matlab，simuink，机械臂，正解，逆解，dh参数，验证等

心已赠人 2022-12-31 01:16 221阅读 0赞

## 参考： ##

[https://blog.csdn.net/jldemanman/article/details/80785075][https_blog.csdn.net_jldemanman_article_details_80785075]

[https://blog.csdn.net/jldemanman/article/details/79314435][https_blog.csdn.net_jldemanman_article_details_79314435]

## **dh参数** ##

### **1. 标准的STD\_DH dh建模** ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 1][]

**Trans zi-1（di）:沿着zi-1轴平移di； Rot zi-1（![2020122715104978.png][] ）:沿着zi-1轴旋转![2020122715104978.png][] ；Trans xi（ai）:沿着xi轴配平移 ai ；Rot xi-1（![20201227151236814.png][]）沿着xi-1轴旋转 ![20201227151236814.png][]**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 2][]

### **2.改进型MOD\_DH dh建模** ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 3][]

### ![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 4][] ###

### ![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 5][] ###

### 3. 标准的STD\_DH dh建模与改进型MOD\_DH dh建模 区别比较： ###

## 标准DH参数和改进DH参数之间的差异是连接到连杆的坐标系的位置和齐次变换的顺序。 ##

**3.1标准的DH参数原点 Oi 坐标建立在末端，改进的DH参数的原点 Oi 坐标建立在首端**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 6][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 7][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 8][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 4][]

变换矩阵：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 9][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 5][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 10][]

### 4.dh建模 参考ur改进的DH建模 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 11][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 12][]

**把初始位置竖起来：**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 13][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 14][]

###  5.验证dh参数是否准确 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 15][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 16][]![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 17][]

**5.1.验证dh参数是否准确**

** d：连杆偏距 ； a：杆长 ；alpha：连杆转角 ； offset初始关节角度；**

clear,clc,close all;
    %建立机器人DH参数，初始状态为竖直状态 
    % d：连杆偏距 ； a：杆长 ；alpha：连杆转角 ； offset初始关节角度；
    L1=Link('d',144,'a',0,'alpha',0,'modified'); 
    L2=Link('d',0,'a',0,'alpha',pi/2,'offset',-pi/2,'modified'); 
    L3=Link('d',0,'a',-264,'alpha',0,'modified');
    L4=Link('d',106,'a',-236,'alpha',0,'offset',-pi/2,'modified');
    L5=Link('d',114,'a',0,'alpha',pi/2,'modified');
    L6=Link('d',67,'a',0,'alpha',-pi/2,'modified');
    %建立机器人
    robot=SerialLink([L1 L2 L3 L4 L5 L6],'name','Arm6') ;
    % 初始角度 都为0
    Theta=[0 0 0 0 0 0];
     %初始角度换算成弧度 
    Theta=Theta/180*pi;
    %求正解的齐次变换矩阵 
     forwarda=robot.fkine(Theta)
     W=[-1000,+1000,-1000,+1000,-1000,+1000];
      %显示三维动画 
     robot.plot(Theta,'tilesize',150,'workspace',W);
     %显示roll/pitch/yaw angles，GUI可调界面
    robot.teach(forwarda,'rpy' )

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 18][]

转换成rpy姿态

rpy2r：rpy转换成旋转矩阵

r2rpy：旋转矩阵转换成rpy

R=rpy2r(0.1,0.2,0.3,'xyz')
    R=r2rpy(R,'xyz')

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 19][]

### 6.正解： ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 20][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 21][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 22][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 23][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 24][]

