Python机器人坐标换算神器：transforms3d+numpy

大家晚上好，我是小智，今天就再挑个开源库讲讲。

在平时的工作当中，小智用的最多的就是numpy和transform3d这两个库了，一个做矩阵运算，一个做坐标转换，今天就从安装说起，讲一下常用的一些方法。

numpy 参考文档：www.runoob.com/numpy/numpy…

transforms3d参考文档：matthew-brett.github.io/transforms3…

一、安装

1.numpy

pip install numpy

2.transforms3d

pip install transforms3d

如果安装过慢，可以尝试换清华源

临时使用：

pip install -i https://pypi.tuna.tsinghua.edu.cn/simple some-package

设为默认：

pip config set global.index-url https://pypi.tuna.tsinghua.edu.cn/simple

二、常用方法

1.numpy

将A转换为3*3的矩阵

np.asarray(A).reshape(size*3,3) 

A、B相乘

np.dot(A,B) 

求A的逆

np.linalg.pinv(A)

将A开方

np.sqrt(A) 

A,B相加

np.add(A,B)

将A的每一位都除以2

np.divide(A,2)

A-B

np.subtract(A,B)

2.transform3d

将欧拉角转换为旋转矩阵

tfs.euler.euler2mat(math.radians(rx),math.radians(ry),math.radians(rz))

合并成齐次矩阵

tfs.affines.compose(np.squeeze(np.asarray((x,y,z))), rmat, [1, 1, 1])

旋转矩阵转四元数

tfs.quaternions.mat2quat(m[0:3,0:3])

四元数转旋转矩阵

tfs.quaternions.quat2mat([w,q[0],q[1],q[2]])

三、应用：Tsai_Lenz手眼标定算法实现

#!/usr/bin/env python
# coding: utf-8
import transforms3d as tfs
import numpy as np
import math

def get_matrix_eular_radu(x,y,z,rx,ry,rz):
    rmat = tfs.euler.euler2mat(math.radians(rx),math.radians(ry),math.radians(rz))
    rmat = tfs.affines.compose(np.squeeze(np.asarray((x,y,z))), rmat, [1, 1, 1])
    return rmat

def skew(v):
    return np.array([[0,-v[2],v[1]],
                     [v[2],0,-v[0]],
                     [-v[1],v[0],0]])

def rot2quat_minimal(m):
    quat =  tfs.quaternions.mat2quat(m[0:3,0:3])
    return quat[1:]

def quatMinimal2rot(q):
    p = np.dot(q.T,q)
    w = np.sqrt(np.subtract(1,p[0][0]))
    return tfs.quaternions.quat2mat([w,q[0],q[1],q[2]])

hand = [1.1988093940033604, -0.42405585264804424, 0.18828251788562061, 151.3390418721659, -18.612399542280507, 153.05074895025035,
        1.1684831621733476, -0.183273375514656, 0.12744868246620855, -161.57083804238462, 9.07159838346732, 89.1641128844487,
        1.1508343174145468, -0.22694301453461405, 0.26625166858469146, 177.8815855486261, 0.8991159570568988, 77.67286224959672]
camera = [-0.16249272227287292, -0.047310635447502136, 0.4077761471271515, -56.98037030812389, -6.16739631361851, -115.84333735802369,
          0.03955405578017235, -0.013497642241418362, 0.33975949883461, -100.87129330834215, -17.192685528625265, -173.07354634882094,
          -0.08517949283123016, 0.00957852229475975, 0.46546608209609985, -90.85270962096058, 0.9315977976503153, 175.2059707654342]


Hgs,Hcs = [],[]
for i in range(0,len(hand),6):
    Hgs.append(get_matrix_eular_radu(hand[i],hand[i+1],hand[i+2],hand[i+3],hand[i+4],hand[i+5]))    
    Hcs.append(get_matrix_eular_radu(camera[i],camera[i+1],camera[i+2],camera[i+3],camera[i+4],camera[i+5]))

Hgijs = []
Hcijs = []
A = []
B = []
size = 0
for i in range(len(Hgs)):
    for j in range(i+1,len(Hgs)):
        size += 1
        Hgij = np.dot(np.linalg.inv(Hgs[j]),Hgs[i])
        Hgijs.append(Hgij)
        Pgij = np.dot(2,rot2quat_minimal(Hgij))
        
        Hcij = np.dot(Hcs[j],np.linalg.inv(Hcs[i]))
        Hcijs.append(Hcij)
        Pcij = np.dot(2,rot2quat_minimal(Hcij))
        
        A.append(skew(np.add(Pgij,Pcij)))
        B.append(np.subtract(Pcij,Pgij))
MA = np.asarray(A).reshape(size*3,3)
MB = np.asarray(B).reshape(size*3,1)
Pcg_  =  np.dot(np.linalg.pinv(MA),MB)
pcg_norm = np.dot(np.conjugate(Pcg_).T,Pcg_)
Pcg = np.sqrt(np.add(1,np.dot(Pcg_.T,Pcg_)))
Pcg = np.dot(np.dot(2,Pcg_),np.linalg.inv(Pcg))
Rcg = quatMinimal2rot(np.divide(Pcg,2)).reshape(3,3)


A = []
B = []
id = 0
for i in range(len(Hgs)):
    for j in range(i+1,len(Hgs)):
        Hgij = Hgijs[id]
        Hcij = Hcijs[id]
        A.append(np.subtract(Hgij[0:3,0:3],np.eye(3,3)))
        B.append(np.subtract(np.dot(Rcg,Hcij[0:3,3:4]),Hgij[0:3,3:4]))
        id += 1

MA = np.asarray(A).reshape(size*3,3)
MB = np.asarray(B).reshape(size*3,1)
Tcg = np.dot(np.linalg.pinv(MA),MB).reshape(3,)
print(tfs.affines.compose(Tcg,np.squeeze(Rcg),[1,1,1]))

四、写到最后

我是小智，机器人领域资深玩家，现深圳某独脚兽机器人算法工程师一枚

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