Aubo 协作机械臂正逆运动学包-python 版本（二）_auboi5的正运动学矩阵

简介

Aubo 协作机械臂正逆运动学包-python 版本（一）这篇博文已经对奥博协作机械臂正逆运动学进行了求解。由于代码相对较长，就分开两个博文分别更新。本文主要会根据官方代码，及官方推荐的最优选解器更新一个Python版本的正运动学包。这里最优选解器的核心和UR的一样，都是选择和参考关节空间最接近的一组解作为最优解。文中代码喜欢的可以直接拿去使用，有问题或者对于代码不理解的地方，欢迎添加关注和微信公众号询问。

代码如下：

#!/usr/bin/env python 
# -*- coding: utf-8 -*-
from math import *
import numpy
"""
a2 = 0.266;
a3 = 0.2565;
d1 = 0.157;
d2 = 0.119;
d5 = 0.1025;
d6 = 0.094;
#endif

#ifdef AUBO_I3s_PARAMS
a2 = 0.229;
a3 = 0.2015;
d1 = 0.1395;
d2 = 0.11055;
d5 = 0.08955;
d6 = 0.09055;
#endif

#define AUBO_I5_PARAMS
#ifdef AUBO_I5_PARAMS
a2 =  0.408;
a3 =  0.376;
d1 =  0.122;
d2 =  0.1215;
d5 =  0.1025;
d6 =  0.094;
#endif

#ifdef AUBO_I5s_PARAMS
a2 = 0.245;
a3 = 0.215;
d1 = 0.1215;
d2 = 0.1215;
d5 = 0.1025;
d6 = 0.094;
#endif

#ifdef AUBO_I5l_PARAMS
a2 = 0.608;
a3 = 0.6395;
d1 = 0.1215;
d2 = 0.1215;
d5 = 0.1025;
d6 = 0.094;
#endif

#ifdef AUBO_I7_PARAMS
a2 = 0.552;
a3 = 0.495;
d1 = 0.1632;
d2 = 0.178;
d5 = 0.1025;
d6 = 0.094;
#endif


#ifdef AUBO_I10_PARAMS
a2 = 0.647;
a3 = 0.6005;
d1 = 0.1632;
d2 = 0.2013;
d5 = 0.1025;
d6 = 0.094;
"""
class Aubo_kinematics():
    def __init__(self):
        self.a2 =  0.408
        self.a3 =  0.376
        self.d1 =  0.122
        self.d2 =  0.1215
        self.d5 =  0.1025
        self.d6 =  0.094
        self.ZERO_THRESH = 1e-4
        self.ARM_DOF=6
    def degree_to_rad(self,q):
        temp=[]
        for i in range(len(q)):
            temp.append(q[i]*pi/180)
        return temp
    def antiSinCos(self,sA,cA):
    
        eps = 1e-8
        angle = 0
        if((abs(sA) < eps)and(abs(cA) < eps)):
        
            return 0
        
        if(abs(cA) < eps):
            angle = pi/2.0*self.SIGN(sA)
        elif(abs(sA) < eps):
        
            if (self.SIGN(cA) == 1):
                angle = 0
            else:
                angle = pi
        
        else:
        
            angle = atan2(sA, cA)
        

        return angle
    def SIGN(self,x):
        return (x > 0) - (x < 0)
    
    def aubo_forward(self,q):
        q=self.degree_to_rad(q)
        T=[]
        for i in range(16):
            T.append(0)
        # print q
        q1 = q[0]
        q2 = q[1]
        q3 = q[2]
        q4 = q[3]
        q5 = q[4]
        q6 = q[5]
        C1 = cos(q1)
        C2 = cos(q2)
        C4 = cos(q4)
        C5 = cos(q5)
        C6 = cos(q6)
        C23 = cos(q2 - q3)
        C234 = cos(q2 - q3 + q4)
        C2345 = cos(q2 - q3 + q4 - q5)
        C2345p = cos(q2 - q3 + q4 + q5)
        S1 = sin(q1)
        S2 = sin(q2)
        S4 = sin(q4)
        S5 = sin(q5)
        S6 = sin(q6)
        S23 = sin(q2 - q3)
        S234 = sin(q2 - q3 + q4)