ForwardSolver\_MDH.m

function    [T06,Pos]=ForwardSolver_MDH(theta)
    %% 建立机器人DH参数，初始状态为竖直状态
    %% d：连杆偏距 ； a：杆长 ；alpha：连杆转角 ； offset初始关节角度；
    %% L1=Link('d',144,'a',0,'alpha',0,'modified'); 
    %% L2=Link('d',0,'a',0,'alpha',pi/2,'offset',-pi/2,'modified');
    %% L3=Link('d',0,'a',-264,'alpha',0,'modified');
    %% L4=Link('d',106,'a',-236,'alpha',0,'offset',-pi/2,'modified');
    %% L5=Link('d',114,'a',0,'alpha',pi/2,'modified');
    %% L6=Link('d',67,'a',0,'alpha',-pi/2,'modified');
        %% [alpha,a, d,offset]  ******DH参数*****
       %%        参数 1：连杆转角alpha ； 参数2：杆长a  ； 参数3：连杆偏距d ； 参数4：初始关节角度offset；
        DH_JXB =[         0                       0              144                 0; 
                          90                      0              0                  -90;
                          0                      -264            0                   0; 
                          0                      -236            106                -90; 
                          90                      0              114                 0; 
                         -90                      0              67                  0 
                 ];
        d=DH_JXB(1:6,3); 
        a0=DH_JXB(1,2); a1=DH_JXB(2,2);a2=DH_JXB(3,2);a3=DH_JXB(4,2);a4=DH_JXB(5,2); a5=DH_JXB(6,2); 
        DH_JXB(1:6,1)=DH_JXB(1:6,1)/180*pi;
        alp0=DH_JXB(1,1); alp1=DH_JXB(2,1);alp2=DH_JXB(3,1);alp3=DH_JXB(4,1);alp4=DH_JXB(5,1); alp5=DH_JXB(6,1);
        offset=[0 -90 0 -90 0 0];
        theta=(theta+offset)*pi/180;
        theta1=theta(1);theta2=theta(2);theta3=theta(3);theta4=theta(4);theta5=theta(5);theta6=theta(6);
        T01=[               cos(theta1),             -sin(theta1),             0,               a0;
                       sin(theta1)*cos(alp0), cos(theta1)*cos(alp0),-sin(alp0),-d(1)*sin(alp0);
                       sin(theta1)*sin(alp0),  cos(theta1)*sin(alp0), cos(alp0), d(1)*cos(alp0);
                                    0,                                  0,                    0,               1
                 ];
        T12=[               cos(theta2),              -sin(theta2),           0,             a1;
                      sin(theta2)*cos(alp1), cos(theta2)*cos(alp1),-sin(alp1),-d(2)*sin(alp1);
                      sin(theta2)*sin(alp1),  cos(theta2)*sin(alp1),  cos(alp1), d(2)*cos(alp1);
                                    0,                                  0,                  0,               1
                ];
        T23=[               cos(theta3),             -sin(theta3),            0,            a2;
                     sin(theta3)*cos(alp2), cos(theta3)*cos(alp2),-sin(alp2),-d(3)*sin(alp2);
                     sin(theta3)*sin(alp2),  cos(theta3)*sin(alp2),  cos(alp2), d(3)*cos(alp2);
                                    0,                              0,                      0,               1
                ];
        T34=[              cos(theta4),             -sin(theta4),            0,              a3;
                    sin(theta4)*cos(alp3), cos(theta4)*cos(alp3),-sin(alp3),-d(4)*sin(alp3);
                    sin(theta4)*sin(alp3),  cos(theta4)*sin(alp3),  cos(alp3), d(4)*cos(alp3);
                                   0,                               0,                     0,                1
                ];
        T45=[            cos(theta5),             -sin(theta5),              0,              a4;
                   sin(theta5)*cos(alp4), cos(theta5)*cos(alp4),-sin(alp4),-d(5)*sin(alp4);
                   sin(theta5)*sin(alp4),  cos(theta5)*sin(alp4), cos(alp4), d(5)*cos(alp4);
                                   0,                               0,                     0,               1
                ];
        T56=[           cos(theta6),            -sin(theta6),               0,              a5;
                  sin(theta6)*cos(alp5), cos(theta6)*cos(alp5),-sin(alp5),-d(6)*sin(alp5);
                  sin(theta6)*sin(alp5),  cos(theta6)*sin(alp5),  cos(alp5), d(6)*cos(alp5);
                                  0,                                0,                    0,                 1
                ];
        disp('Homogeneous transformation matrix T06:')
        T06=T01*T12*T23*T34*T45*T56;
        %% 求末端位置
        X=T06(1,4);Y=T06(2,4);Z=T06(3,4);
        %% 求末端姿态Rotations about X, Y, Z axes (for a robot gripper)
        R=T06;
        if abs(abs(R(1,3)) - 1) < eps  % when |R13| == 1
            % singularity
            rpy(1) = 0;  % roll is zero
            if R(1,3) > 0
            rpy(3) = atan2( R(3,2), R(2,2));   % R+Y
            else
                 rpy(3) = -atan2( R(2,1), R(3,1));   % R-Y
            end
            rpy(2) = asin(R(1,3));
        else
            rpy(1) = -atan2(R(1,2), R(1,1));
            rpy(3) = -atan2(R(2,3), R(3,3));
    
