delta机器人逆解代码

以下是一个简单的delta机器人逆解代码，基于Python语言和SymPy库：

from sympy import symbols, cos, sin, pi, simplify
from sympy.matrices import Matrix

# 符号变量定义
theta1, theta2, theta3 = symbols('theta1:4')
l1, l2, l3 = symbols('l1:4')
d1, d2, d3 = symbols('d1:4')
a1, a2, a3 = symbols('a1:4')

# DH参数
s = {theta1: 0, a1: 0, d1: 0.75, 
     theta2: 0, a2: 0.5, d2: 0, 
     theta3: 0, a3: 0.5, d3: 0}

# 坐标变换矩阵
T0_1 = Matrix([[cos(theta1),             -sin(theta1),            0,             a1],
               [sin(theta1)*cos(s[theta1]), cos(theta1)*cos(s[theta1]), -sin(s[theta1]), -sin(s[theta1])*d1],
               [sin(theta1)*sin(s[theta1]), cos(theta1)*sin(s[theta1]), cos(s[theta1]),  cos(s[theta1])*d1],
               [0,                         0,                        0,             1]])
T1_2 = Matrix([[cos(theta2),             -sin(theta2),            0,             a2],
               [sin(theta2)*cos(s[theta2]), cos(theta2)*cos(s[theta2]), -sin(s[theta2]), -sin(s[theta2])*d2],
               [sin(theta2)*sin(s[theta2]), cos(theta2)*sin(s[theta2]), cos(s[theta2]),  cos(s[theta2])*d2],
               [0,                         0,                        0,             1]])
T2_3 = Matrix([[cos(theta3),             -sin(theta3),            0,             a3],
               [sin(theta3)*cos(s[theta3]), cos(theta3)*cos(s[theta3]), -sin(s[theta3]), -sin(s[theta3])*d3],
               [sin(theta3)*sin(s[theta3]), cos(theta3)*sin(s[theta3]), cos(s[theta3]),  cos(s[theta3])*d3],
               [0,                         0,                        0,             1]])

# 各个坐标系之间的变换
T0_2 = simplify(T0_1 * T1_2)
T0_3 = simplify(T0_2 * T2_3)

# 末端执行器位姿矩阵
T0_3[0, 3] = T0_3[0, 3] - 0.5  # 将工具端点向下移动0.5米
T_end_effector = simplify(T0_3)

# 逆解
px, py, pz = symbols('px py pz')
R3_6 = T_end_effector[0:3, 0:3].transpose()
P3_6 = -R3_6 * T_end_effector[0:3, 3]

# theta1
theta1 = simplify(atan2(py, px))

# theta2
s_theta2 = simplify(-d3/sqrt(px**2 + py**2)*(px*cos(theta1) + py*sin(theta1) - d1))
c_theta2 = simplify((pz - d1) / d3)
theta2 = simplify(atan2(s_theta2, c_theta2))

# theta3
s_theta3 = simplify((px*cos(theta1) + py*sin(theta1)) / (sin(theta2)*a2 + cos(theta2)*a3))
c_theta3 = simplify((P3_6[2] - l1 - l2*sin(theta2) - l3*sin(theta2 + theta3)) / (a2*sin(theta2) + a3*sin(theta2 + theta3)))
theta3 = simplify(atan2(s_theta3, c_theta3))

# 输出结果
print("theta1: ", theta1.evalf())
print("theta2: ", theta2.evalf())
print("theta3: ", theta3.evalf())

这段代码实现了delta机器人的逆解，输入末端执行器的位置坐标(px, py, pz)，输出三个关节角度(theta1, theta2, theta3)。需要注意的是，这段代码仅适用于标准的delta机器人，对于不同的机器人，需要根据实际情况进行修改。