        T[0] = -C6 * S1 * S5 + C1 * (C234 * C5 * C6 - S234 * S6)
        T[1]= S1 * S5 * S6 - C1 * (C4 * C6 * S23 + C23 * C6 * S4 + C234 * C5 * S6)
        T[2] = C5 * S1 + C1 * C234 * S5
        T[3] = (self.d2 + C5 * self.d6) * S1 - C1 * (self.a2 * S2 + (self.a3 + C4 * self.d5) * S23 + C23 * self.d5 * S4 - C234 * self.d6 * S5)

        T[4] = C234 * C5 * C6 * S1 + C1 * C6 * S5 - S1 * S234 * S6
        T[5] = -C6 * S1 * S234 - (C234 * C5 * S1 + C1 * S5) * S6
        T[6] = -C1 * C5 + C234 * S1 * S5
        T[7] = -C1 * (self.d2 + C5 * self.d6) - S1 * (self.a2 * S2 + (self.a3 + C4 * self.d5) * S23 + C23 * self.d5 * S4 - C234 * self.d6 * S5)

        T[8] = C5 * C6 * S234 + C234 * S6
        T[9] = C234 * C6 - C5 * S234 * S6
        T[10] = S234 * S5
        T[11] = self.d1 + self.a2 * C2 + self.a3 * C23 + self.d5 * C234 + self.d6 * C2345/2 - self.d6 * C2345p / 2
        T[12]=0
        T[13]=0
        T[14]=0
        T[15]=1
        return T
    def aubo_inverse(self,T):
        q_reslut_dic={}
        q_reslut=[]
        singularity = False

        num_sols = 0
        nx = T[0]
        ox = T[1]
        ax = T[2]
        px = T[3]

        ny = T[4]
        oy = T[5]
        ay = T[6] 
        py = T[7]
        nz = T[8]
        oz = T[9] 
        az = T[10] 
        pz = T[11]

        #  shoulder rotate joint (q1) //
        q1=[0,0]

        A1 = self.d6 * ay - py
        B1 = self.d6 * ax - px
        R1 = A1 * A1 + B1 * B1 - self.d2 * self.d2


        if R1 < 0.0:
            return num_sols
        else:
            R12 = sqrt(R1)
            q1[0] =  self.antiSinCos(A1, B1) -  self.antiSinCos(self.d2, R12)
            q1[1] =  self.antiSinCos(A1, B1) -  self.antiSinCos(self.d2, -R12)
            for i in range(len(q1)):
            
                while q1[i] > pi:
                    q1[i] -= 2 * pi
                while q1[i] < -pi:
                    q1[i] += 2 * pi
            
        

        #// wrist 2 joint (q5) //
        q5=[[0,0],[0,0]]

        for i in range(len(q5)):
        

            C1 = cos(q1[i])
            S1 = sin(q1[i])
            B5 = -ay * C1 + ax * S1
            M5 = (-ny * C1 + nx * S1)
            N5 = (-oy * C1 + ox * S1)
            R5 = sqrt(M5 * M5 + N5 * N5)

            q5[i][0] = self.antiSinCos(R5, B5)
            q5[i][1] = self.antiSinCos(-R5, B5)
        

        #

        #// wrist 3 joint (q6) //
        q6=0

        q3=[0,0]
        q2=[0,0]
        q4=[0,0]
        for i in range(len(q3)):
        
            for j in range(len(q3)):
            
                #// wrist 3 joint (q6) //
                C1 = cos(q1[i])
                S1 = sin(q1[i])
                S5 = sin(q5[i][j])

                A6 = (-oy * C1 + ox * S1)
                B6 = (ny * C1 - nx * S1)

                if fabs(S5) < self.ZERO_THRESH:# //the condition is only dependent on q1
                
                    singularity = True
                    break
                else:
                    q6 = self.antiSinCos(A6 * S5, B6 * S5)

