - s234*s1*s6; T6++;
*T6 = s6*(c1*s5 - c234*c5*s1) - s234*c6*s1; T6++;
*T6 = - c1*c5 - c234*s1*s5; T6++;
*T6 =s1*(a3*c23 + a2*c2) - d4*c1 - d6*(c1*c5 + c234*s1*s5) + d5*s234*s1; T6++;
*T6 = c234*s6 + s234*c5*c6; T6++;
*T6 = c234*c6 - s234*c5*s6; T6++;
*T6 = -s234*s5; T6++;
*T6 = d1 + a3*s23 + a2*s2 - d5*c234 - d6*s234*s5; T6++;
*T6 = 0; T6++;
*T6 = 0; T6++;
*T6 = 0; T6++;
*T6 = 1; T6++;
}
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
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;
}
};
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
#define IKFAST_HAS_LIBRARY
#include <ur_kinematics/ikfast.h>
using namespace ikfast;
// check if the included ikfast version matches what this file was compiled with
#define IKFAST_COMPILE_ASSERT(x) extern int __dummy[(int)x]
IKFAST_COMPILE_ASSERT(IKFAST_VERSION==61);
#ifdef IKFAST_NAMESPACE
namespace IKFAST_NAMESPACE {
#endif
void to_mat44(double * mat4_4, const IkReal* eetrans, const IkReal* eerot)
{
for(int i=0; i< 3;++i){
mat4_4[i*4+0] = eerot[i*3+0];
mat4_4[i*4+1] = eerot[i*3+1];
mat4_4[i*4+2] = eerot[i*3+2];
mat4_4[i*4+3] = eetrans[i];
}
mat4_4[3*4+0] = 0;
mat4_4[3*4+1] = 0;
mat4_4[3*4+2] = 0;
mat4_4[3*4+3] = 1;
}
void from_mat44(const double * mat4_4, IkReal* eetrans, IkReal* eerot)
{
for(int i=0; i< 3;++i){
eerot[i*3+0] = mat4_4[i*4+0];
eerot[i*3+1] = mat4_4[i*4+1];
eerot[i*3+2] = mat4_4[i*4+2];
eetrans[i] = mat4_4[i*4+3];
}
}
IKFAST_API bool ComputeIk(const IkReal* eetrans, const IkReal* eerot, const IkReal* pfree, IkSolutionListBase<IkReal>& solutions) {
if(!pfree) return false;
int n = GetNumJoints();
double q_sols[8*6];
double T[16];
to_mat44(T, eetrans, eerot);
int num_sols = ur_kinematics::inverse(T, q_sols,pfree[0]);
std::vector<int> vfree(0);
for (int i=0; i < num_sols; ++i){
std::vector<IkSingleDOFSolutionBase<IkReal> > vinfos(n);
for (int j=0; j < n; ++j) vinfos[j].foffset = q_sols[i*n+j];
solutions.AddSolution(vinfos,vfree);
}
return num_sols > 0;
}
IKFAST_API void ComputeFk(const IkReal* j, IkReal* eetrans, IkReal* eerot)
{
double T[16];
ur_kinematics::forward(j,T);
from_mat44(T,eetrans,eerot);
}
IKFAST_API int GetNumFreeParameters() { return 1; }
IKFAST_API int* GetFreeParameters() { static int freeparams[] = {5}; return freeparams; }
IKFAST_API int GetNumJoints() { return 6; }
IKFAST_API int GetIkRealSize() { return sizeof(IkReal); }
#ifdef IKFAST_NAMESPACE
} // end namespace
#endif
#ifndef IKFAST_NO_MAIN
using namespace std;
using namespace ur_kinematics;
int main(int argc, char* argv[])
{
double q[6] = {0.0, 0.0, 1.0, 0.0, 1.0, 0.0};
double* T = new double[16];
forward(q, T);
for(int i=0;i<4;i++) {
for(int j=i*4;j<(i+1)*4;j++)
printf("%1.3f ", T[j]);
printf("\n");
}
double q_sols[8*6];
int num_sols;
num_sols = inverse(T, q_sols);
for(int i=0;i<num_sols;i++)
printf("%1.6f %1.6f %1.6f %1.6f %1.6f %1.6f\n",
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]);
for(int i=0;i<=4;i++)
printf("%f ", PI/2.0*i);
printf("\n");
return 0;
}