puma560逆运动学解

Puma560是一种六轴机械臂，逆运动学解是指已知机械臂末端的位置和姿态，求解机械臂各关节的角度。Python中可以使用sympy库来求解Puma560的逆运动学解。以下是一个简单的示例代码：

from sympy import symbols, atan2, sqrt

# 定义符号变量
q1, q2, q3, q4, q5, q6 = symbols('q1:7')
d1, d2, d3, d4, d5, d6 = symbols('d1:7')
a0, a1, a2, a3, a4, a5 = symbols('a0:6')
alpha0, alpha1, alpha2, alpha3, alpha4, alpha5 = symbols('alpha0:6')

# DH参数
s = {alpha0: 0,     a0: 0,      d1: 0.67,
     alpha1: -90,   a1: 0.4318, d2: 0,
     alpha2: 0,     a2: 0.0203, d3: 0.15005,
     alpha3: -90,   a3: 0,      d4: 0.4318,
     alpha4: 90,    a4: 0,      d5: 0,
     alpha5: -90,   a5: 0,      d6: 0.05}

# 正运动学矩阵
def T(alpha, a, d, q):
    return Matrix([[            cos(q),           -sin(q),           0,             a],
                   [ sin(q)*cos(alpha), cos(q)*cos(alpha), -sin(alpha), -sin(alpha)*d],
                   [ sin(q)*sin(alpha), cos(q)*sin(alpha),  cos(alpha),  cos(alpha)*d],
                   [                 0,                 0,           0,             1]])

T0_1 = T(alpha0, a0, d1, q1).subs(s)
T1_2 = T(alpha1, a1, d2, q2).subs(s)
T2_3 = T(alpha2, a2, d3, q3).subs(s)
T3_4 = T(alpha3, a3, d4, q4).subs(s)
T4_5 = T(alpha4, a4, d5, q5).subs(s)
T5_6 = T(alpha5, a5, d6, q6).subs(s)

T0_6 = T0_1 * T1_2 * T2_3 * T3_4 * T4_5 * T5_6

# 末端坐标
px = T0_6[0, 3]
py = T0_6[1, 3]
pz = T0_6[2, 3]

# 末端姿态
theta = atan2(T0_6[2, 0], -T0_6[0, 0])
phi = atan2(sqrt(T0_6[0,