                #/// joints (q3,q2,q4) //
                C6 = cos(q6)
                S6 = sin(q6)

                pp1 = C1 * (ax * self.d6 - px + self.d5 * ox * C6 + self.d5 * nx * S6) + S1 * (ay * self.d6 - py + self.d5 * oy * C6 + self.d5 * ny * S6)
                pp2 = -self.d1 - az * self.d6 + pz - self.d5 * oz * C6 - self.d5 * nz * S6
                B3 = (pp1 * pp1 + pp2 * pp2 - self.a2 * self.a2 - self.a3 * self.a3) / (2 * self.a2 * self.a3)


                if((1 - B3 * B3) < self.ZERO_THRESH):
                    singularity = True
                    continue
                else:
                    Sin3 = sqrt(1 - B3 * B3)
                    q3[0] = self.antiSinCos(Sin3, B3)
                    q3[1] = self.antiSinCos(-Sin3, B3)

                for k in range(len(q3)):
                

                    C3 = cos(q3[k])
                    S3 = sin(q3[k])
                    A2 = pp1 * (self.a2 + self.a3 * C3) + pp2 * (self.a3 * S3)
                    B2 = pp2 * (self.a2 + self.a3 * C3) - pp1 * (self.a3 * S3)

                    q2[k] = self.antiSinCos(A2, B2)
                    C2 = cos(q2[k])
                    S2 = sin(q2[k])

                    A4 = -C1 * (ox * C6 + nx * S6) - S1 * (oy * C6 + ny * S6)
                    B4 = oz * C6 + nz * S6
                    A41 = pp1 - self.a2 * S2
                    B41 = pp2 - self.a2 * C2

                    q4[k] = self.antiSinCos(A4, B4) - self.antiSinCos(A41, B41)
                    while(q4[k] > pi):
                        q4[k] -= 2 * pi
                    while(q4[k] < -pi):
                        q4[k] += 2 * pi
                    q_reslut=[q1[i],q2[k],q3[k],q4[k],q5[i][j],q6]

                    q_reslut_dic.update({num_sols:q_reslut})
                    num_sols+=1
                
        return q_reslut_dic,num_sols
        """
        The Frobenius norm, sometimes also called the Euclidean norm (a term unfortunately also used for the vector L^2-norm), 
        is matrix norm of an m×n matrix A defined as the square root of the sum of the absolute squares of its elements,
        """
    def List_Frobenius_Norm(self,list_a,list_b):
        new_list=[]
        if len(list_a)==len(list_b):
            for i in range(len(list_a)):
                new_list.append(abs(list_a[i]-list_b[i])**2)
        else:
            print("please make sure the list has the same length")
        
        return sqrt(self.sum_list(new_list))
    def sum_list(self,list_data):
        sum_data=0
        for i in range(len(list_data)):
            sum_data+=list_data[i]
        return sum_data
    # //choose solution ;input all q_sols,and last q_old;
    # //out put the nearest q solution;
    # /**
    #  * @brief chooseIKonRefJoint , choose mode == 0;
    #  * @param q_sols rad
    #  * @param q_ref
    #  * @param q_choose
    #  * @return
    #  */
    def chooseIKonRefJoint(self,q_sols,q_ref):
    
        nn = len(q_sols)
        if(nn == 0):
            return False,[]
        # print "nn---",nn
        sum_data = self.List_Frobenius_Norm(q_ref,q_sols[0])
        err=0
        index = 0
        for i in range(len(q_sols)):
        
            err = self.List_Frobenius_Norm(q_ref,q_sols[i])
            # print "err",err
            if(err < sum_data):
                index = i
                sum_data = err
            