            rpy(2) = atan(R(1,3)*cos(rpy(1))/R(1,1));
        end
        RPY=rpy*180/pi;
        Rall=RPY(1);Pitch=RPY(2);Yaw=RPY(3);
        Pos=[X,Y,Z,Rall,Pitch,Yaw];
    end

### 7. 6关节逆解 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 25][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 26][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 27][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 28][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 29][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 30][]

InverseSolver\_MDH.m

function AllSloverTheta =InverseSolver_MDH(Pos)
    %#codegen
    %% coder.extrinsic 声明外部函数。
    %% 在仿真期间，代码生成器会为外部函数的调用生成代码，但不会生成函数的内部代码。
    coder.extrinsic('disp');
    %% 建立机器人DH参数，初始状态为竖直状态
    %% L1=Link('d',144,'a',0,'alpha',0,'modified'); 
    %% L2=Link('d',0,'a',0,'alpha',pi/2,'offset',-pi/2,'modified');
    %% L3=Link('d',0,'a',-264,'alpha',0,'modified');
    %% L4=Link('d',106,'a',-236,'alpha',0,'offset',-pi/2,'modified');
    %% L5=Link('d',114,'a',0,'alpha',pi/2,'modified');
    %% L6=Link('d',67,'a',0,'alpha',-pi/2,'modified');
        AllSloverTheta = zeros(8,6);A=zeros(1,4);
        %%        [alpha,a, d,offset] 
        DH_JXB =[0 0 144 0; 
                        90 0 0 -90;
                        0 -264 0 0; 
                        0 -236 106 -90; 
                        90 0 114 0; 
                        -90 0 67 0];
        p2=DH_JXB(2,4);p4=DH_JXB(4,4);
        a2=DH_JXB(3,2);a3=DH_JXB(4,2);d1=DH_JXB(1,3);d4=DH_JXB(4,3);d5=DH_JXB(5,3);
        X=Pos(1);Y=Pos(2);Z=Pos(3);
        gama=Pos(4)*pi/180;beta=Pos(5)*pi/180;alpha=Pos(6)*pi/180;
        theta7=0;a6=0;afa6=0;d7=DH_JXB(6,3);
        T67=[   cos(theta7),-sin(theta7),0,a6;
                    sin(theta7)*cos(afa6),cos(theta7)*cos(afa6),-sin(afa6),-sin(afa6)*d7;
                    sin(theta7)*sin(afa6),cos(theta7)*sin(afa6),cos(afa6),cos(afa6)*d7;
                    0,0,0,1
                 ];
       T_goat=[  cos(beta)*cos(gama),-cos(beta)*sin(gama),sin(beta),X;
                       sin(alpha)*sin(beta)*cos(gama)+cos(alpha)*sin(gama), ...
                       -sin(alpha)*sin(beta)*sin(gama)+cos(alpha)*cos(gama), -sin(alpha)*cos(beta),Y;
                      -cos(alpha)*sin(beta)*cos(gama)+sin(alpha)*sin(gama),...
                      cos(alpha)*sin(beta)*sin(gama)+sin(alpha)*cos(gama),  cos(alpha)*cos(beta),Z;
                      0,0,0,1
                  ];
        T06=T_goat/T67;
        
        nx=T06(1,1);ny=T06(2,1);
        ox=T06(1,2);oy=T06(2,2);
        ax=T06(1,3);ay=T06(2,3);az=T06(3,3);
        px=T06(1,4);py=T06(2,4);pz=T06(3,4);
        
        k=0;
        ForJudgment=px^2+py^2-d4^2;
        
        if ForJudgment<-1e-6
            disp('Out of workspace Unable to solve');
        else      
            if ForJudgment>=-1e-6&&ForJudgment<0
                ForJudgment=0;
            end
            theta1_1=atan2(py,px)-atan2(-d4,sqrt(ForJudgment));
            theta1_2=atan2(py,px)-atan2(-d4,-sqrt(ForJudgment));
            
