简介
相信很多搞机械臂的人都用过UR这款机械臂，目前主流的正逆运动学是C++版本的，我早期写过一个Python版本的，今天也贡献出来给大家，需要的可以直接获取，想自己优化代码的也可以自己优化，有问题的欢迎关注发私信或者关注微信公众号，我会进行解释。感谢大家的支持。
代码如下
#!/usr/bin/python
"""
author:yuexiaoshu
time:20180812
version:v2
info:1,change class function 2,add best sol function
"""
import math
import numpy
#UR5 parmas
d1 = 0.089159
a2 = -0.42500
a3 = -0.39225
d4 = 0.10915
d5 = 0.09465
d6 = 0.0823
PI = math.pi
ZERO_THRESH = 0.00000001
class Kinematic:
def __init__(self):
global d1
global a2
global a3
global d4
global d5
global d6
global PI
global ZERO_THRESH
def Forward(self,q):
T=[0]*16
#00
s1 = math.sin(q[0])
c1 = math.cos(q[0])
##01
q234 = q[1]
s2 = math.sin(q[1])
c2 = math.cos(q[1])
##02
s3 = math.sin(q[2])
c3 = math.cos(q[2])
q234 += q[2]
##03
q234 += q[3]
##04
s5 = math.sin(q[4])
c5 = math.cos(q[4])
##05
s6 = math.sin(q[5])
c6 = math.cos(q[5])
s234 = math.sin(q234)
c234 = math.cos(q234)
#4*4 roate arrary
#00 parameter
T[0] = ((c1 * c234 - s1 * s234) * s5) / 2.0 - c5 * s1 + ((c1 * c234 + s1 * s234) * s5) / 2.0
# 01 parameter
T[1] = (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)
# 02 parameter
T[2] = (-(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))
# 03 parameter
T[3] = ((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)
# 04 parameter
T[4] = c1 * c5 + ((s1 * c234 + c1 * s234) * s5) / 2.0 + ((s1 * c234 - c1 * s234) * s5) / 2.0
# 05 parameter
T[5] = (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))
# 06 parameter
T[6] = (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))
# 07 parameter
T[7] = ((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)
# 08 parameter
T[8] = ((c234 * c5 - s234 * s5) / 2.0 - (c234 * c5 + s234 * s5) / 2.0)
# 09 parameter
T[9] = ((s234 * c6 - c234 * s6) / 2.0 - (s234 * c6 + c234 * s6) / 2.0 - s234 * c5 * c6)
# 10 parameter
T[10] = (s234 * c5 * s6 - (c234 * c6 + s234 * s6) / 2.0 - (c234 * c6 - s234 * s6) / 2.0)
# 11 parameter
T[11] = (d1 + (d6 * (c234 * c5 - s234 * s5)) / 2.0 + a3 * (s2 * c3 + c2 * s3) + a2 * s2 -
(d6 * (c234 * c5 + s234 * s5)) / 2.0 - d5 * c234)
# 12 parameter
T[12] = 0.0
# 13 parameter
T[13] = 0.0
# 14 parameter
T[14] = 0.0
# 15 parameter
T[15] = 1.0
return T
def SIGN(self,x):
return (x>0)-(x<0)
def Forward_all(self,q):
#result
result=[]
T1=[]
T2=[]
T3=[]
T4=[]
T5=[]
T6=[]
#q01
s1 = math.sin(q[0])
c1 = math.cos(q[0])
#q02
q23 = q[1]
q234 = q[1]
s2 = math.sin(q[1])
c2 = math.cos(q[1])
#q03
s3 = math.sin(q[2])
c3 = math.cos(q[2])
q23 += q[2]
q234 += q[2]
#q04
q234 += q[3]
#q05
s5 = math.sin(q[4])
c5 = math.cos(q[4])
#q06
s6 = math.sin(q[5])
c6 = math.cos(q[5])
s23 = math.sin(q23)
c23 = math.cos(q23)
s234 = math.sin(q234)
c234 = math.cos(q234)
#01T
#00-15 param
T1[0] = c1
T1[1] = 0
T1[2] = s1
T1[3] = 0
T1[4] = s1