        # print sum_data
        q_choose = q_sols[index]

        return True,q_choose
    """aubo rotation joint:-175 degree/175 degree,here is rad I wanna take a break so use degree"""
    def selectIK(self,q_sols,AngleLimit):
        q_sols_selected={}
        N = len(q_sols)
        # print "selectIK ---N---",N
        if( N == 0):
            return False,{}
        num = 0
        valid = True
        for i in range(N):
        
            valid = True;
            for j in range(self.ARM_DOF):
            #drop greater than offical degree
                if(q_sols[i][j] > AngleLimit[j][1] or q_sols[i][j] < AngleLimit[j][0]):
                    valid = False
                    break
                
            #delete the sols about joint angular increase 2*pi greater than the legal angular
            if(valid):
                temp=q_sols[i]
                temp_1=q_sols[i]
                for j in range(self.ARM_DOF):
                    temp[j] += 2*pi
                    temp_1[j]-=2*pi
                    if temp[j]>AngleLimit[j][1] or temp_1[j]<AngleLimit[j][0]:
                        valid = False
                        break
                if valid:
                    q_sols_selected.update({num:q_sols[i]})
                    num+=1

        num_sols = num;

        if(num > 0):
            return True,q_sols_selected
        else:
            return False,{}
    

    def GetInverseResult(self,T_target,q_ref):
    
        num_sols = 0

        maxq = 175.0/180.0*pi
        AngleLimit = [(-maxq,maxq),(-maxq,maxq),(-maxq,maxq),(-maxq,maxq),(-maxq,maxq),(-maxq,maxq)]

        #inverse and remove zero list
        q_sols_all,num_sols = self.aubo_inverse(T_target)
        
        if(len(q_sols_all) != 0):
            for i in q_sols_all:
                print("num:"+str(i)+' '+"sols",q_sols_all[i])
            #remove not in limited data 
            ret2,q_sols_inlimit = self.selectIK(q_sols_all, AngleLimit)
            # print "q_sols_inlimit",q_sols_inlimit
            if((len(q_sols_inlimit) != 0) and (True == ret2)):
            
                ret3,q_result = self.chooseIKonRefJoint(q_sols_inlimit, q_ref)

                if(True == ret3):
                
                    print(" find solution choose  ")
                    return q_result
                
                else:
                
                    print(" No solution choose  ")
            else:
            
                print("no valid sols ")

            
        
        else:
        
            print("inverse result num is 0")
            # return False
        
    
def main():
    ak47=Aubo_kinematics()
    # print ak47.aubo_forward([-3.3364,12.406,-81.09,-91.207,-86.08,0.164])
    # print numpy.matrix(ak47.aubo_forward([-3.3364,12.406,-81.09,-91.207,-86.08,0.164])).reshape((4,4))
    tt=[0.010016939985065143, -0.039901099098502056, -0.9991534232559417, -0.3, -0.999934201568705, 0.005186605233011846, -0.010231894219208601, -0.09507448660946277, 0.005590478198847001, 0.999190172798396, -0.039846519755429126, 0.5962177031402299, 0, 0, 0, 1]
    # tt=[1.0, 0.0, 0.0, -0.4, 0.0, -1.0, -0.0, -0.8500000000000001, 0.0, 0.0, -1.0, -0.4, 0.0, 0.0, 0.0, 1.0]
    # tt=[1.0, 0.0, 0.0, -0.4, 0.0, -1.0, -0.0, -0.4500000000000001, 0.0, 0.0, -1.0, -0.4, 0.0, 0.0, 0.0, 1.0]
    # q_dict,num=ak47.aubo_inverse(tt)
    # print q_dict,num
    # for i in range(len(q_dict)):
    #     print i,q_dict[i]
    # print ak47.degree_to_rad([-3.3364,12.406,-81.09,-91.207,-86.08,0.164])
    print ak47.GetInverseResult(tt,ak47.degree_to_rad([-3.3364,12.406,-81.09,-91.207,-86.08,0.164]))
if __name__=="__main__":
    main()
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
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
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
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432

最后

写代码不易，转载请注明出处，有问题的可以咨询，但是不一定保证快速响应。