            S5_1=sqrt((-sin(theta1_1)*nx+cos(theta1_1)*ny)^2+(-sin(theta1_1)*ox+cos(theta1_1)*oy)^2);
            theta5_1=atan2(S5_1,sin(theta1_1)*ax-cos(theta1_1)*ay);
            S5_2=-sqrt((-sin(theta1_1)*nx+cos(theta1_1)*ny)^2+(-sin(theta1_1)*ox+cos(theta1_1)*oy)^2);
            theta5_2=atan2(S5_2,sin(theta1_1)*ax-cos(theta1_1)*ay);
            S5_3=sqrt((-sin(theta1_2)*nx+cos(theta1_2)*ny)^2+(-sin(theta1_2)*ox+cos(theta1_2)*oy)^2);
            theta5_3=atan2(S5_3,sin(theta1_2)*ax-cos(theta1_2)*ay);
            S5_4=-sqrt((-sin(theta1_2)*nx+cos(theta1_2)*ny)^2+(-sin(theta1_2)*ox+cos(theta1_2)*oy)^2);
            theta5_4=atan2(S5_4,sin(theta1_2)*ax-cos(theta1_2)*ay);
            
            S234 = [0; 0; 0; 0];C234 = [0; 0; 0; 0];
            B = [0; 0; 0; 0];B1 = [0; 0; 0; 0];B2 = [0; 0; 0; 0];
            C = [0; 0; 0; 0];
            theta2 = [0; 0; 0; 0; 0; 0; 0; 0];
            theta23 = [0; 0; 0; 0; 0; 0; 0; 0];
            theta234 = [0; 0; 0; 0; 0; 0; 0; 0];
            theta3 = [0; 0; 0; 0; 0; 0; 0; 0];
            theta4 = [0; 0; 0; 0; 0; 0; 0; 0];
            