T1[5] = 0
T1[6] = -c1
T1[7] = 0
T1[8] = 0
T1[9] = 1
T1[10] = 0
T1[11] =d1
T1[12] = 0
T1[13] = 0
T1[14] = 0
T1[15] = 1
result.append(("T1",T1))
#01T*12T=02T
#00-15 parameters
T2[0] = c1 * c2
T2[1] = -c1 * s2
T2[2] = s1
T2[3] =a2 * c1 * c2
T2[4] = c2 * s1
T2[5] = -s1 * s2
T2[6] = -c1
T2[7] =a2 * c2 * s1
T2[8] = s2
T2[9] = c2
T2[10] = 0
T2[11] = d1 + a2 * s2
T2[12] = 0
T2[13] = 0
T2[14] = 0
T2[15] = 1
result.append(("T2",T2))
#01T*12T*23T=03T
T3[0] = c23 * c1
T3[1] = -s23 * c1
T3[2] = s1
T3[3] =c1 * (a3 * c23 + a2 * c2)
T3[4] = c23 * s1
T3[5] = -s23 * s1
T3[6] = -c1
T3[7] =s1 * (a3 * c23 + a2 * c2)
T3[8] = s23
T3[9] = c23
T3[10] = 0
T3[11] = d1 + a3 * s23 + a2 * s2
T3[12] = 0
T3[13] = 0
T3[14] = 0
T3[15] =1
result.append(("T3",T3))
#01T*12T*23T*34T=04T
T4[0] = c234 * c1
T4[1] = s1
T4[2] = s234 * c1
T4[3] =c1 * (a3 * c23 + a2 * c2) + d4 * s1
T4[4] = c234 * s1
T4[5] = -c1
T4[6] = s234 * s1
T4[7] =s1 * (a3 * c23 + a2 * c2) - d4 * c1
T4[8] = s234
T4[9] = 0
T4[10] = -c234
T4[11] =d1 + a3 * s23 + a2 * s2
T4[12] =0
T4[13] = 0
T4[14] = 0
T4[15] = 1
result.append(("T4",T4))
#01T*12T*23T*34T*45T=05T
T5[0] = s1 * s5 + c234 * c1 * c5
T5[1] = -s234 * c1
T5[2] = c5 * s1 - c234 * c1 * s5
T5[3] =c1 * (a3 * c23 + a2 * c2) + d4 * s1 + d5 * s234 * c1
T5[4] = c234 * c5 * s1 - c1 * s5
T5[5] = -s234 * s1
T5[6] = - c1 * c5 - c234 * s1 * s5
T5[7] =s1 * (a3 * c23 + a2 * c2) - d4 * c1 + d5 * s234 * s1
T5[8] = s234 * c5
T5[9] = c234
T5[10] = -s234 * s5
T5[11] = d1 + a3 * s23 + a2 * s2 - d5 * c234
T5[12] = 0
T5[13] = 0
T5[14] = 0
T5[15] =1
result.append(("T5",T5))
#01T*12T*23T*34T*45T*56T=06T
T6[0] = c6 * (s1 * s5 + c234 * c1 * c5) - s234 * c1 * s6
T6[1] = - s6 * (s1 * s5 + c234 * c1 * c5) - s234 * c1 * c6
T6[2] = c5 * s1 - c234 * c1 * s5
T6[3] =d6 * (c5 * s1 - c234 * c1 * s5) + c1 * (a3 * c23 + a2 * c2) + d4 * s1 + d5 * s234 * c1
T6[4] = - c6 * (c1 * s5 - c234 * c5 * s1) - s234 * s1 * s6
T6[5] = s6 * (c1 * s5 - c234 * c5 * s1) - s234 * c6 * s1
T6[6] = - c1 * c5 - c234 * s1 * s5
T6[7] =s1 * (a3 * c23 + a2 * c2) - d4 * c1 - d6 * (c1 * c5 + c234 * s1 * s5) + d5 * s234 * s1
T6[8] =c234 * s6 + s234 * c5 * c6
T6[9] = c234 * c6 - s234 * c5 * s6
T6[10] = -s234 * s5
T6[11] = d1 + a3 * s23 + a2 * s2 - d5 * c234 - d6 * s234 * s5
T6[12] = 0
T6[13] = 0
T6[14] = 0
T6[15] = 1
result.append(("T6", T6))
return result
def Iverse(self,T,q6_des):
q_sols=[0]*48
num_sols = 0
T02 = - T[0]
T00 = T[1]
T01 = T[2]
T03 = -T[3]
T12 = - T[4]
T10 = T[5]
T11 = T[6]
T13 = - T[7]
T22 = T[8]
T20 = - T[9]
T21 = - T[10]
T23 = T[11]
#####shoulder rotate joint(q1) ###########################
q1=[0,0]
A = d6 * T12 - T13
B = d6 * T02 - T03
R = A * A + B * B
if math.fabs(A) < ZERO_THRESH:
if math.fabs(math.fabs(d4) - math.fabs(B)) < ZERO_THRESH:
div = -self.SIGN(d4) * self.SIGN(B)
else:
div = -d4 / B
arcsin = math.asin(div)
if math.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
elif math.fabs(B) < ZERO_THRESH:
if math.fabs(math.fabs(d4) - math.fabs(A)) < ZERO_THRESH:
div = self.SIGN(d4) * self.SIGN(A)
else:
div = d4 / A
arccos = math.acos(div)
q1[0] = arccos
q1[1] = 2.0 * PI - arccos
elif d4 * d4 > R:
return num_sols
else:
arccos = math.acos(d4 / math.sqrt(R))
arctan = math.atan2(-B, A)
pos = arccos + arctan
neg = -arccos + arctan
if math.fabs(pos) < ZERO_THRESH:
pos = 0.0
if math.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
###### wrist2 joint(q5) ##########################
q5=numpy.zeros((2,2))#define 2*2 q5 array
for i in range(2):
numer = (T03 * math.sin(q1[i]) - T13 * math.cos(q1[i]) - d4)
if math.fabs(math.fabs(numer) - math.fabs(d6)) < ZERO_THRESH:
div = self.SIGN(numer) * self.SIGN(d6)
else:
div = numer / d6
arccos = math.acos(div)
q5[i][0] = arccos
q5[i][1] = 2.0 * PI - arccos
#############################################################
for i in range(2):
for j in range(2):
c1 = math.cos(q1[i])
s1 = math.sin(q1[i])
c5 = math.cos(q5[i][j])
s5 = math.sin(q5[i][j])
######################## wrist 3 joint (q6) ################################
if math.fabs(s5) < ZERO_THRESH:
q6 = q6_des
else:
q6 = math.atan2(self.SIGN(s5) * -(T01 * s1 - T11 * c1),self.SIGN(s5) * (T00 * s1 - T10 * c1))
if math.fabs(q6) < ZERO_THRESH:
q6 = 0.0
if (q6 < 0.0):
q6 += 2.0 * PI
q2=[0,0]
q3=[0,0]
q4=[0,0]
#####################RRR joints (q2, q3, q4) ################################
c6 = math.cos(q6)
s6 = math.sin(q6)
x04x = -s5 * (T02 * c1 + T12 * s1) - c5 * (s6 * (T01 * c1 + T11 * s1) - c6 * (T00 * c1 + T10 * s1))
x04y = c5 * (T20 * c6 - T21 * s6) - T22 * s5
p13x = d5 * (s6 * (T00 * c1 + T10 * s1) + c6 * (T01 * c1 + T11 * s1)) - d6 * (T02 * c1 + T12 * s1) +T03 * c1 + T13 * s1
p13y = T23 - d1 - d6 * T22 + d5 * (T21 * c6 + T20 * s6)
c3 = (p13x * p13x + p13y * p13y - a2 * a2 - a3 * a3) / (2.0 * a2 * a3)
if math.fabs(math.fabs(c3) - 1.0) < ZERO_THRESH:
c3 = self.SIGN(c3)
elif math.fabs(c3) > 1.0:
# TODO NO SOLUTION
continue
arccos = math.acos(c3)
q3[0] = arccos
q3[1] = 2.0 * PI - arccos
denom = a2 * a2 + a3 * a3 + 2 * a2 * a3 * c3
s3 = math.sin(arccos)
A = (a2 + a3 * c3)
B = a3 * s3
q2[0] = math.atan2((A * p13y - B * p13x) / denom, (A * p13x + B * p13y) / denom)
q2[1] = math.atan2((A * p13y + B * p13x) / denom, (A * p13x - B * p13y) / denom)
c23_0 = math.cos(q2[0] + q3[0])
s23_0 = math.sin(q2[0] + q3[0])
c23_1 = math.cos(q2[1] + q3[1])
s23_1 = math.sin(q2[1] + q3[1])
q4[0] = math.atan2(c23_0 * x04y - s23_0 * x04x, x04x * c23_0 + x04y * s23_0)
q4[1] = math.atan2(c23_1 * x04y - s23_1 * x04x, x04x * c23_1 + x04y * s23_1)
