簡介
最近身邊有的小伙伴需要用到aubo機械臂，并且需要使用python版本的正運動學，我就根據官網給的參考代碼，寫了一個python版本的，喜歡或者需要的朋友可以直接拿去用，這里主要使用幾何法來進行運動學求解，后面會更新具有最優解選擇器的代碼。具有官方推薦的最優解的程序請參考Aubo 協作機械臂正逆運動學包-python 版本（二）。
注意
：這里代碼只需要把DH參數更換即可用到aubo其他機械臂上，代碼主要基于簡單的數據結構，想優化的可以把它優化一下，后面我有時間會把部分優化一下，木有時間的情況，就會繼續這么用。
代碼如下
from math import *
import numpy
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
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_sols(0,num_sols) = q1(i)
# q_sols(1,num_sols) = q2(k)
# q_sols(2,num_sols) = q3(k)
# q_sols(3,num_sols) = q4(k)
# q_sols(4,num_sols) = q5(i,j)
# q_sols(5,num_sols) = q6
q_reslut_dic.update({num_sols:q_reslut})
num_sols+=1
return q_reslut_dic#,num_sols
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]
q_dict,num=ak47.aubo_inverse(tt)
print q_dict,num
for i in range(len(q_dict)):
print i,q_dict[i]
if __name__=="__main__":
main()
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