            if abs(S5_1)>1e-6
                theta6_1=atan2((-sin(theta1_1)*ox+cos(theta1_1)*oy)/S5_1,(sin(theta1_1)*nx-cos(theta1_1)*ny)/S5_1);
                S234(1)=-az/S5_1;C234(1)=-(cos(theta1_1)*ax+sin(theta1_1)*ay)/S5_1;theta234(1)=atan2(S234(1),C234(1));
                B1(1)=cos(theta1_1)*px+sin(theta1_1)*py-d5*S234(1);B2(1)=pz-d1+d5*C234(1);
                A(1)=-2*B2(1)*a2;B(1)=2*B1(1)*a2;C(1)=B1(1)^2+B2(1)^2+a2^2-a3^2;
                if A(1)^2+B(1)^2-C(1)^2>=0
                    theta2(1)=atan2(B(1),A(1))-atan2(C(1),sqrt(A(1)^2+B(1)^2-C(1)^2));
                    theta2(2)=atan2(B(1),A(1))-atan2(C(1),-sqrt(A(1)^2+B(1)^2-C(1)^2));
                    theta23(1)=atan2((B2(1)-a2*sin(theta2(1)))/a3,(B1(1)-a2*cos(theta2(1)))/a3);
                    theta23(2)=atan2((B2(1)-a2*sin(theta2(2)))/a3,(B1(1)-a2*cos(theta2(2)))/a3);
                    theta4(1)=theta234(1)-theta23(1);
                    theta4(2)=theta234(1)-theta23(2);
                    theta3(1)=theta23(1)-theta2(1);
                    theta3(2)=theta23(2)-theta2(2);
                    AllSloverTheta(k+1,:)=[theta1_1 theta2(1)-p2*pi/180 theta3(1) theta4(1)-p4*pi/180 theta5_1 theta6_1];
                    AllSloverTheta(k+2,:)=[theta1_1 theta2(2)-p2*pi/180 theta3(2) theta4(2)-p4*pi/180 theta5_1 theta6_1];
                    k=k+2;
                end
            end
            if abs(S5_2)>1e-6
                theta6_2=atan2((-sin(theta1_1)*ox+cos(theta1_1)*oy)/S5_2,(sin(theta1_1)*nx-cos(theta1_1)*ny)/S5_2);
                S234(2)=-az/S5_2;C234(2)=-(cos(theta1_1)*ax+sin(theta1_1)*ay)/S5_2;theta234(2)=atan2(S234(2),C234(2));
                B1(2)=cos(theta1_1)*px+sin(theta1_1)*py-d5*S234(2);B2(2)=pz-d1+d5*C234(2);
                A(2)=-2*B2(2)*a2;B(2)=2*B1(2)*a2;C(2)=B1(2)^2+B2(2)^2+a2^2-a3^2;
                if A(2)^2+B(2)^2-C(2)^2>=0
                    theta2(3)=atan2(B(2),A(2))-atan2(C(2),sqrt(A(2)^2+B(2)^2-C(2)^2));
                    theta2(4)=atan2(B(2),A(2))-atan2(C(2),-sqrt(A(2)^2+B(2)^2-C(2)^2));
                    theta23(3)=atan2((B2(2)-a2*sin(theta2(3)))/a3,(B1(2)-a2*cos(theta2(3)))/a3);
                    theta23(4)=atan2((B2(2)-a2*sin(theta2(4)))/a3,(B1(2)-a2*cos(theta2(4)))/a3);
                    theta4(3)=theta234(2)-theta23(3);
                    theta4(4)=theta234(2)-theta23(4);
                    theta3(3)=theta23(3)-theta2(3);
                    theta3(4)=theta23(4)-theta2(4);
                    AllSloverTheta(k+1,:)=[theta1_1 theta2(3)-p2*pi/180 theta3(3) theta4(3)-p4*pi/180 theta5_2 theta6_2];
                    AllSloverTheta(k+2,:)=[theta1_1 theta2(4)-p2*pi/180 theta3(4) theta4(4)-p4*pi/180 theta5_2 theta6_2];
                    k=k+2;
                end
            end
            if abs(S5_3)>1e-6
                theta6_3=atan2((-sin(theta1_2)*ox+cos(theta1_2)*oy)/S5_3,(sin(theta1_2)*nx-cos(theta1_2)*ny)/S5_3);
                S234(3)=-az/S5_3;C234(3)=-(cos(theta1_2)*ax+sin(theta1_2)*ay)/S5_3;theta234(3)=atan2(S234(3),C234(3));
                B1(3)=cos(theta1_2)*px+sin(theta1_2)*py-d5*S234(3);B2(3)=pz-d1+d5*C234(3);
                A(3)=-2*B2(3)*a2;B(3)=2*B1(3)*a2;C(3)=B1(3)^2+B2(3)^2+a2^2-a3^2;
                if A(3)^2+B(3)^2-C(3)^2>=0
                    theta2(5)=atan2(B(3),A(3))-atan2(C(3),sqrt(A(3)^2+B(3)^2-C(3)^2));
                    theta2(6)=atan2(B(3),A(3))-atan2(C(3),-sqrt(A(3)^2+B(3)^2-C(3)^2));
                    theta23(5)=atan2((B2(3)-a2*sin(theta2(5)))/a3,(B1(3)-a2*cos(theta2(5)))/a3);
                    theta23(6)=atan2((B2(3)-a2*sin(theta2(6)))/a3,(B1(3)-a2*cos(theta2(6)))/a3);
                    theta4(5)=theta234(3)-theta23(5);
                    theta4(6)=theta234(3)-theta23(6);
                    theta3(5)=theta23(5)-theta2(5);
                    theta3(6)=theta23(6)-theta2(6);
                    AllSloverTheta(k+1,:)=[theta1_2 theta2(5)-p2*pi/180 theta3(5) theta4(5)-p4*pi/180 theta5_3 theta6_3];
                    AllSloverTheta(k+2,:)=[theta1_2 theta2(6)-p2*pi/180 theta3(6) theta4(6)-p4*pi/180 theta5_3 theta6_3];
                    k=k+2;
                end
            end
            if abs(S5_4)>1e-6
                theta6_4=atan2((-sin(theta1_2)*ox+cos(theta1_2)*oy)/S5_4,(sin(theta1_2)*nx-cos(theta1_2)*ny)/S5_4);
                S234(4)=-az/S5_4;C234(4)=-(cos(theta1_2)*ax+sin(theta1_2)*ay)/S5_4;theta234(4)=atan2(S234(4),C234(4));
                B1(4)=cos(theta1_2)*px+sin(theta1_2)*py-d5*S234(4);B2(4)=pz-d1+d5*C234(4);
                A(4)=-2*B2(4)*a2;B(4)=2*B1(4)*a2;C(4)=B1(4)^2+B2(4)^2+a2^2-a3^2;
                if A(4)^2+B(4)^2-C(4)^2>=0
                    theta2(7)=atan2(B(4),A(4))-atan2(C(4),sqrt(A(4)^2+B(4)^2-C(4)^2));
                    theta2(8)=atan2(B(4),A(4))-atan2(C(4),-sqrt(A(4)^2+B(4)^2-C(4)^2));
                    theta23(7)=atan2((B2(4)-a2*sin(theta2(7)))/a3,(B1(4)-a2*cos(theta2(7)))/a3);
                    theta23(8)=atan2((B2(4)-a2*sin(theta2(8)))/a3,(B1(4)-a2*cos(theta2(8)))/a3);
                    theta4(7)=theta234(4)-theta23(7);
                    theta4(8)=theta234(4)-theta23(8);
                    theta3(7)=theta23(7)-theta2(7);
                    theta3(8)=theta23(8)-theta2(8);
                    AllSloverTheta(k+1,:)=[theta1_2 theta2(7)-p2*pi/180 theta3(7) theta4(7)-p4*pi/180 theta5_4 theta6_4];
                    AllSloverTheta(k+2,:)=[theta1_2 theta2(8)-p2*pi/180 theta3(8) theta4(8)-p4*pi/180 theta5_4 theta6_4];
                    k=k+2;
                end
            end
            