###########################################
for k in range(2):
if math.fabs(q2[k]) < ZERO_THRESH:
q2[k] = 0.0
elif q2[k] < 0.0:
q2[k] += 2.0 * PI
if math.fabs(q4[k]) < ZERO_THRESH:
q4[k] = 0.0
elif 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+=1
return num_sols,q_sols
"""
q_inverse:ur kinematics solution joint q
q_last:last joint q
"""
def solve_2pi_pro(self,q_inverse,q_last):
if abs(q_inverse-PI*2.0-q_last)
<= 2. * numpy.pi and
abs(test_ang - q_guess[i]) < abs(test_sol[i] - q_guess[i])):
test_sol[i] = test_ang
if numpy.all(test_sol != 9999.):
valid_sols.append(test_sol)
if len(valid_sols) == 0:
return None
best_sol_ind = numpy.argmin(numpy.sum((weights * (valid_sols - numpy.array(q_guess))) ** 2, 1))
print "#########################the best sol##################"
print valid_sols[best_sol_ind]
return valid_sols[best_sol_ind]
def best_sol_for_other_py(self,weights,q_guess,T):
sols=self.get_ik_data(T)
valid_sols = []
for sol in sols:
test_sol = numpy.ones(6) * 9999.
for i in range(6):
for add_ang in [-2. * numpy.pi, 0, 2. * numpy.pi]:
test_ang = sol[i] + add_ang
if (abs(test_ang) <= 2. * numpy.pi and
abs(test_ang - q_guess[i]) < abs(test_sol[i] - q_guess[i])):
test_sol[i] = test_ang
if numpy.all(test_sol != 9999.):
valid_sols.append(test_sol)
if len(valid_sols) == 0:
return None
best_sol_ind = numpy.argmin(numpy.sum((weights * (valid_sols - numpy.array(q_guess))) ** 2, 1))
print "#########################the best sol##################"
print valid_sols[best_sol_ind].tolist()
#print best_sol_ind
print sols[best_sol_ind]
return valid_sols[best_sol_ind].tolist()
def main():
q = [0, 0, 1, 0, 1, 0]
q1=[-1.5654299894915982, -1.6473701635943812, 0.05049753189086914, -1.4097726980792444, -1.140495349565615, -0.8895475069154913]
q2=[-0.25277, -0.8561733333333333, 1.2195411111111112, -3.557096666666667, -1.3205444444444445, -1.1349355555555556]
q3=[0,0,0,0,0,0]
q4=[3.3985266666666667, -1.3765411111111112, -1.944881111111111, 0.14112555555555556, -4.9428833333333335, 5.663687777777778]
q5=[-3.59860155164,-1.82648800883,-1.41735542252,0.0812199084238,1.27000134315,0.734254316924]
# q5=[-3.66249992472,-1.27642603705,-1.9559700595,0.0701396996895,1.3338858418,0.73287290524]
c=Kinematic()
# c.display(q5,0,3)
weights=[1.] * 6
T=[-0.13464668997929136, 0.9394821469191765, -0.3150294660785803, 0.0, 0.13751164454300352, 0.3325644757714387, 0.9330012953206159, 0.0, 0.981305669245164, 0.08230531620134232, -0.17396844090897007, 0.5790479214783786, 0.0, 0.0, 0.0, 1.0]
print c.Iverse(T,q5)
# c.best_sol(weights,q5,c.Forward(q5))
# c.best_sol_for_other_py(weights,q,c.Forward())
# print type(c.Forward())
#c.best_sol_new(c.Forward(q2))
if __name__ == '__main__':
main()