            if k>0
                AllSloverTheta=AllSloverTheta*180/pi;%将弧度转化成角度
                for i=1:k
                    for j=1:6
                        if AllSloverTheta(i,j)<=-180
                            AllSloverTheta(i,j)=AllSloverTheta(i,j)+360;%将角度限定在-180—+180
                        elseif AllSloverTheta(i,j)>180
                            AllSloverTheta(i,j)=AllSloverTheta(i,j)-360;%将角度限定在-180—+180
                        end
                    end
                end
            else 
                disp('Singular position Unable to solve');
            end
        end
    end

**限位 **

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE1MjA0MTc5_size_16_color_FFFFFF_t_70 31][]

### 8.建立机器人 ###

MDH\_Verify.m

clear,clc,close all;
    %% 建立机器人DH参数，初始状态为竖直状态
    % d：连杆偏距 ； a：杆长 ；alpha：连杆转角 ； offset初始关节角度；
    L1=Link('d',144,'a',0,'alpha',0,'modified'); 
    L2=Link('d',0,'a',0,'alpha',pi/2,'offset',-pi/2,'modified');
    L3=Link('d',0,'a',-264,'alpha',0,'modified');
    L4=Link('d',106,'a',-236,'alpha',0,'offset',-pi/2,'modified');
    L5=Link('d',114,'a',0,'alpha',pi/2,'modified');
    L6=Link('d',67,'a',0,'alpha',-pi/2,'modified');
    %建立机器人
    robot=SerialLink([L1 L2 L3 L4 L5 L6],'name','Arm6')
    % 初始角度 都为0
    %Theta=[0 0 0 0 0 0];
    Theta=[-30.0000  -58.2807   30.0000  -61.7193  -30.0000  -30.0000];
    Theta=Theta/180*pi;                         %换算成弧度
    forwarda=robot.fkine(Theta)             %求正解的齐次变换矩阵
    W=[-1000,+1000,-1000,+1000,-1000,+1000];  %限制坐标轴的范围
    robot.plot(Theta,'tilesize',150,'workspace',W);  %显示三维动画
    robot.teach(forwarda,'rpy' )              %显示roll/pitch/yaw angles，GUI可调界面

###  9. 验证正逆解的结果 利用机器人工具箱 ###

![20201227173744228.png][]

ToolBoxVerify\_MDH.m

clear,clc,close all;
    %% 建立机器人DH参数，初始状态为竖直状态
    % 连杆偏移d,连杆长度a,连杆扭转角alpha  modified：改进dh参数来表示的
    L1=Link('d',144,'a',0,'alpha',0,'modified'); 
    L2=Link('d',0,'a',0,'alpha',pi/2,'offset',-pi/2,'modified');
    L3=Link('d',0,'a',-264,'alpha',0,'modified');
    L4=Link('d',106,'a',-236,'alpha',0,'offset',-pi/2,'modified');
    L5=Link('d',114,'a',0,'alpha',pi/2,'modified');
    L6=Link('d',67,'a',0,'alpha',-pi/2,'modified');
    robot=SerialLink([L1 L2 L3 L4 L5 L6],'name','Arm6');
    %% 正解，给定关节角，求末端位姿，样例
    % Theta = [0 0 0 0 0 0];  %给定6个关节角度值
    % Theta=[30 30 30 30 30 30];
    % Theta=[-30 -30 -30 -30 -30 -30];
    %%调用正解函数，后面不加分号表示会打印输出变量
    % [T60,Pos]=ForwardSolver_MDH(Theta)        % Pos=[X,Y,Z,Rall,Pitch,Yaw];
    %% 逆解，给定末端位姿求关节角，(X,Y,Z单位为mm)，(Rall,Pitch,Yaw单位为deg)
    Pos=[308.0304 -367.2397  524.1307   43.8979  -25.6589   56.3099];             %给定末端位姿
    % Pos=[300 400 300 0 0 0];
    AllSloverTheta=InverseSolver_MDH(Pos)    %根据末端位姿求所有解
    Theta=AllSloverTheta(1,1:end)                      %选择第一组解，PTP程序是默认为第一组解
    %% 验证正逆解的结果
    Theta=Theta/180*pi;                         %换算成弧度
    forwarda=robot.fkine(Theta)             %求正解的齐次变换矩阵
    %位置
    X=forwarda(1).t(1);
    Y=forwarda(1).t(2);
    Z=forwarda(1).t(3);
    W=[-1000,+1000,-1000,+1000,-1000,+1000];%限制坐标轴的范围 w：限制plot工作空间
    robot.plot(Theta,'tilesize',150,'workspace',W);  %显示三维动画 w：限制工作空间 tilesize：限制地板方块的尺寸
    q1=robot.ikine(forwarda)*180/pi      %求逆解验证关节角 给齐次变换矩阵forwarda 反求角度值
    rpy=tr2rpy(forwarda, 'xyz')*180/pi    %求末端姿态，工具法兰为绕XYZ轴旋转；齐次变换矩阵反求rpy  'xyz'：绕XYZ轴的顺序进行旋转
    robot.teach(forwarda,'rpy' )              %显示roll/pitch/yaw angles，GUI可调界面  调用教学模型来实时观看机械臂变化 'rpy'：rpy显示否则欧拉角显示

命令行输入 ： format compact  %紧凑显示输出

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[https_blog.csdn.net_jldemanman_article_details_80785075]: https://blog.csdn.net/jldemanman/article/details/80785075
[https_blog.csdn.net_jldemanman_article_details_79314435]: https://blog.csdn.net/jldemanman/article/details/79314435
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[2020122715104978.png]: https://img-blog.csdnimg.cn/2020122715104978.png
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